TEST BANK FOR Using and Understanding Mathematics A Quantative Reasoning Approach 8th Edi on By Jeff by StudyGuide

Exam

Chapter 1

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 1) 9 + 5 = 14 or 6 × 7 = 42 1)

Draw a Venn diagram to represent the given information. 2) In a complex of 60 apartments, 40 apartments have cable television, 25 apartments have a dishwasher, and 13 apartments have both cable television and a dishwasher. Decide whether the statement makes sense. Explain your reasoning. 3) Insurance policy A costs $250 and has no deductible. Insurance policy B costs $275 and has a $500 yearly deductible. Candace thinks the extra $25 per month is worth it to get the $500 deductible, so she buys policy B.

Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of every region. If a region has no members, state that fact clearly. 4) salty things, sweet things, tangy things 4)

Decide whether the statement makes sense. Explain your reasoning. 5) I know more of the names of the common fallacies in arguments than my father, so I can recognize fallacies better than he can.

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 6) "As your Senator, I cannot in good conscience oppose those who are against 6) deregulation." A seemingly simple argument is given. Identify at least two hidden assumptions. 7) Cardiovascular exercise is important, because to be healthy you need a strong heart.

Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 8) beverages and soft drinks 8) A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 9) Movies are entertaining. 9)

Use your knowledge of the listed sets to draw a A Venn diagram illustrating the relationships among them. 10) real numbers, integers, positive numbers, negative numbers, irrational numbers 10)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 11) The House of Representatives voted to override the veto of the communications bill. 11) The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 12) The sun is bigger than the moon and the sun rotates around the earth. 12) The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 13) There are 25 letters in the English alphabet or the letter c is a vowel. 13)

Analyze the situation and explain how you would make a decision. 14) Your current cell phone company charges $30 per month for unlimited minutes. Another company charges $20 per month for the first 500 minutes plus 5¢ a minute for any additional minutes. Should you keep your current service or switch to the other company?

14)

A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 15) Some singers are not children. 15) Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 16) even numbers and odd numbers 16)

Describe how the sentence is ambiguous. 17) There was a 15% decrease in donations to the homeless shelter between 1996 and 2000, a year in which $50,000 was collected.

17)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 18) Premise: 6 + 13 = 19 18) Premise: 16 + 9 = 25 Premise: 34 + 35 = 69 Conclusion: Whenever we add an even number and an odd number, the result is an odd number. Provide an appropriate response. 19) The members of a union are on strike. They are satisfied with their hourly wage rate and benefits, but they want their overtime wage rate to be increased by 15% in their next contract. The head of management makes the following statement to the head of the union: "If you end the strike today and sign the contract, we will meet your demand and increase the overtime wage rate by 15%." Should the union head accept the offer? Explain.

19)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 20) George Washington was the first president of the United States of America and France is 20) in Europe.

A seemingly simple argument is given. Identify at least two hidden assumptions. 21) I should not go outside, because it is raining.

21)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 22) Denying the conclusion 22)

Identify the type of argument and determine its validity with a Venn diagram. 23) Premise: If you cut me, I bleed. Premise: I do not bleed. Conclusion: You did not cut me.

23)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 24) Affirming the hypothesis 24)

Decide whether the statement makes sense. Explain your reasoning. 25) A and B are disjoint sets, so an object is either a member of set A or a member of set B, but not a member of both sets. Identify the type of argument and determine its validity with a Venn diagram. 26) Premise: If you break curfew, then you will be punished. Premise: Thelma was punished. Conclusion: Thelma broke curfew. Draw a Venn diagram to represent the given information. 27) There are 12 girls and 15 boys in a kindergarten class. 8 of the girls and 10 of the boys are right handed.

25)

26)

27)

Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 28) motor vehicles and cars 28)

Analyze the situation and explain how you would make a decision. 29) The costs per day of driving to work are $5 for gas, $10 for parking, and $1 for wear-and-tear on the car. Taking the train to work costs $6.50 each way, plus $1.50 per day to park at the train station. Should you drive or take the train? Draw a Venn diagram to represent the given information. 30) In a survey of 80 pet owners, 50 had a dog, 33 had a cat, and 12 had both a cat and a dog. Draw a Venn diagram to determine whether the argument is valid. 31) Premise: All snakes have fangs. Premise: Teri's pet does not have fangs. Conclusion: Teri's pet is not a snake.

29)

30)

31)

The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 32) The grass is wet or the grass is dry. 32) Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of every region. If a region has no members, state that fact clearly. 33) teachers, bowlers, and men 33)

Identify the type of argument and determine its validity with a Venn diagram. 34) Premise: If you try hard, then you will succeed. Premise: You did not try hard. Conclusion: You will not succeed.

34)

The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 35) Cats reads books or dogs bark. 35)

Use your knowledge of the listed sets to draw a A Venn diagram illustrating the relationships among them. 36) clothes, shirts, pants, shoes, fancy duds 36) Decide whether the statement makes sense. Explain your reasoning. 37) The argument is weak, so its conclusion must be false.

37)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 38) (Diversion) We've just remodeled the restaurant, so our food is delicious! 38) Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 39) Premise: Monday is one of the days of the week. 39) Premise: Thursday is one of the days of the week. Premise: Saturday is one of the days of the week. Conclusion: All the days of the week have names that end in "day." A seemingly simple argument is given. Identify at least two hidden assumptions. 40) We should not vote for the incumbent because he has already been in office for three consecutive terms. Decide whether the statement makes sense. Explain your reasoning. 41) I am very upset because the results of my biopsy were not positive for cancer.

40)

41)

A reason for a particular political position is given. There may be other issues that are left unstated. Identify at least one unstated issue that could be the "real issue" of concern. 42) The dictator of a foreign country has enacted a ban on all firearms, citing prevention of 42) accidental deaths among children as the rationale.

Decide whether the statement makes sense. Explain your reasoning. 43) Your argument is valid, but it isn't sound.

43)

Describe how the sentence is ambiguous. 44) Our goal is to increase voter participation from 25% of the eligible voters, or 4000, to 50%.

44)

Decide whether the statement makes sense. Explain your reasoning. 45) I drew a Venn diagram for two sets, and I only used one circle.

45)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 46) Affirming the conclusion 46) A reason for a particular political position is given. There may be other issues that are left unstated. Identify at least one unstated issue that could be the "real issue" of concern. 47) Smoking should be banned in all public places. Second-hand smoke is harmful, causing 47) lung cancer and heart disease.

Decide whether the statement makes sense. Explain your reasoning. 48) The premises are true and the conclusion is true, so the argument must be valid. Provide an appropriate response. 49) IRS guidelines state that a married person under 65 years of age who can be claimed as a dependent on another person's tax return must file a return if (i) unearned income was over $750; or (ii) earned income was over $3925; or (iii) total of earned and unearned income was at least $5 and your spouse files a separate return and itemizes deductions; or (iv) total of earned and unearned income was more than the greater of a) $750; or b) earned income (up to $3675) plus $250.

48)

49)

Julia is 45 years old and can be claimed as a dependent by her father. She had earned income of $3800 and unearned income of $200. Julia's husband Bret files a separate return but does not itemize deductions. Must Julia file a return? Explain.

51) No positive numbers are negative numbers.

51)

Decide whether the statement makes sense. Explain your reasoning. 52) Wayne's bank charges a $1 service charge for every transaction. To save money, he withdraws $100 cash every other week instead of withdrawing $50 every week.

52)

53) Your argument has no fallacies, so your conclusion must be true. A seemingly simple argument is given. Identify at least two hidden assumptions. 54) Jeremy needs a new bike, because the new models have a safer braking system. Draw a Venn diagram to determine whether the argument is valid. 55) Premise: All clowns wear makeup. Premise: Bozo is a clown. Conclusion: Bozo wears makeup. Describe how the sentence is ambiguous. 56) Two stores with more than 1000 pieces of merchandise will have grand openings at the mall this weekend. Decide whether the statement makes sense. Explain your reasoning. 57) Your argument is sound, but it isn't valid.

53)

54)

55)

56)

57)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 58) (False Cause) Since I brought my umbrella, it didn't rain. 58) Decide whether the statement makes sense. Explain your reasoning. 59) If you have $5, then you will buy a hot dog; and, contrapositively, if you don't have $5, then you won't buy a hot dog. (Hint: focus on whether the word "contrapositively" is used correctly.)

60) If "unconscious" means "not located in the United States," then Florida is not unconscious.

59)

60)

A set of propositions is listed. Draw a Venn diagram that represents all the information in the propositions and use it (and no other assumptions) to answer the question. Explain your reasoning. 61) No dogs are cats. No gerbils are cats. All dogs have fleas. Some cats are thirsty. No thirsty 61) creatures have fleas. Question: Could a gerbil be a dog?

Decide whether the statement makes sense. Explain your reasoning. 62) The propositions "I am hungry" and "I am not hungry" are both true, since sometimes I am hungry and sometimes I am not hungry. Analyze the situation and explain how you would make a decision. 63) You are flying out on Monday morning and returning home Tuesday night. You need to decide how to get to and from your home airport. Driving each way costs $2 in gas, and long-term parking costs $10 per full or partial day. If you take taxis, it will cost $11 each way. Which option is better?

62)

63)

Provide an appropriate response. 64) Consider the following ballot initiative: "Shall there be an amendment to the state constitution to prohibit the state legislature from adopting any law which inhibits the freedom of religious expression?" Explain the meaning of a "no" vote. Decide whether the statement makes sense. Explain your reasoning. 65) I did not convince my friend that I was right, so I must not have argued logically.

64)

65)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 66) Premise: I get lower grades than my best friend in math, chemistry, and English. 66) Conclusion: My friend is smarter than I am. The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 67) There are seven days in a week and there are 24 hours in a day. 67) A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 68) All horses are animals. 68)

Provide an appropriate response. 69) Consider the following clause in a rental lease: "Lessee may terminate this lease at the end of the initial term by providing Lessor with at least sixty (60) days prior written notice, to commence upon the first day of the month following the month in which said notice is delivered or immediately if delivered on the first day of any month." If the initial term of the lease ends on March 31 and the Lessee provides the Lessor written notice on April 1, as of what date can the lease be terminated? What if he provides notice on April 2?

69)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 70) 6 + 7 = 13 and 9 × 4 = 45 70)

Draw a Venn diagram to determine whether the argument is valid. 71) Premise: No surfers speak French. Premise: Pierre speaks French. Conclusion: Pierre is not a surfer.

71)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 72) Denying the hypothesis 72) Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 73) fish and birds 73)

74) athletes and high school students

74)

Decide whether the statement makes sense. Explain your reasoning. 75) The time I spend studying is a subset of the time I spend playing basketball. Analyze the situation and explain how you would make a decision. 76) You want a new car but plan to use it for only 2 years. The cost of leasing is $2,000 down and $300 per month. The cost of buying is $20,000, and you can expect to sell it in two years for approximately $12,000. Which is the better option?

77) You need a rental car for four days. The daily rate is $20 per day plus 20¢ per mile. The

75)

76)

77)

weekly rate is $100, and mileage is included. Which is the better option?

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 78) (Straw Man) Mayor Brown opposes a tax increase to build new schools. His opponent in 78) the upcoming election states: Mayor Brown is not concerned with improving the quality of education for our children. Identify the type of argument and determine its validity with a Venn diagram. 79) Premise: If you are hot, then you will sweat. Premise: James is hot. Conclusion: James will sweat.

79)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 81) Premise: Calvin Coolidge was over 35 years old when he became President of the United 81) States. Premise: Bill Clinton was over 35 years old when he became President of the United States. Premise: Ronald Reagan was over 35 when he became President of the United States. Conclusion: Every United States politician is at least 35 years old. The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 82) The councilman does not oppose the anti-pollution measure. 82) The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 83) (Appeal to Emotion) A television commercial shows a happy, attractive family dining at 83) Ma & Pa's Restaurant. The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 84) Springfield is the capital of Illinois and Chicago is the capital of Illinois. 84)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 85) (Hasty Generalization) Isabelle had vegetarian food for lunch every day last week, so she 85) must be a vegetarian. Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of every region. If a region has no members, state that fact clearly. 86) truck drivers, employed, unemployed 86)

A seemingly simple argument is given. Identify at least two hidden assumptions. 87) All bills should be paid on time because a bad credit report will make it difficult to get a loan.

87)

A set of propositions is listed. Draw a Venn diagram that represents all the information in the propositions and use it (and no other assumptions) to answer the question. Explain your reasoning. 88) All cars have wheels. All trucks have wheels. Some toys have wheels. No grandmothers 88) have wheels. Question: Could a car be both a truck and a toy? Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 89) astronauts and fathers 89)

Provide an appropriate response. 90) IRS guidelines state that a married person under 65 years of age who can be claimed as a dependent on another person's tax return must file a return if (i) unearned income was over $750; or (ii) earned income was over $3925; or (iii) total of earned and unearned income was at least $5 and your spouse files a separate return and itemizes deductions; or (iv) total of earned and unearned income was more than the greater of a) $750; or b) earned income (up to $3675) plus $250.

90)

Kevin is 25 years old and can be claimed as a dependent by his mother. He had earned income of $3500 and unearned income of $700. Kevin's wife Linda files a separate return but does not itemize deductions. Must Kevin file a return? Explain.

91) You mention to an acquaintance that you wish to buy a Rolex watch, but the model you're

91)

interested in is too expensive for your budget. He says that his cousin sells watches, and he'll see if he can get you a deal. Sure enough, his cousin offers you the same watch for 50% of the price. Does this sound like a deal worth taking?

Decide whether the statement makes sense. Explain your reasoning. 92) The answer to the question is a whole number but it is not an integer.

92)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 93) The state assembly repealed the ban on anti-smoking resolutions. 93)

A seemingly simple argument is given. Identify at least two hidden assumptions. 94) It is important to visit the dentist every 6 months to insure healthy teeth and gums. Analyze the situation and explain how you would make a decision. 95) You are leasing a summer home for twelve weeks and are required to cut the grass every week. You can buy a new power mower for $340 and sell it at the end of the summer for $100. You can rent a power mower for $20 per day. The neighbor's son will charge you $10 per hour for 2 hours and provide his own equipment. Which is the best option?

94)

95)

Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 96) doctors and poets 96)

Decide whether the statement makes sense. Explain your reasoning. 97) Javier takes a shower to save time. When he gets into the shower at 6:50, he is out by 7:10. When he used to take baths, it would take him a quarter of an hour. Analyze the situation and explain how you would make a decision. 98) Betty has to go to New Orleans on business. If she flies there and back on the same day her round trip airfare will cost $700. If she stays overnight, her round trip airfare will cost $400, her hotel will cost $100, and three extra meals will cost $75. Which is the better option?

97)

98)

A reason for a particular political position is given. There may be other issues that are left unstated. Identify at least one unstated issue that could be the "real issue" of concern. 99) I think term limits should be enacted for the Senate. A senator should not be allowed to 99) serve more than two consecutive terms, because professional politicians become too focused on getting reelected. A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 100) Some dogs are adorable. 100)

A seemingly simple argument is given. Identify at least two hidden assumptions. 101) The campfire should be extinguished before we go fishing because the park ranger can cite us for illegal activities.

101)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 102) Premise: Baseball, football, basketball, golf, hockey, and tennis are all played with a ball. 102) Conclusion: All sports are played with a ball. Decide whether the statement makes sense. Explain your reasoning. 103) Your conditional deductive argument is valid. Therefore, it must be an example of "Affirming the Hypothesis."

103)

Draw a Venn diagram to determine whether the argument is valid. 104) Premise: All lawyers wear suits. Premise: Jack wears a suit. Conclusion: Jack is a lawyer.

104)

Draw a Venn diagram to represent the given information. 105) In a freshman class of 50 students, 30 students are taking math, 24 students are taking history, and 15 students are taking both math and history.

105)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is a proposition. 106) One inch is 2.54 meters. A) Not a proposition

106) B) Proposition

Evaluate the validity of the chain of conditionals. 107) Premise: If you loved me, then you would buy me a new car. Premise: If you wanted me to be happy, then you would buy me a new car. Conclusion: If you loved me, then you would want me to be happy. A) Valid B) Invalid

107)

Rephrase the statement as a conditional proposition with the form "if p, then q." 108) Showing up at the party is sufficient to get a door prize. A) If you got a door prize, then you showed up at the party.

108)

B) If you show up at the party, then you will get a door prize. C) If you don't show up at the party, then you will not get a door prize. D) If you get a door prize, then you don't have to show up at the party. Solve the problem. 109) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many cookies have neither chocolate chips nor walnuts.

A) 17

B) 7

C) 10

D) 3

109)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 110) -13 110) A) Integers B) Whole numbers

C) Natural numbers

D) Rational numbers

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 111) not (p or q); (not p)and (not q) 111) A) No B) Yes Solve the problem. 112) The following Venn diagram describes the cars on a used car lot. Use it to determine how many Fords are on the lot.

A) 23

B) 17

C) 30

Determine whether the statement is true or false. 113) If 9 + 2 = 19, then Canada is in North America. A) True

112)

D) 20

113) B) False

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 114) 16 114) A) Integers B) Natural numbers

C) Real numbers

D) Whole numbers

Solve the problem. 115) The following Venn diagram describes the cars on a used car lot. Use it to determine how many cars on the lot are not red.

A) 55

B) 58

C) 35

D) 38

The argument given or described involves some kind of fallacy. Identify the fallacy. 116) After getting new dishes, I started to sneeze. I must be allergic to the new dishes. A) Hasty generalization B) False cause

C) Circular reasoning

115)

116)

D) Personal attack (ad hominem)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 117) q and (not r) and s

B) q r s q and (not r) and s T T T F T T F F T F T T T F F T F T T F F T F F F F T F F F F F

q r s q and (not r) and s T T T F T T F T T F T F T F F F F T T F F T F F F F T F F F F F

D) q r s q and (not r) and s T T T F T T F F T F T T T F F F F T T F F T F F F F T F F F F F

q r s q and (not r) and s T T T T T T F F T F T F T F F F F T T F F T F F F F T F F F F F

117)

Write the negation of the proposition. 118) Some athletes are musicians. A) No athlete is a musician.

118) B) All athletes are musicians. D) Not all athletes are musicians.

C) Some athletes are not musicians. Determine whether the statement is a proposition. 119) 0.3 = .03 A) Not a proposition

119) B) Proposition

Decide whether the argument is inductive or deductive. 120) For any positive number p, -p = p. Therefore,|-12| = 12 A) Deductive B) Inductive

120)

Solve the problem. 121) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how many people ordered cake.

121)

A) 43

B) 21

C) 7

D) 28

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 122) p or q; not [(not p) and (not q)] 122) A) Yes B) No The argument given or described involves some kind of fallacy. Identify the fallacy. 123) You should brush your teeth every day because brushing your teeth is very important. A) Diversion (red herring) B) False cause

C) Circular reasoning

123)

D) Hasty generalization

Use braces to write the members of the set, or state that the set has no members. 124) The letters needed to spell the following words: tear, rate, rat, tea A) {a, e, r, t} B) {t, e, a, r, r, a, t, e, r, a, t, t, e, a}

C) {tear, rate, rat, tea}

D) {r, a, t}

124)

Write the converse, inverse, or contrapositive off the proposition, as indicated. 125) If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive) A) If a geometric figure is not a triangle, then the sum of the interior angles is 180 degrees.

125)

B) If the sum of the interior angles of a geometric figure is not 180 degrees, then the figure is

not a triangle. C) If a geometric figure is not a triangle, then the sum of the interior angles is not 180 degrees.

D) If a geometric figure is a triangle, then the sum of the interior angles is 180 degrees. Write the negation of the proposition. 126) Susie lives in a green house. A) Susie lives in a blue house.

126)

B) Susie does not live in a house that is not green. C) Billy lives in a green house. D) Susie does not live in a green house. Use braces to write the members of the set, or state that the set has no members. 127) The days of the week A) {Saturday, Sunday}

127)

B) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} C) {Monday, Tuesday, Wednesday, Thursday, Friday} D) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 128) 23 128) A) Rational numbers B) Natural numbers

C) Whole numbers

D) Real numbers

Rephrase the statement as a conditional proposition with the form "if p, then q." 129) I will lose weight if I diet. A) If I lose weight, then I will diet. B) If I diet, then I will lose weight.

C) If I don't diet, then I won't lose weight.

129)

D) If I diet, then I will gain weight.

State whether or is being used in the exclusive or inclusive sense in the given statement. 130) The insurance policy will not cover misuse or acts of God. A) Exclusive B) Inclusive

131) The prize is a new car or $10,000 cash. A) Inclusive

130)

131) B) Exclusive

Decide whether the argument is inductive or deductive. 132) Every coach must know his sport well. Steve Spurrier is a football coach, so Steve Spurrier knows football well. A) Deductive B) Inductive

132)

Use braces to write the members of the set, or state that the set has no members. 133) The integers from 2 to 6 (inclusive) A) {3, 4, 5} B) {2, 3, 4, 5, 6} C) {2, 3, 4, 5}

133) D) {3, 4, 5, 6}

Rephrase the statement as a conditional proposition with the form "if p, then q." 134) Cats chase mice. A) If a cat is chasing it, then it is a mouse. B) If it is a cat, then it chases mice.

C) If cats chase, then they chase mice.

134)

D) If cats, then mice.

135) Having a computer is necessary for taking this class. A) If you have a computer, then you must take this class. B) If you take this class, then you must have a computer. C) If you take this computer, then you must have a class. D) If don't take this class, then you must not have a computer.

135)

136) All chocolate is good. A) If it isn't good, then it's chocolate. C) If it's good, then it's chocolate.

136) B) If it's chocolate, then it's good. D) If it isn't chocolate, then it isn't good.

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 137) not (p and q); (not p) or q 137) A) No B) Yes Determine whether the statement is true or false. 138) If a triangle is a parallelogram, then all rectangles are squares. A) True B) False Evaluate the validity of the chain of conditionals. 139) Premise: If I take a shower, I use soap. Premise: If I use soap, my skin becomes dry. Conclusion: If I take a shower, my skin becomes dry. A) Valid B) Invalid

138)

139)

Decide whether the argument is inductive or deductive. 140) Fresh fruit is expensive in winter. This is January, so these fresh strawberries will be expensive. A) Inductive B) Deductive

140)

Determine whether the statement is a proposition. 141) Go fly a kite. A) Proposition

141) B) Not a proposition

142) Do you like this color? A) Proposition

142) B) Not a proposition

Decide whether the argument is inductive or deductive. 143) The last four stoplights were green. Therefore, the next one will be green. A) Deductive B) Inductive

144) All U.S. Presidents have come from the contiguous 48 states. No person from Alaska can be President. A) Inductive

143)

144)

B) Deductive

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 145) r and not s

145)

B) r s r and not s T T T T F F F T F F F F

r s r and not s T T T T F T F T F F F T

D) r s r and not s T T F T F T F T F F F F

r s p and not s T T F T F T F T F F F F

Write the negation of the proposition. 146) Everyone is asleep. A) Nobody is awake.

146) B) Not everyone is asleep. D) Everyone is awake.

C) Nobody is asleep.

Evaluate the validity of the chain of conditionals. 147) Premise: If I pay my bills on time, then my credit will be good. Premise: If my credit is good, then I will become a movie star. Conclusion: If I pay my bills on time, then I will become a movie star. A) Valid B) Invalid

147)

Decide whether the argument is inductive or deductive. 148) 31 + 19 = 50, 13 + 47 = 60, 5 + 37 = 42. Therefore, the sum of two prime numbers is even. A) Inductive B) Deductive

148)

Determine whether the statement is a proposition. 149) 5 + 7 = 13 A) Proposition

149) B) Not a proposition

The argument given or described involves some kind of fallacy. Identify the fallacy. 150) When confronted with questions from the press about alleged scandals, a congressman replies that the allegations against him should be ignored since his accuser is part of a vast right-wing conspiracy. A) Circular reasoning B) Limited choice

C) Appeal to popularity

150)

D) Personal attack (ad hominem)

Use braces to write the members of the set, or state that the set has no members. 151) The positive-integer powers of 3 A) {3, 6, 9, 12, 15, . . .} B) {1, 3, 9, 27, 81, 243, . . .}

C) {3, 9, 27, 81, 243, . . .}

151)

D) {1, 8, 27, 64, 125, . . .}

State whether or is being used in the exclusive or inclusive sense in the given statement. 152) I don't know if I should wear my new skirt or my new dress tonight. A) Exclusive B) Inclusive

152)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 153) -4 153) A) Real numbers B) Integers

C) Rational numbers

D) Whole numbers

Determine whether the statement is true or false. 154) If baseball is a sport, then the letter e is a consonant. A) True

154) B) False

Solve the problem. 155) The following Venn diagram describes the optional features ordered by new telephone customers in a certain region. Use it to determine how many customers did not order caller ID.

A) 67

B) 103

C) 76

Determine whether the statement is true or false. 156) If Florida is in the United States, then all rectangles are squares. A) True B) False

155)

D) 77

156)

Evaluate the validity of the chain of conditionals. 157) Premise: If the moon is made of cheese, then what goes up must come down. Premise: If what goes up must come down, then most Americans like apple pie. Conclusion: If the moon is made of cheese, then most Americans like apple pie. A) Invalid B) Valid The argument given or described involves some kind of fallacy. Identify the fallacy. 158) We must limit immigration to the United States in order to sustain the prosperous economy. A strong economy is vital to the health and wealth of the American people and the future of our children. A) False cause B) Diversion (red herring)

C) Appeal to force

157)

158)

D) Straw man

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 159) -21.1 159) A) Rational numbers B) Natural numbers

C) Real numbers

D) Integers

Solve the problem. 160) The following Venn diagram describes the optional features ordered by new telephone customers in a certain region. Use it to determine how many customers ordered call waiting.

A) 77

B) 36

C) 76

160)

D) 40

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 161) -64 161) A) Natural numbers B) Real numbers

C) Whole numbers

D) Integers

Write the converse, inverse, or contrapositive off the proposition, as indicated. 162) If I pass, then I'll celebrate. (contrapositive) A) If I don't celebrate, then I didn't pass. B) If I pass, then I won't celebrate.

C) If I celebrate, then I'll pass.

D) If I don't pass, then I won't celebrate.

162)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 163) 0 163) A) Natural numbers B) Integers

C) Rational numbers

D) Whole numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 164) One candidate favors eliminating affirmative action programs. The other candidate states: My opponent doesn't think there's anything wrong with discrimination." A) Straw man B) Personal attack (ad hominem)

C) Limited choice

164)

D) Hasty generalization

Use braces to write the members of the set, or state that the set has no members. 165) The integers between 3 and 7 (not inclusive) A) {4, 5, 6, 7} B) {3, 4, 5, 6, 7} C) {3, 4, 5, 6}

165) D) {4, 5, 6}

The argument given or described involves some kind of fallacy. Identify the fallacy. 166) If Proposition Q fails, your children won't have good schools. A) Appeal to ignorance B) Appeal to emotion

C) Hasty generalization

166)

D) Diversion (red herring)

167) A television commercial shows two people who fall in love while wearing a certain brand of blue

167)

jeans.

A) Limited choice C) Hasty generalization

B) Appeal to ignorance D) Appeal to emotion

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 168) not (p and q); (not p) and (not q) 168) A) Yes B) No State whether or is being used in the exclusive or inclusive sense in the given statement. 169) Shaun will win the race if he eats carbohydrates beforehand or if he has slept well. A) Exclusive B) Inclusive

169)

Write the negation of the proposition. 170) Emily has brown eyes. A) Jason has brown eyes.

170) B) Emily does not have green eyes. D) Emily has green eyes.

C) Emily does not have brown eyes.

Write the converse, inverse, or contrapositive off the proposition, as indicated. 171) If the sun shines, they will bask. (inverse) A) If the sun does not shine, then they will not bask.

B) If they bask, then the sun shines. C) If they do not bask, then the sun shines. D) If they do not bask, then the sun does not shine. 20

171)

Write the negation of the proposition. 172) Some people don't like walking. A) Some people don't like driving.

172) B) Nobody likes walking. D) Everyone likes walking.

C) Some people like walking. 173) No fifth graders play soccer. A) Not all fifth graders play soccer. C) At least one fifth grader plays soccer.

173) B) No fifth grader does not play soccer. D) All fifth graders play soccer.

Determine whether the statement is a proposition. 174) Not all flowers are roses. A) Not a proposition

174) B) Proposition

Determine whether the statement is true or false. 175) If horses have six legs, then Benjamin Franklin was the first president of the United States. A) True B) False

175)

Determine whether the statement is a proposition. 176) Mary has a cat. A) Not a proposition

176) B) Proposition

Draw a Venn diagram to represent the given information. 177) Patients in a (hypothetical) hospital on a single day were taking antibiotics (A), blood pressure medication (BP), and pain medication (P) in the following numbers: A only BP only P only None

10 A and BP only 7 A and P only 22 BP and P only 2 All three

14 25 18 20

Draw a three-circle Venn diagram that summarizes the results in the table.

177)

Write the converse, inverse, or contrapositive off the proposition, as indicated. 178) If you received a refund of over $1000, then you cannot make a claim. (inverse) A) If you can make a claim, then you received a refund of over $1000.

B) If you cannot make a claim, then you did not receive a refund of over $1000. C) If you did not receive a refund of over $1000, then you can make a claim. D) If you can make a claim, then you did not receive a refund of over $1000.

178)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 179) if q, then not r

179)

B) q r if q, then not r T T T T F F F T F F F F

q r if q, then not r T T F T F T F T F F F F

D) q r if q, then not r T T F T F T F T T F F T

q r if q, then not r T T T T F F F T T F F T

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 180) 2.1 180) A) Real numbers B) Integers

C) Natural numbers

D) Rational numbers

Rephrase the statement as a conditional proposition with the form "if p, then q." 181) Being in California is sufficient for being in Los Angeles. A) If you are in California, then you are not in Los Angeles.

181)

B) If you are in Los Angeles, then you are in California. C) If you are in Los Angeles, then you might be in California. D) If you are in California, then you are in Los Angeles. 182) Attending practice is necessary for staying on the team. A) If you don't stay on the team, then you must not attend practice. B) If you stay on the team, then you must attend practice. C) If you attend practice, then you must stay on the team. D) If you don't attend practice, then you must stay on the team. Use braces to write the members of the set, or state that the set has no members. 183) The whole numbers greater than 1 and less than 5 A) {1, 2, 3, 4} B) {2, 3, 4} C) {1, 2, 3, 4, 5}

182)

183) D) {2, 3, 4, 5}

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 184) 3,645 184) A) Natural numbers B) Whole numbers

C) Integers

D) Rational numbers

Write the converse, inverse, or contrapositive off the proposition, as indicated. 185) If the alarm beeps every thirty seconds, then you have to replace the battery. (converse) A) If you have to replace the battery, then the alarm does not beep every thirty seconds.

185)

B) If you have to replace the battery, then the alarm beeps every thirty seconds. C) If the alarm does not beep every thirty seconds, then you do not have to replace the battery. D) If you do not have to replace the battery, then the alarm does not beep every thirty seconds. Solve the problem. 186) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many chocolate chip cookies do not also have walnuts.

A) 25

B) 10

C) 15

Write the negation of the proposition. 187) Not all people like football. A) Some people like football.

D) 32

187) B) All people like football. D) Some people do not like football.

C) All people do not like football.

Solve the problem. 188) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how many people ordered ice cream but not cake.

A) 36

186)

B) 21

C) 7

D) 15

188)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 189) 3 189) 5

A) Rational numbers C) Integers

B) Real numbers D) Natural numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 190) Each of my brother's three dogs has fleas. Therefore, all dogs have fleas. A) False cause B) Straw man

C) Hasty generalization

190)

D) Circular reasoning

Determine whether the statement is true or false. 191) If Florida is in the United States, then all squares are rectangles. A) True B) False

191)

Write the negation of the proposition. 192) She earns more than me. A) She earns the same as me.

192) B) She earns less than me. D) She does not earn less than me.

C) She does not earn more than me.

Decide whether the argument is inductive or deductive. 193) Practice makes perfect. Therefore, if I practice, I'll be perfect. A) Inductive B) Deductive

193)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 194) (p or q) or r; p or (q or r) 194) A) Yes B) No Make a truth table for the given statement. The letters p, q, r, s represent propositions. 195) p or q

B) p q p or q T T T T F F F T T F F F

C) p q p or q T T T T F F F T F F F F

p q p or q T T T T F T F T T F F F

195) D) p q p or q T T F T F F F T F F F T

Answer Key Testname: CHAPTER 1

1) True. Both individual propositions are true. The disjunction is true if either or both propositions are true. 2) Answers may vary. Possible answer:

3) Does not make sense. Candace is paying an additional $25 per month ($300 per year) to get a $500 deductible.

However the deductible (what you pay out of pocket before the insurance kicks in) is a cost, not a benefit! All other things being equal, policy A is clearly the better deal. (Explanations will vary.)

I = things that are salty, but neither sweet nor tangy II = things that are both salty and sweet, but not tangy III = things that are sweet, but neither salty nor tangy IV = things that are salty and tangy, but not sweet V = things that are salty, sweet, and tangy VI = things that are sweet and tangy, but not salty VII = things that are tangy, but neither sweet nor salty VIII = things that are neither salty, sweet, nor tangy 5) Does not make sense. Learning the fancy names for the fallacies is far less important than learning to recognize the faulty reasoning. (Explanations will vary.) 6) Answers may vary. One possibility: There are four negations in that statement: cannot, oppose, those who are against, and deregulation. A quadruple negation (not not not not p) has the same truth value as the original proposition p. In short, the Senator is for regulation of the area in question. 7) Answers may vary. One possibility: Cardiovascular exercise leads to a strong heart. Being healthy is important.

Answer Key Testname: CHAPTER 1

The set "soft drinks" is a subset of the set "beverages." All soft drinks are beverages, but some beverages (e.g., water) are not soft drinks. 9) In standard form: All movies are things that are entertaining. The subject set is "movies" and the predicate set is "things that are entertaining."

10) Answers may vary. One possibility:

Note that there is exactly one element in region I, since the number 0 is the only integer that is neither negative nor positive. Note also that there are no elements in region II, since each irrational number is either negative or positive.

Answer Key Testname: CHAPTER 1

11) Answers may vary. One possibility: This is a double negation. The veto of the bill (presumably by the President) is the

first negation. The overriding of the veto is the second negation. The two cancel each other out, and the result is that the communications bill is passed. In general, a double negation (not not p) has the same same truth value as the original proposition p. 12) False. Is is true that the sun is bigger than the moon, but it is not true that the sun rotates around the earth. (The earth rotates around the sun.) Since one of the individual propositions if false, the conjunction is false. 13) False. Since there are 26 letters in the English alphabet, the first proposition is false. Since the letter c is not a vowel but a consonant, the second proposition is false. Since both propositions are false, the disjunction is false. 14) Answers may vary. One possibility: The relative cost of the two options depends primarily on how many minutes per month you use. The new company's plan would cost $30 for up to 700 minutes a month, since $20 + $0.05(700 - 500) = $30. Therefore, if you expect to use less than 700 minutes a month, you would tend to profit from switching companies. However, there are other factors to consider: Does one company have more dependable cellular service? Better sound quality? Better customer service? You should also look for hidden costs. For example, if you switch companies, you may need to buy a new cell phone. 15) The subject set is "singers" and the predicate set is "children."

The X indicates that the non-overlapping region of the "singers" circle has at least one member. No claim is made about whether other regions also have members.

16)

The set "even numbers" is disjoint from the set "odd numbers" because the two sets have no members in common. An even number cannot be odd, and an odd number cannot be even. 17) It is unclear whether the year in which $50,000 was collected was 1996 or 2000. 18) Answers may vary. Possible answer: The premises are true. The argument is relatively strong, and the conclusion is true. 19) Answers may vary. One possibility: The union head should ask for more information. Even though management has apparently agreed to the demand for a 15% increase in the overtime wage rate, it is not clear that the overall deal is a good one. It is entirely possible that management has lowered the hourly wage rate, reduced the benefits, or made other changes to the contract to the detriment of the members of the union. Before making any promises, before giving up leverage by ending the strike, and certainly before signing anything; these issues must be clarified.

Answer Key Testname: CHAPTER 1

20) True. Both individual propositions are true, so the conjunction is true. 21) Answers may vary. One possibility:

I do not want to get wet. It is not raining inside; that is, the roof is keeping the rain outside. 22) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: q is not true. Conclusion: p is not true. The argument is valid.

23)

The type of argument is called Denying the Conclusion. We have p = you cut me and q = I bleed. The second premise asserts that q is false for me, which we show by putting an X outside the q circle. Since the p circle is inside the q circle, the X is outside the p circle, too. The Venn diagram shows that the premises lead necessarily to the conclusion, so the argument is valid. 24) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: p is true. Conclusion: q is true. The argument is valid. 25) Does not make sense. It is true that if A and B are disjoint sets, then an object cannot be a member of both sets. However, that does not mean it has to be a member of either set. It can also be a member of neither. The X in the following diagram represents an object that is a member of neither set A nor set B. If set A were the set of animals, and set B were the set of vegetables, then the X might represent a mineral. (Explanations will vary.)

Answer Key Testname: CHAPTER 1

26)

The type of argument is called Affirming the Conclusion. We have p = you break curfew and q = you will be punished. The second premise asserts that Thelma was punished, which we show by putting an X in the q circle. However, the premise says nothing about whether Thelma broke curfew, so we put the X on the border of the p circle to indicate that we don't know whether the X belongs inside or outside this circle. The Venn diagram shows that the premises do not lead necessarily to the conclusion, so the argument is invalid. Thelma may have been punished for some other reason. 27) Answers may vary. Possible answer:

28)

The set "cars" is a subset of the set "motor vehicles." Every car is a motor vehicle, but there are some motor vehicles, such as trucks, that are not cars. 29) Answers may vary. One possibility: Since driving costs $16 ($5 + $10 + $1 = $16) per day and taking the train costs $14.50 ($6.50 × 2 + $1.50 = $14.50) per day, it appears that taking the train is a better option. However, you should also consider other factors. If you have a spouse who might need the car during the day, then that's another reason to take the train (that would also save you the $1.50 parking fee). If you take the train, you might be able to read the newspaper or do work on the way to work. However, if the train tends to be crowded and you prefer being alone, then it might be worth the extra $1.50 per day to drive.

Answer Key Testname: CHAPTER 1

30) Answers may vary. Possible answer:

31)

The X represents Teri's pet. The conclusion follows necessarily from the premises, and the argument is valid. 32) True. If the first proposition is false (the grass is not wet), then the second proposition is true (the grass is dry). If the second proposition is false (the grass is not dry), then the first proposition is true (the grass is wet). Thus, one of the propositions is true, so the disjunction is true.

33)

I = female teachers who are not bowlers II = female teachers who are bowlers III = female bowlers who are not teachers IV = male teachers who are not bowlers V = male teachers who are bowlers VI = male bowlers who are not teachers VII = men who are neither teachers nor bowlers VIII = women who are neither teachers nor bowlers

Answer Key Testname: CHAPTER 1

34)

The type of argument is called Denying the Hypothesis. We have p = you try hard and q = you will succeed. The second premise asserts that p is false for you, which we show by putting an X outside the p circle. However, we do not know whether the X should also be outside the q circle, because the premise says nothing about whether you succeeded. Thus, we put the X on the border of the q circle. The Venn diagram shows that the premises do not lead necessarily to the conclusion, so the argument is invalid. It is possible that, despite your not trying hard, you might still succeed. 35) True. Although cats do not read books, dogs do bark. The disjunction is false only if both individual propositions are false. 36) Answers may vary. One possibility:

37) Does not make sense. The strength of an inductive argument is not necessarily related to the truth of its conclusion.

The argument "The earth rotates around the sun because I said so" is extremely weak, but its conclusion happens to be true. For a long time people found the argument "The sun rotates around the earth" to be quite compelling, but its conclusion turned out to be false. (Explanations will vary.) 38) Answers may vary. Possible answer: The conclusion of this argument (our food is delicious) is not related to the premise (We've just remodeled the restaurant). This argument represents the fallacy of diversion because it attempts to divert attention from the real issue (the taste of the food) by focusing on another issue (the remodeling of the restaurant). The issue to which attention is diverted is sometimes called a red herring. 39) Answers may vary. Possible answer: The premises are true. The strength of the argument is relatively weak, since things aren't always named logically and consistently. (For example, the months September, November, and December all end in "ember", but none of the other nine months do!) The conclusion is true.

Answer Key Testname: CHAPTER 1

40) Answers may vary. One possibility:

Four consecutive terms is too many. The incumbent is running in the election. 41) Does not make sense. In this context, the word "positive" means "indicating the presence of." The fact that the results were not positive for cancer suggests that you don't have cancer. Perhaps there is an unusual explanation for why that would make you upset (e.g., masochism), but in general it does not make sense. (Explanations will vary.) 42) Answers may vary. One possibility: The dictator may believe that an unarmed populace is easier to control. 43) Makes sense. An argument is valid if its conclusion follows necessarily from its premises, regardless of the truth of its premises or conclusions. An argument is sound if it is valid and its premises are all true. Many valid arguments have false premises and are thus not sound. For example: Premise: When I close my eyes, I become invisible. Premise: When I am invisible, I can speak Portugese. Conclusion: When I close my eyes, I can speak Portugese. The argument is valid, but its premises are clearly false so it isn't sound. (Explanations will vary.) 44) It is unclear whether 4000 is the number of eligible voters or 25% of the number of eligible voters (which would make 16,000 the number of eligible voters). 45) Makes sense. Generally it takes two circles to draw a Venn diagram for two sets, for example when the sets are overlapping or disjoint. Even when one set is the subset of the other, it generally takes two circles to draw a Venn diagram. However, if the two sets are equal, then they have precisely the same members and the same circle describes both sets. Incidentally, if two sets are equal then they are both subsets of each other. (Explanations will vary.) 46) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: q is true. Conclusion: p is true. The argument is invalid. 47) Answers may vary. One possibility: The person stating this opinion may not like the smell of cigarettes and cigars. He may not like the smell getting into his clothes and causing him to spend more money on dry cleaning. In addition, he may find second-hand smoke unpleasant because it irritates his eyes. 48) Does not make sense. For an argument to be valid, its conclusion must follow necessarily from its premises. Just because the premises and the conclusion are true does not mean the conclusion follows necessarily from the premises. For example, consider the following argument: Premise: Dogs bark. Premise: Cats meow. Conclusion: Pigs oink. The premises and the conclusion are all true, but the conclusion has nothing to do with the premises. (Explanations will vary.) 49) Yes, Julia must file a return. She is a married person under 65 years of age who can be claimed as a dependent on another person's tax return. As such, she must file a return if any of (i)-(iv) apply. (i) does not apply since $200 < $750; (ii) does not apply because $3800 < $3925; (iii) does not apply because although her spouse (Bret) files a separate return, he does not itemize; (iv) does apply. Part (b) is a little confusing. It says to start with earned income, but only earned income up to $3675. Since $3800 > $3675, we start with $3675. Then we add $250 to get $3925. The greater of (a) $750 or (b) $3925 is clearly $3925. The total of Julia's earned and unearned income is $4000 ($3800 + $200). Since $4000 > $3925, (iv) applies and Julia must file a return. (Explanations will vary.)

Answer Key Testname: CHAPTER 1

50) The subject set is "flight attendants" and the predicate set is "men."

The X indicates that the overlapping region has at least one member. No claim is made about whether other regions also have members. 51) The subject set is "positive numbers" and the predicate set is "negative numbers."

52) Makes sense. By taking out the same amount of money but reducing the number of withdrawals, he saves money on

service charges ($0.50 per week). What would make even more sense would be to find a bank that doesn't charge a fee for every transaction. (Explanations will vary.) 53) Does not make sense. By using false assumptions for premises, it is possible to create a solid argument even for a conclusion that is clearly false. (Explanations will vary.) 54) Answers may vary. One possibility: Safer bikes are better bikes. Buying a new braking system for Jeremy's old bike is not a reasonable option.

55)

The X represents Bozo. The conclusion follows necessarily from the premises, and the argument is valid.

56) It is unclear whether the two stores combined have more than 1000 pieces of merchandise or whether each store itself has more than 1000 pieces of merchandise.

Answer Key Testname: CHAPTER 1

57) Does not make sense. An argument is valid if its conclusion follows necessarily from its premises, regardless of the

truth of its premises or conclusions. An argument is sound if it is valid and its premises are all true. By definition, if an argument is sound it is also valid. To put it another way, the set of sound arguments is a subset of the set of valid arguments. (Explanations will vary.) 58) Answers may vary. Possible answer: The premises tells us that one thing (bringing the umbrella) happened before another (it didn't rain), but they don't prove any connection between them. That is, we cannot conclude that bringing the umbrella was the cause of the fact that it didn't rain. The fact that one event came before another is not proof that the first event caused the second event. 59) Does not make sense. The contrapositive of "If p, then q" is "If not q, then not p." The contrapositive of "If you have $5, then you will buy a hot dog" is "If you will not buy a hot dog, then you don't have $5." What is actually given is the inverse. (Explanations will vary.) 60) Makes sense. You might think the statement does not make sense since the definition of "unconscious" is not actually "not located in the United States"and the assertion about Florida does not, on its own, make sense. However, the only question is whether if the definition were correct, the assertion about Florida would be correct. If "unconscious" means "not located in the United States," then "Florida is not unconscious" could be rephrased as "Florida is not not located in the United States" and then, replacing the double negation, "Florida is located in the United States." That assertion is clearly true. (Explanations will vary.) 61) Answers may vary. One possibility:

Yes, a gerbil could be a dog. We know from the first proposition that the set "dogs" is disjoint from the set "cats," and we know from the second proposition that the set "gerbils" is disjoint from the set "cats." However, we do not know the relationship between the sets "dogs" and "gerbils." It is possible that the two sets are not disjoint; if so, they will overlap in region a. A gerbil who is a dog would necessarily have fleas, since all dogs have fleas. Such a gerbil would not be thirsty, since no thirsty creatures have fleas. 62) Does not make sense. The second proposition is the negation of the first proposition. If a proposition is true, then its negation must be false, and vice versa. Thus, the two propositions cannot both be true. But, you argue, I was hungry at 7:00 this morning, but then I ate breakfast and I was not hungry at 8:00. The explanation is that "I was hungry at 7:00 this morning" and "I was hungry at 8:00 this morning" are two different propositions. The first one is true and its negation is false, while the second one is false and its negation is true. (Explanations will vary.)

Answer Key Testname: CHAPTER 1

63) Answers may vary. One possibility: Taking taxis will cost you $22 (2 trips × $11/trip), while driving will cost you $24

(2 days × $10/day + 2 trips × $2/trip). Driving appears to be a better option. However, before you make your decision, you should consider hidden costs and benefits. What if your trip is extended or your return flight is delayed? Each additional day of long-term parking will cost you $10. In addition, there is the wear-and-tear on the car and the fact that your car would be left in a public lot, where the risk of theft or vandalism might be greater. Those factors would make taking taxis the better option. On the other hand, if you are on a tight schedule, you might not want to rely on a taxi to pick you up on time. 64) Answers may vary. One possibility: A "no" vote means that you believe that the state legislature should have the authority to restrict religious expression. 65) Does not make sense. Arguing logically may not change the other person's position, but it can help the other person understand you, and vice versa. (Explanations will vary.) 66) Answers may vary. Possible answer: Since the example is fictitious, there is no way to determine the truth of the premise. The argument is weak. Perhaps my friend studies harder than I do, perhaps my friend cheats in his classes, or perhaps I get higher grades in biology, history, and art. Moreover, academic smarts are only one measure of intelligence. Since the example is fictitious, there is no way to assess the truth of the conclusion. 67) True. Both individual propositions are true, so the conjunction is true. 68) The subject set is "horses" and the predicate set is "animals."

69) Answers may vary. One possibility: If written notice is provided on April 1, then the lease can be terminated on May

30. If written notice is provided on April 2, then the lease cannot be terminated until June 29. In delaying notice until after the first of the month, the tenant makes himself responsible for another month of rent. That's one expensive day! 70) False. The proposition 6 + 7 = 13 is true, but the proposition 9 × 4 = 45 is false. Since one of the individual propositions is false, the conjunction is false.

71)

The X represents Pierre. The conclusion follows necessarily from the premises, and the argument is valid.

Answer Key Testname: CHAPTER 1

72) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: p is not true. Conclusion: q is not true. The argument is invalid.

73)

The set "fish" is disjoint from the set "birds" because the two sets have no members in common. A fish cannot be a bird, and a bird cannot be a fish.

74)

The sets are overlapping. It is possible for a person to be both an athlete and a high school students, but not all athletes are high school students and not all high school students are athletes. 75) Does not make sense. For this to be true, all the time you spent studying would have to be time you also spent playing basketball. This could be true if you spend literally no time studying or if you did all your reading while dribbling a basketball, but both possibilities strain credulity. (Explanations will vary.) 76) Answers may vary. One possibility: If you lease the car for two years, it will cost $9200 ($2000 + 24 months × $300/month). If you buy it, it will cost $8000 ($20,000 - $12,000). At first glance, it appears that buying is a better option. However, you need to consider other factors before you make your decision. How do you know that you will be able to sell the used car for $12,000 in two years? If your estimate is off by only 10% ($1200), then leasing will already be as cost-effective. In addition, you need to consider how the time value of money makes buying a less attractive option. The higher the interest rate, the more it will implicitly cost to buy the car (whether you borrow and pay interest expense or pay cash and forego interest income). Moreover, you should read all the fine print of the lease agreement. Are you locked into the lease for two years? Can you keep it longer if you wish? Are there any additional costs due when you return the car?

Answer Key Testname: CHAPTER 1

77) Answers may vary. One possibility: The answer depends on how many miles you drive the car. If you know you will drive less than 100 miles, then the daily rate is a better option, since $20/day × 4 days + $0.20/mi × 100 mi = $100. If you know you will drive more than 100 miles, then the weekly rate is a better option. If you aren't sure, then the weekly rate is probably preferable since the risk is limited. Even if you drove the minimum (zero miles), you would only spend $20 more by choosing the weekly rate. But for every 100 miles after the first 100, you would save $20 with the weekly rate. If you drive 500 miles, that's $80 in savings. You should also consider a hidden factor. If you might end up only needing the car 1-3 days, then the daily rate will tend to be a better option. However, if you might end up needing the car for 5-7 days, then the weekly rate is a better option since those days will not cost you extra. 78) Answers may vary. Possible answer: Mayor Brown has not said that he is not concerned with improving the quality of children's education, merely that he opposes this particular tax increase to build new schools. (Perhaps he would prefer a tax increase to improve the current schools instead of building new ones, or perhaps he thinks the quality of education can be improved without raising taxes) Mayor Brown's opponent has distorted his views. Any argument based on a distortion of someone else's ideas or beliefs is called a straw man.

79)

The type of argument is called Affirming the Hypothesis. We have p = you are hot and q = you will sweat. The second premise asserts that James is hot, which we show by putting an X in the p circle. Because the X is also in the q circle, q must also be true for James. The Venn diagram shows that the premises lead necessarily to the conclusion, so the argument is valid. 80) In standard form: No beggars are choosers. The subject set is "beggars" and the predicate set is "choosers."

81) Answers may vary. Possible answer: The premises are true. The strength of the argument is relatively weak. First, the examples may have been cherry picked from all the presidents (43 and counting). Second, the examples are of presidents, not of United States politicians in general. The conclusion is false. Although one must be at least 35 years old to be President of the United States, one can be younger and still occupy many other positions. 82) Answers may vary. One possibility: Since "does not oppose" is a double negation, the councilman supports the measure. The term "anti-pollution" is an additional negation, so in supporting the measure, the councilman is acting against pollution. A triple negation (not not not p) has the opposite truth value as the original proposition p.

Answer Key Testname: CHAPTER 1

83) Answers may vary. Possible answer: If we can consider this an argument at all, it has the form

Premise: You want your family to be happy and attractive. Conclusion: You should eat at Ma & Pa's Restaurant. The argument appeals to emotion, not logic. The advertisers hope that the image of happy and attractive people will evoke positive emotions and make you want to eat at the restaurant. In other cases, the appeal is to negative emotions. 84) False. Springfield is the capital of Illinois, but Chicago is not the capital of Illinois. (Even if you don't know the capital of Illinois, you can determine that at least one of the propositions is false.) Since one of the individual propositions is false, the conjunction is false. 85) Answers may vary. Possible answer: The premise of this argument cites one case in which Isabelle ate vegetarian food. But one case is not enough to establish a pattern, let alone to conclude that Isabelle always eats vegetarian food.

86)

I = truck drivers who are neither employed nor unemployed II = employed truck drivers III = non-truck drivers who are employed IV = unemployed truck drivers V = truck drivers who are both employed and unemployed VI = non-truck drivers who are both employed and unemployed VII = non-truck drivers who are unemployed VIII = non-truck drivers who are neither employed nor unemployed This region has no members. 87) Answers may vary. One possibility: Paying bills late will result in bad credit. It is important to be able to get a loan.

Answer Key Testname: CHAPTER 1

88) Answers may vary. One possibility:

Yes, a car could be both a truck and a toy. We know from the first two propositions that the set "cars" and the set "trucks" are subsets of the set "things that have wheels," but we do not know whether the two subsets are disjoint or overlapping or whether one is a subset of the other. We know from the third proposition that the set "toys" overlaps the set "things that have wheels," but we do not know whether it also overlaps either or both of the sets "cars" and "trucks." Depending on whether or not "cars," "trucks," and "toys" overlap; the regions a, b, c, and d may or may not have any elements. Since region b might have elements, a car could be both a truck and a toy.

89)

The sets are overlapping. It is possible for a person to be both an astronaut and a father, but not all astronauts are fathers and certainly not all fathers are astronauts. 90) Yes, Kevin must file a return. He is a married person under 65 years of age who can be claimed as a dependent on another person's tax return. As such, he must file a return if any of (i)-(iv) apply. (i) does not apply since $700 < $750; (ii) does not apply because $3500 < $3925; (iii) does not apply because although his spouse (Linda) files a separate return, she does not itemize; (iv) does apply. The total of earned and unearned income ($3500 + $700 = $4200) is greater than both (a) $750 and (b) earned income (up to $3675) plus $250 ($3500 + $250 = $3750). Thus, Kevin must file a return. (Explanations will vary.) 91) Answers may vary. One possibility: No. There is too much missing information and too many red flags. Why is the cousin of an acquaintance willing to give you such a good deal? Perhaps he's just a generous guy, but there are other possibilities to consider. He claims it's "the same watch," but how do you know it's not counterfeit? Even if it's authentic, how do you know it's not used or broken? Even if it's in mint condition, how do you know it's not stolen? In trying to save money, you might cost yourself money or even end up in jail.

Answer Key Testname: CHAPTER 1

92) Does not make sense. The set of integers includes the whole numbers and their negatives, and thus the set of whole

numbers is a subset of the set of integers. As such, all members of the set of whole numbers are also members of the set of integers. Therefore, if the answer to the question is a whole number it must also be an integer. (Explanations will vary.) 93) Answers may vary. One possibility: The expression "repealed the ban" is a double negation. In repealing the ban on the resolutions in question, the state assembly in effect allowed them. Since the resolutions are "anti-smoking," a third negation is involved. A triple negation (not not not p) has the opposite truth value as the original proposition p. In short, the assembly is now allowing resolutions that prohibit smoking. If one were a lobbyist for the tobacco companies, this might be a setback. 94) Answers may vary. One possibility: Healthy teeth are important. Healthy gums are important. 95) Answers may vary. One possibility: Option 1 (buying a power mower) will cost you $240 ($340 - $100). Option 2 (renting a power mower) will cost you $240 (12 × $20). Option 3 (hiring the neighbor's son) will cost you $240 ($10 × 2 × 12). The cost of each of the three options appears to be equal. Let's see if there are hidden factors that might help you make a decision. Options 1 and 2 require you to mow the lawn yourself each week. Your time could be spent doing other things (including earning money!), so this is a hidden expense. Then again, you might appreciate the opportunity to exercise, get a tan, and meet the neighbors; so depending on your preferences this could actually be a hidden benefit. Option 1 requires you to resell the mower at the end of the summer. Unless there is a buyer in place (e.g., has the owner of the home or the hardware store already offered to buy it back?), you will have to spend time and energy negotiating the sale of the used mower. Option 2 most likely requires you to pick up and drop off the mower each week. When all the costs are considered, Option 3 might end up being the least expensive, but there are some hidden factors there, too. What happens if the neighbor's son does an unsatisfactory job? What if it takes him more than 2 hours to complete the job? Are you obliged to pay him for the additional time?

96)

The sets are overlapping. It is possible for a person to be both a doctor and a poet, but a doctor is not necessarily a poet and a poet is not necessarily a doctor. 97) Does not make sense. A quarter of an hour is 15 minutes, while the time between 6:50 and 7:10 is 20 minutes. It takes him five more minutes to shower, so to do it to save time doesn't make sense. (Explanations will vary.) 98) Answers may vary. One possibility: It will cost her $575 to stay overnight ($400 + $100 + $75), and it will cost her $700 to fly back the same day. It appears that staying overnight is the better option, since it will save her $125. However, she could consider other factors before making a decision. Will staying overnight force her to miss all or part of a day of work? If so, that could cost her more than $125. Is it important to her to be home with her family? If so, the potential $125 savings may be illusory. Then again, she might enjoy having a night to herself and ordering room service.

Answer Key Testname: CHAPTER 1

99) Answers may vary. One possibility: The person stating this opinion may not like one of his current senators (or may

even want the job for himself!). In addition, he may want the balance of power to shift from the legislative branch to the executive branch and may feel that term limits will give senators less overall influence. 100) In standard form: Some dogs are creatures that are adorable. The subject set is "dogs" and the predicate set is "creatures that are adorable."

The X indicates that the overlapping region has at least one member. No claim is made about whether other regions also have members. 101) Answers may vary. One possibility: An unattended campfire is illegal. Getting a citation from the park ranger would be a bad thing. 102) Answers may vary. Possible answer: The premise is false. Most of the sports listed are played with a ball, but hockey is played with a puck. The argument is weak, and the conclusion is false. Many sports, in addition to hockey, do not involve a ball, including wrestling, swimming, and skiing. 103) Does not make sense. There are four basic structures for conditional arguments. Two of them, "Affirming the Conclusion" and "Denying the Hypothesis," are invalid. The other two, "Affirming the Hypothesis" and "Denying the Conclusion," are valid. Since it might be an example of ""Denying the Conclusion," it is not true that it must be an example of "Affirming the Hypothesis." (Explanations will vary.)

104)

The X represents Jack. We do not have enough information to know whether the X should be inside or outside the "lawyers" circle. Therefore, the conclusion does not follow necessarily from the premises, and the argument is invalid.

Answer Key Testname: CHAPTER 1

105) Answers may vary. Possible answer:

106) B 107) B 108) B 109) B 110) A 111) B 112) A 113) A 114) B 115) A 116) B 117) C 118) A 119) B 120) A 121) D 122) A 123) C 124) A 125) C 126) D 127) D 128) D 129) B 130) B 131) B 132) A 133) B 134) B 135) B 136) B 137) A 138) A 43

Answer Key Testname: CHAPTER 1

139) A 140) B 141) B 142) B 143) B 144) A 145) C 146) B 147) A 148) A 149) A 150) D 151) C 152) A 153) A 154) B 155) A 156) B 157) B 158) B 159) A 160) C 161) D 162) A 163) D 164) A 165) D 166) B 167) D 168) B 169) B 170) C 171) A 172) D 173) C 174) B 175) A 176) B 177) A 178) C 179) C 180) D 44

Answer Key Testname: CHAPTER 1

181) D 182) B 183) B 184) A 185) B 186) C 187) B 188) D 189) A 190) C 191) A 192) C 193) B 194) A 195) C

Exam

Chapter 2

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether the statement makes sense. Explain your reasoning. 1) To convert from Kelvin to Celsius, you subtract 273.15. For example, -100 K = -373.15 °C.

2) I can walk on my hands for 5 meters before falling down, but my goal is to walk a full

1) 2)

decimeter without losing my balance.

Solve the problem. 3) Two bicyclists, 42 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 15 miles per hour and the other 20 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 38 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?

4) A trader bought a stock for $20 and then sold it for $30. He bought it back for $44 and

5) Paul and Saul ran a 50-meter race. When Paul crossed the finish line, Saul had run only

then sold it again for $54. How much did he gain or lose on these transactions?

48 meters. Then they ran a second race, with Paul starting 2 meters behind the starting line. Assuming that both runners ran at the same pace as in the first race, who won the second race?

Decide whether the statement makes sense. Explain your reasoning. 6) Our utility company charges 10 cents per joule for the energy we use. Solve the problem. 7) Suppose that 8 turns of a wire are wrapped around a pipe with a length of 60 inches and a circumference of 4 inches. What is the length of the wire?

8) Abe, Boris, Cal, and David all proposed to Ellie on Friday. Abe proposed at 5:00, Boris

9) Suppose that you have 10 white socks and 6 black socks in a clothes dryer. How many

proposed at 6:00, Cal proposed at 7:00, and David proposed at 8:00. Ellie accepted the last of the four proposals. Some clues: (1) The times may be A.M. or P.M. (2) Boris proposed before Abe (3) At least one suitor proposed between the proposals of Cal and David. (4) Cal did not propose between Boris and Al. Whose proposal did Ellie accept?

socks must you withdraw from the dryer (without looking) to be certain of having a pair of white socks?

10) A curved bridge rises over a river, so that the two endpoints of the bridge are 180 yards

10)

apart horizontally. You walk across the bridge with a device to measure its length and discover that the walking distance is 188 yards. Approximately how high does the bridge rise above the horizontal?

Decide whether the statement makes sense. Explain your reasoning. 11) I found a rock at the bottom of our swimming pool. It had a mass of 500 grams and a volume of 1000 cubic centimeters, so its density was 0.5 g/cm3 . Solve the problem. 12) Suppose that you begin with a red bucket containing 12 red marbles and a yellow bucket containing 12 yellow marbles. You move three marbles from the red bucket to the yellow bucket, and then you move any four marbles from the yellow bucket to the red bucket. Which is greater, the number of yellow marbles in the red bucket or the number of red marbles in the yellow bucket? Decide whether the statement makes sense. Explain your reasoning. 13) I drove really far, almost 200 kilometers per hour. Solve the problem. 14) Cheddar cheese comes in 2-pound bags, and mozzarella cheese comes in 5-pound bags. Using entire bags, you make a 47-pound mixture of cheese. How many bags of each type of cheese did you use? Find all the possible solutions to the problem.

11)

12)

13)

14)

Decide whether the statement makes sense. Explain your reasoning. 15) The container was big enough to hold a barrel of water, but it wasn't big enough to hold a barrel of petroleum.

15)

16) I figured out the number of seconds in a week by multiplying 7 by 24 by 60 by 60.

16)

17) To convert square yards to square inches, I multiplied by 122 or 144.

17)

Solve the problem. 18) How do you measure 6 minutes with a 7-minute hourglass and a 5-minute hourglass? Assume that the hourglasses can only measure 7-minute and 5-minute intervals, respectively, and cannot be used to measure other time intervals. Decide whether the statement makes sense. Explain your reasoning. 19) Whether it's a problem in mathematics or something else, I always find it's best to complete the work by looking back to check, interpret, and explain my solution. Solve the problem. 20) A father and son are in a terrible car accident. The father is killed. The son, badly injured, is brought to the hospital for emergency surgery. The surgeon takes one look at the patient and exclaims, "That's my son!" How is this possible?

18)

19)

20)

Decide whether the statement makes sense. Explain your reasoning. 21) My friend wants to lose 15 pounds, but I think that's too much. I think 10 kilograms would make more sense. Solve the problem. 22) A curved bridge rises over a canyon. The two endpoints of the bridge are one mile apart horizontally. The bridge rises to a height of 368 feet above the horizontal. Approximately what is the walking distance along the bridge, in feet?

21)

22)

23) It takes you 78 seconds to walk from the first (ground) floor of a building to the fourth

23)

24) You are considering buying 15 silver coins that look alike, but you have been told that one

24)

floor. How long will it take to walk from the first floor to the 10th floor (at the same pace, assuming that all floors have the same height)?

of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale?

Decide whether the statement makes sense. Explain your reasoning. 25) I got pulled over by a police officer for speeding. I was going 150 kiloliters per second.

25)

26) If you complete the four-step problem-solving process carefully and thoroughly, then

26)

you will have no uncertainty about your final answer.

Solve the problem. 27) There is a large jar of marbles, containing red, blue, yellow, black, and white marbles. How many marbles must you draw (without looking) from the jar to be sure of getting at least three of one color? Decide whether the statement makes sense. Explain your reasoning. 28) It is not recommended that you use approximations to solve a problem, because then your solution is only an approximation. Solve the problem. 29) Three boxes are labeled "CDs," "DVDs," and "CDs & DVDs." Each label is wrong. Bey selecting just one item from just one box, how can you determine the correct labeling of the boxes? Decide whether the statement makes sense. Explain your reasoning. 30) I donated 64 fluid ounces of blood today.

31) The boat leaked and started filling with water. There must be 50 gallons of water in it already.

27)

28)

29)

30) 31)

Solve the problem. 32) A traffic counter consists of a thin black tube stretched across a street or highway and connected to a "brain box" at the side of the road. The device registers one "count" each time a set of wheels (that is, wheels on a single axle) rolls over the tube. A normal automobile (two axles) registers two counts, and a light truck (three axles) registers three counts. Suppose that, during a one-hour period, a particular counter registers 41 counts on a residential street on which only two-axle vehicles (cars) and three-axle vehicles (light trucks) are allowed. How many cars and light trucks passed over the traffic counter? Find all the possible solutions to the problem.

33) Suppose that China's population policy is modified so that every family could have

32)

33)

children until either a boy is born or two children are born, whichever comes first. Assuming that every family chooses to have as many children as possible under this policy, and that boys and girls are equally likely, how many children would be born in a typical group of 1000 families?

Decide whether the statement makes sense. Explain your reasoning. 34) I figured out the distance we had traveled by dividing our speed by the amount of time we had traveled.

35) We will need 1800 cubic feet of carpeting to cover the floors in our three-story house. Solve the problem. 36) There are 20 bags filled with coins that all look alike. The coins in 19 of the bags are authentic and weigh 10 ounces each. The coins in one of the bags are counterfeit and weigh 11 ounces each. With only one weighing on a scale, how can you determine which bag contains the counterfeit coins?

34)

35)

36)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the following question involving a conversion within the USCS system. 37) The customer bought a peck of flour. How many cubic inches of flour did he buy? A) 33.6 in.3 B) 67.2 in.3 C) 268.8 in.3 D) 537.6 in.3

37)

State how much larger or smaller the first unit is than the second. 38) gigagram, microgram A) Larger by a factor of 1018 B) Larger by a factor of 1015

38)

C) Larger by a factor of 109

D) Larger by a factor of 1012

Use units to help you answer the question. If necessary, round your answer to two decimal places. 39) A stockbroker sold 90 shares of stock for $18.32 each. What was the total amount of the sale? A) $1,648.9 B) $1,648.91 C) $1,648.80 D) $1,648.7

39)

Solve the problem. 40) Recently, one U.S. dollar was worth about 0.6158 British pounds. How much would a car have cost in U.S. dollars that cost 11,340 British pounds? A) $22,062.26 B) $5,828.76 C) $6,983.17 D) $18,415.07

41) A warehouse is 44 yards long and 31 yards wide with a height of 14 yards. What is the volume of the warehouse? A) 1,364 yd2

B) 1,364 ft2

C) 19,096 yd3

40)

41)

D) 19,096 ft3

Evaluate.

42) 1 + 1 5

42)

A) 40 13

B) 13

C) 13

D) 13 40

Convert the measurement to the units specified. Round your answer to the nearest tenth. 43) 14 cubic inches to milliliters A) 0.9 milliliters B) 414 milliliters

C) 0.5 milliliters

43)

D) 229.4 milliliters

Use the following table of exchange rates to solve the problem. Round your answer when appropriate. Currency Dollars per Foreign Foreign per Dollar British pound 1.624 0.6158 Canadian dollar 1.005 0.9950 European euro 1.320 0.7576 Japanese yen 0.0120 83.33 Mexican peso 0.07855 12.73

44) Which is worth most, 1 British pound, 1 Canadian dollar, 1 European euro, or 1 dollar? A) 1 European euro B) 1 dollar C) 1 Canadian dollar D) 1 British pound Solve the problem. 45) 106 - 104

A) 110,000

44)

45) B) 1,010,000

C) 100

Answer the following question involving a conversion within the USCS system. 46) If a horse ran 9 furlongs, how many yards did it run? A) 1,980 yd B) 15,840 yd C) 7,920 yd

D) 990,000

46) D) 47,520 yd

Evaluate.

47) 2 × 17 17

47)

A) 2 9

B) 9

C) 1

D) 2

48) 15 × 1 11

48)

A) 2

B) 1

C) 3

D) 3

Solve the problem. 49) Your electrical bill states that you used 630 kilowatt-hours of energy in September. Determine your average power use, in watts. A) 1,050 watts B) 875 watts C) 962.5 watts D) 846.8 watts Identify the units you would expect for the given quantity. 50) The amount of electricity utilized, calculated by multiplying power in kilowatts by time in hours. A) kilowatt-hours B) kilowatts per hour

C) kilowatts per second

49)

50)

D) hours per kilowatt

Answer the following question involving a conversion within the USCS system. 51) How many quarts are in 58 barrels of water? A) 2,436 qt B) 1,798 qt C) 9,744 qt

51) D) 7,192 qt

Decide which of the two given prices is the better deal. 52) The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 10-oz bottles for $2.50 Seven 14-oz bottles for $5.29 A) equal value B) Five 10-oz bottles

C) Seven 14-oz bottles

52)

D) not enough information

Answer the following question involving a conversion within the USCS system. 53) The container holds 6 gallons of water. How many fluid ounces is that? A) 768 fl oz B) 384 fl oz C) 192 fl oz

53) D) 1,536 fl oz

Convert the measurement to the units specified. Round your answer to the nearest tenth. 54) 35 pounds to grams A) 77.2 grams B) 15,876 grams C) 15.9 grams D) 77,175 grams Use units to help you answer the question. If necessary, round your answer to two decimal places. 55) You are buying carpet to cover a room that measures 12 feet by 17 feet. The carpet costs $27.50 per square yard. How much will the carpet cost? A) $741.82 B) $623.33 C) $204.00 D) $1870.00 Solve the problem. 56) Suppose you burn 400 Calories while exercising for 50 minutes. What is your average power while exercising, in watts? A) 557.9 watts B) 446.3 watts C) 836.8 watts D) 669.4 watts

54)

55)

56)

57) Find a conversion factor between cubic inches and cubic yards. Write it in three forms. A) 1 in.3 = (36 yd)3 = 46,656 yd3 B) 1 yd3 = (36 in.)3 = 46,656 in.3 C) 1 yd2 = (36 in.)2 = 1296 in.2 D) 1 yd3 = (3 ft)3 = 27 ft3 Decide which of the two given prices is the better deal. 58) You can buy laundry product in a 24-ounce bottle for $2.88 or in a 20-ounce bottle for $2.20. A) 20-ounce bottle for $2.20 B) equal value

C) 24-ounce bottle for $2.88

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 60) -35°C, into Fahrenheit A) 12.6°F B) -31°F C) -95°F D) -3°F Solve the problem. 108

C) 104

B) 10-4

60)

D) 1012

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 62) 109 77

A) 1.416

59)

61)

104

A) 1032

58)

D) not enough information

Solve the problem. 59) Suppose a necklace is made from 18-karat gold and weighs 54 grams. Find the weight, in grams, of the pure gold in the necklace. A) 18 grams B) 6 grams C) 40.5 grams D) 54 grams

61)

57)

B) 1.226

C) 1.526

D) 0.706

Use units to help you answer the question. If necessary, round your answer to two decimal places. 63) Assume that you breathe once every 10 seconds. How many breaths do you take in 3 weeks? A) 181,440 B) 25,920 C) 260,480 D) 3024 Solve the problem. 64) Recently, one U.S. dollar was worth about 12.73 Mexican pesos. How much would 585 U.S. dollars be worth in Mexican pesos? A) $45.95 B) $7,447.05 C) $6,616.35 D) $53.82 Carry out the indicated unit conversion. Round your answer, if appropriate. 65) Convert a lot size of 2 acre to square feet (1 acre = 43,560 ft2 ). 9

A) 968 square feet C) 979 square feet

B) 9,790 square feet D) 9,680 square feet

62)

63)

64)

65)

Decide which of the two given prices is the better deal. 66) You can buy hair product in a 8-ounce bottle for $2.16 or in a 6-ounce bottle for $1.50. A) 8-ounce bottle for $2.16 B) not enough information

C) equal value

66)

D) 6-ounce bottle for $1.50

Identify the units you would expect for the given quantity. 67) The price of pudding, found by dividing its cost in dollars by its weight in ounces. A) dollars per ounce B) dollar-ounces

C) ounce-dollars

67)

D) ounces per dollar

Use units to help you answer the question. If necessary, round your answer to two decimal places. 68) Assuming that your heart beats 70 times per minute, how many times does your heart beat in 6 days? A) 36,288,000 B) 604,800 C) 201,600 D) 25,200

68)

Identify the units you would expect for the given quantity. 69) The gas mileage of a car, when you travel 5,020 kilometers using 10 gallons of gas. A) gal/km B) $/gal C) 50 D) km/gal

69)

State how much larger or smaller the first unit is than the second. 70) centiliter, microliter A) Smaller by a factor of 10,000 B) Larger by a factor of 10,000

70)

C) Larger by a factor of 1000

D) Smaller by a factor of 1000

Solve the problem. 71) 102 + 109

71)

A) 100,000,100 C) 100,000,000,000

B) 1,000,001,000 D) 1,000,000,100

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 72) -70°C, into Kelvin A) 147.15 K B) -343.15 K C) 103.15 K D) 203.15 K Use units to help you answer the question. If necessary, round your answer to two decimal places. 73) An acre is equal to 43,560 square feet, and there are 5280 feet in a mile. If a farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles, what is the area of the farm in acres? A) 1050 acres B) 0.16 acres C) 11.14 acres D) 864 acres Convert the measurement to the units specified. Round your answer to the nearest tenth. 74) 21 feet to meters A) 8.5 meters B) 19.2 meters C) 6.4 meters D) 68.9 meters

72)

73)

74)

Solve the problem. 75) An average 12-ounce can of beer contains about 15 grams of alcohol. Consider a person with approximately 6 liters (6000 milliliters) of blood, who quickly drinks two cans of beer. If all the alcohol were immediately absorbed into the bloodstream, what blood alcohol content would we find? A) 0.025 g/100 ml B) 0.25 g/100 ml C) 0.05 g/100 ml D) 0.5 g/100 ml

76) A 14-gram object has a volume of 35 cubic centimeters. Find its density. A) 21 cm3 B) 490 g-cm3 C) 2.5 cm3 /g

76) D) 0.4 g/cm3

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 77) 384 64

A) 7

B) 5

C) 6

75)

77)

D) 6.4

78) 651

78)

878

A) 0.551

B) 0.851

C) 0.748

D) 0.741

Evaluate.

79) 5 + 3 3

79)

A) 6

B) 19

C) 12

D) 19 6

80) You return from a trip with 3,200 Japanese yen. How much are your yen worth in dollars? A) $2,424.32 B) $266,656 C) $38.40 D) $251.36 Solve the problem. 81) Your electrical bill states that you used 680 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules. A) 2,448,000,000 joules B) 217,600,000 joules

C) 244,800,000 joules

80)

81)

D) 2,176,000,000 joules

82) How many cubic inches are in 11 cubic feet? A) 19,008 in.3 B) 1,584 in.3

82) C) 14,256 in.3

D) 513,216 in.3

83) A swimming pool 3 meters deep, 11 meters long, and 6 meters wide is filled with water. What is the area of the water's surface? A) 198 m 3 B) 66 m 2

C) 18 m 2

D) 33 m 2

Use units to help you answer the question. If necessary, round your answer to two decimal places. 84) A community garden contains 25 rectangular plots each measuring 6 yd by 10 yd. What is the total area available for gardening? A) 1,525 yd2 B) 800 yd2 C) 60 yd2 D) 1,500 yd2 Answer the following question involving a conversion within the USCS system. 85) How many gallons are in 76 barrels of petroleum? A) 2,356 gal B) 3,192 gal C) 1.8 gal

83)

84)

85) D) 3,952 gal

86) A boat is moving at 41 miles per hour. What is its speed in knots (nautical miles per hour)? A) 33.6 knots B) 35.6 knots C) 49.2 knots D) 47.2 knots Solve the problem. 87) A supermarket in Japan sells soy milk for 393 yen per liter. If there are 83.12 yen per dollar, then what is the price in dollars per quart? A) $3.76 per quart B) $4.47 per quart C) $4.73 per quart D) $5.00 per quart

86)

87)

Evaluate.

88) 1 - 1 5

88)

A) - 1

B) 1

C) 1

D) - 1 5

89) 7 - 1 5

89)

A) 9 7

Write as a common fraction. 90) 0.23 A) 16 5

B) 44

C) 53

D) 54 35

90) B) 8

C) 23

100

D) 23 10

Solve the problem. 91) Find a conversion factor between square feet and square yards. Write it in three forms. A) 1 yd2 = (3 ft)2 = 9 ft2 B) 1 yd3 = (3 ft)3 = 27 ft3

C) 1 ft2 = (3 yd)2 = 9 yd2

D) 1 ft3 = (3 yd)3 = 27 yd3

91)

92) How many Mexican pesos can you buy for $120? A) 1.44 pesos B) 1,527.6 pesos

92) C) 9.426 pesos

D) 9,999.6 pesos

Convert the measurement to the units specified. Round your answer to the nearest tenth. 93) 2,200 square yards to square meters A) 2,633 square meters B) 1,839.5 square meters

C) 2,406.8 square meters

93)

D) 2,011.7 square meters

Solve the problem. 94) An object has a total volume of 6 liters (which is 6,000 cubic centimeters) and a mass of 4 kilograms. What is its density? Will it sink or float in water? A) 1.5 g/cm3; sink B) 0.67 g/cm3 ; float

C) 0.67 g/cm3 ; sink

94)

D) 1.5 g/cm3; float

Use units to help you answer the question. If necessary, round your answer to two decimal places. 95) Suppose water flows from a shower at a rate of 0.32 cubic feet per minute. Do you use more water by taking a 12-minute shower or by filling a bathtub with 0.4 cubic yards of water, and by how much? A) Shower uses an additional 3.44 ft3 of water

95)

B) Shower uses an additional 6.96 ft3 of water C) Bath uses an additional 3.44 ft3 of water D) Bath uses an additional 6.96 ft3 of water Convert the measurement to the units specified. Round your answer to the nearest tenth. 96) 9 kilometers to yards A) 76,473.9 yards B) 25,491.3 yards C) 9,843 yards D) 29,528.9 yards Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 97) 13 45

A) 3.462

B) 0.199

C) 0.289

D) 0.449

96)

97)

98) A fresh juice stand in Montreal sells a large glass of orange juice for 4.90 Canadian dollars. If you buy 4 glasses, how much have you spent in (U.S.) dollars? A) $14.85 B) $25.87 C) $19.50

D) $19.70

State how much larger or smaller the first unit is than the second. 99) cubic micrometer, cubic meter A) Smaller by a factor of 1012 B) Smaller by a factor of 1018

C) Smaller by a factor of 109

Write as a common fraction. 101) 7.35 A) 147 2

B) 10

C) 1.5

100)

D) 3.5

101) B) 753

C) 147

100

D) 147 200

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 102) 8 11

A) 0.615

99)

D) Smaller by a factor of 106

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 100) 5 2

A) 2.5

98)

B) 0.8

C) 0.072

D) 0.727

Solve the problem. 103) How many cubic furlongs are in a cubic mile? (1 mile = 8 furlongs) A) 4096 cubic furlongs B) 8 cubic furlongs

C) 512 cubic furlongs

102)

103)

D) 64 cubic furlongs

State how much larger or smaller the first unit is than the second. 104) square decimeter, square kilometer A) Smaller by a factor of 106 B) Smaller by a factor of 103

C) Smaller by a factor of 104

D) Smaller by a factor of 108

104)

Solve the problem. 105) A certain land area is 450,000 square miles, and it holds a population of 65.3 million people. Calculate the population density. A) 69 people/mi2 B) 689 people/mi2

C) 1,451 people/mi2 Write as a common fraction. 106) 0.0009 A) 9 10000

D) 145 people/mi2

106) B) 9 1000

C) 9 100

Carry out the indicated unit conversion. Round your answer, if appropriate. 107) Convert a distance of 42 feet into yards. A) 126 yards B) 14 yards C) 17 yards Write as a common fraction. 108) 0.991 A) 991 1000

105)

D) 9 100000

107) D) 28 yards

108) B) 991

C) 991

10000

100

D) 991 10

Solve the problem. 109) A swimming pool 3 meters deep, 12 meters long, and 8 meters wide is filled with water. What volume of water does the pool contain? A) 24 m 2 B) 96 m 2 C) 288 m 3 D) 309 m 3 Identify the units you would expect for the given quantity. 110) The price of gravel, found by dividing its total cost in dollars by its total weight in tons. A) dollars per ton B) ton-dollars C) cubic tons D) tons per dollar Solve the problem. 111) There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms. A) 1 m 3 = (1000 km)3 = 1,000,000 km3 B) 1 km3 = (1000 m)3 = 1,000,000,000 m 3

C) 1 km2 = (1000 m)2 = 1,000 m 2

109)

110)

111)

D) 1 km3 = (1000 m)3 = 100,000 m 3

Evaluate.

112) 3 ÷ 5 5

112)

A) 9

B) 3

C) 25

D) 1

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 113) 330 K, into Celsius A) 156.85°C B) 256.85°C C) 56.85°C D) -89.82°C

113)

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 114) 5 7

A) 0.833

B) 0.714

C) 0.719

Solve the problem. 115) You find a 7-pound nugget that is 20% gold. What is its purity in karats? A) 20 karats B) 16.8 karats C) 24 karats

D) 0.711

115) D) 4.8 karats

State how much larger or smaller the first unit is than the second. 116) gram, milligram A) Larger by a factor of 106 B) Larger by a factor of 103

C) Smaller by a factor of 103

114)

116)

D) Smaller by a factor of 106

Identify the units you would expect for the given quantity. 117) A speed found by dividing a distance measured in meters by a time measured in seconds. A) meter-seconds B) seconds per meter

C) meters per second

117)

D) square meters

Solve the problem. 118) A column has a circular base with an area of 5 square feet and is 11 feet tall. What is its total volume? A) 275 ft3 B) 275 ft3 C) 55 ft3 D) 55 ft3

118)

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 119) 75°F, into Celsius A) 43.00°C B) 23.89°C C) 59.44°C D) 41.67°C

119)

Carry out the indicated unit conversion. Round your answer, if appropriate. 120) Convert a distance of 19 miles into yards; there are 1760 yards in a mile. A) 3,344 yards B) 34,580 yards C) 35,720 yards

120) D) 33,440 yards

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 121) 80°F, into Celsius A) 26.67°C B) 44.44°C C) 86.40°C D) 48.00°C

121)

Carry out the indicated unit conversion. Round your answer, if appropriate. 122) Use a chain of conversions with familiar measures of time to convert 4 weeks into seconds. A) 345,600 seconds B) 100,800 seconds

122)

C) 40,320 seconds

D) 2,419,200 seconds

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 123) 35°C, into Fahrenheit A) 51.4°F B) 31°F C) 95°F D) 67°F

123)

Identify the units you would expect for the given quantity. 124) The density of a meteor, found by dividing its mass in kilograms by its volume in cubic meters. A) kg/m 3 B) kg3 /m C) kg/m 2 D) m 3/kg

124)

Convert the measurement to the units specified. Round your answer to the nearest tenth. 125) 98 kilometers per hour to miles per hour A) 136.6 miles per hour B) 157.7 miles per hour

125)

C) 71 miles per hour Write as a common fraction. 126) 9.5 A) 59 10

D) 60.9 miles per hour

126) B) 19

C) 59

100

Solve the problem. 127) A field is 130 yards long and 50 yards wide. Find its area in square feet. A) 6,500 ft2 B) 19,500 ft2 C) 175,500 ft2 Write as a common fraction. 128) 0.6 A) 2 3

D) 19 2

127) D) 58,500 ft2

128) B) 3

C) 6

D) 3 5

Carry out the indicated unit conversion. Round your answer, if appropriate. 129) A car is driving at 420 miles per hour. What is its speed in miles per minute? A) 7 miles per minute B) 1,512,000 miles per minute

C) 480 miles per minute

129)

D) 25,200 miles per minute

Evaluate.

130) 1 + 1 + 1 3

130)

A) 43 60

Solve the problem. 131) 10-12 × 10-8

A) 10-4

B) 49

C) 3

D) 47

B) 1020

C) 10-20

D) 1096

131)

132) What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour? A) 30 cents

B) 60 cents

C) 45 cents

D) 67 cents

132)

Use units to help you answer the question. If necessary, round your answer to two decimal places. 133) Suppose you could spend $5 every hour, night and day. How much could you spend in a year? (Assume that there are 365 days in a year.) A) $7,200 B) $43,800 C) $2,628,000 D) $8760 Solve the problem. 134) 107 × 10-5

A) 102

133)

134) B) 10-35

C) 10-12

D) 1012

Evaluate.

135) 3 ÷ 1 4

135)

A) 9

B) 1

C) 9

D) 1 4

Solve the problem. 136) A packing crate measures 5 feet by 15 feet by 7 feet. What is the area of its smallest side? A) 35 ft2 B) 525 ft3 C) 105 ft2 D) 75 ft2

137) 102 × 109 A) 1018

136)

137) B) 1013

C) 1011

D) 1016

Evaluate.

138) 1 × 1 × 1 4

138)

A) 1

120

B) 1

C) 15

D) 1

Use units to help you answer the question. If necessary, round your answer to two decimal places. 139) Your car gets 33 miles per gallon of gasoline, and you drive at an average speed of 44 miles per hour. How much gas do you use in an hour? A) 0.69 gal B) 1.33 gal C) 1.45 gal D) 0.75 gal Solve the problem. 103

140)

10-6

A) 109

139)

B) 10-9

C) 10-3

D) 10-18

State how much larger or smaller the first unit is than the second. 141) nanometer, meter A) Smaller by a factor of 109 B) Larger by a factor of 106

C) Smaller by a factor of 106

D) Larger by a factor of 109

141)

Solve the problem. 142) How many square inches are in 8 square yards? A) 1,152 in.2 B) 96 in.2

143) 10

142) C) 288 in.2

D) 10,368 in.2

-10

143)

10-4

A) 10-14

C) 106

B) 10-40

Answer the following question involving a conversion within the USCS system. 144) The baby weighs 7.8 pounds. How many ounces is that? A) 93.6 ounces B) 78 ounces C) 0.49 ounces

D) 10-6

144) D) 124.8 ounces

Use units to help you answer the question. If necessary, round your answer to two decimal places. 145) A paint mixture contains 21 gallons of base for every gallon of color. In 528 gallons of paint, how many gallons of color are there? A) 504 gal B) 24 gal C) 264 gal D) 176 gal Carry out the indicated unit conversion. Round your answer, if appropriate. 146) Convert a weight of 19 pounds into ounces; there are 16 ounces in 1 pound. A) 304 ounces B) 380 ounces C) 152 ounces

146) D) 608 ounces

147) There are 8 ounces in a cup, 4 cups in a quart, and 4 quarts in a gallon. Using a chain with these conversions, convert 7 gallons into ounces. A) 224 ounces B) 112 ounces

C) 1,792 ounces

Solve the problem. 149) A piece of land in Ottawa with an area of 0.3 square kilometers is priced at 5,500 Canadian dollars. If there are 0.9945 Canadian dollars per (U.S.) dollar, then what is the price in dollars per square mile? A) $47,743.11 per square mile B) $7,118.08 per square mile

D) $47,219.38 per square mile

147)

D) 896 ounces

Convert the measurement to the units specified. Round your answer to the nearest tenth. 148) 28 liters to gallons A) 29.6 gallons B) 26.5 gallons C) 7.4 gallons D) 106 gallons

C) $29,667.00 per square mile

145)

148)

149)

Answer Key Testname: CHAPTER 2

1) Does not make sense. The general formula is correct, but the numbers don't make sense. A temperature of 0 K is the

coldest possible temperature, known as absolute zero. A temperature of -100 K is theoretically impossible. (Explanations will vary.) 2) Does not make sense. A decimeter is a tenth of a meter, and this person can already travel 50 times that. Perhaps he wants to be able to walk on his hands for a full decameter, or 10 meters. (Explanations will vary.) 3) 45.6 mi 4) He gained $20 on the transactions. 5) Paul 6) Does not make sense. The units are fine, but the magnitude is ridiculous. A regular 100-watt bulb consumes energy at a rate of 100 joules per second. If the utility charged 10 cents per joule, it would cost $1 just to keep a 100-watt bulb on for a single second. That's $86,400 a day! (Explanations will vary.) 7) 68 in. 8) Cal's proposal 9) 8 socks 10) 27.1 yards 11) Does not make sense. The calculation is correct, and the units are fine, but an object with a density under 1 g/cm3

would not sink in water. (Explanations will vary.) 12) The number of yellow marbles in the red bucket is greater. 13) Does not make sense. Kilometers per hour are a unit of speed, not distance. If you drive fast but only for a short period of time, you will not go far. (Explanations will vary.) 14) 1 bag cheddar and 9 bags mozzarella; 6 bags cheddar and 7 bags mozzarella; 11 bags cheddar and 5 bags mozzarella; 16 bags cheddar and 3 bags mozzarella; 21 bags cheddar and 1 bag mozzarella. 15) Makes sense. A barrel of liquid and a barrel of petroleum are two distinct measures of volume. A barrel of liquid, such as water, is 31 gallons, but a barrel of petroleum is 42 gallons. If the container were 31-41 gallons, it could hold a barrel of water but not a barrel of petroleum. (Explanations will vary.) 16) Makes sense. 1 wk × 7 days × 24 hr × 60 min × 60 sec = (7 × 24 × 60 × 60) seconds, since all the other units cancel. 1 wk 1 day 1 hr 1 min There are 604,800 seconds in a week. (Explanations will vary.)

17) Does not make sense. There are 12 inches per foot, but there are 36 inches per yard. To convert square yard to square

inches, multiply by 362 or 1296. (Explanations will vary.) 18) Answers may vary. One possibility: Start both hourglasses simultaneously. When the 5-minute hourglass runs out, immediately turn it upside down and start the timing of the 6-minute interval. There will be 2 minutes of time left in the 7-minute hourglass. When it runs out, immediately turn both hourglasses upside down. There will be 2 minutes of time left in the 5-minute hourglass (the 2 minutes that ran down before it was flipped). When it runs out, immediately turn the 7-minute hourglass upside down. There will be 2 minutes of time left in it (again, the 2 minutes that ran down before it was flipped). When it runs out, the timing of the 6-minute interval is complete (2 + 2 + 2 minutes = 6 minutes). Incidentally, if you continue in this fashion, you can measure any interval of an even number of minutes using these two hourglasses. Of course, some intervals (e.g., 10 minutes, 14 minutes) can be measured much more simply using just one hourglass. 19) Makes sense. This is essentially step 4 in the four-step process. Although you may be tempted to think you have finished after you find a result in step 3, this final step is the most important. After all, a result is not very useful if it is wrong or misinterpreted or cannot be explained to others. (Explanations will vary.) 20) The surgeon is a woman. She is the mother of the patient. 21) Does not make sense. 10 kilograms is about 22 pounds. If 15 pounds is too much, then certainly 22 pounds is too much. (Explanations will vary.) 22) 5,331.1 feet 23) 234 seconds 18

Answer Key Testname: CHAPTER 2

24) Answers may vary. One possible answer: Separate the coins into three sets of five coins. Weigh two of the sets. The

lightweight coin is in the lighter of the two sets, or if the two sets balance, it is in the third set. Now weigh two pairs of coins from the lightweight set of five coins. If they balance, the fifth coin is the lightweight coin; otherwise, weigh the coins in the lightweight pair to find the lightweight coin. 25) Does not make sense. Kiloliters are a unit of volume, and speed is measured in units of distance divided by time. (Explanations will vary.) 26) Does not make sense. The four-step process is a useful guide to problem solving, but the four steps offer only general advice. Following them will not automatically lead to a unique solution, since some questions do not lend themselves to unique solutions. This is fairly obvious when the question is one of politics or policy. For example, what is the best way to improve the economy? Different experts will recommend different-even contradictory-things (e.g., raise taxes, lower taxes), and no single best answer may be available. The same is true of mathematical problems, particularly when the information provided is incomplete or lacks context. Nonunique solutions often occur because not enough information is available to distinguish among a variety of possibilities. (Explanations will vary.) 27) 11 marbles 28) Does not make sense. Most real problems involve approximate numbers to begin with, so an approximation is often good enough for a final answer. In other cases, an approximation will reveal the essential character of a problem, making it easer to reach an exact solution. Approximations also provide a useful check. If you come up with an "exact solution" that isn't close to the approximate one, something may have gone wrong. (Explanations will vary.) 29) Select an item from the box labeled "CDs & DVDs." Since the label is wrong, it must be either a box of CDs or a box of DVDs. First assume that the item you selected is a CD. This box is therefore a box of CDs and should be labeled "CDs." Since the box labeled "DVDs" is also labeled incorrectly, it must be either a box of CDs or a box of both CDs and DVDs. Since you have already identified the first box as a box of CDs, the second box must therefore be a box of CDs and DVDs and should be labeled "CDs & DVDs." Finally, the box incorrectly labeled "CDs" should have the remaining label, "DVDs." Now assume that the item you selected is a DVD. By similar reasoning, this box should be labeled "DVDs," the box incorrectly labeled "CDs" should be labeled "CDs & DVDs," and the box incorrectly labeled "DVDs" should be labeled "CDs." 30) Does not make sense. The units are fine, but 64 fluid ounces are equivalent to 4 pints. A typical blood donation is one pint; donating four pints would be dangerous. (Explanations will vary.) 31) Makes sense. Gallons are a measure of volume and, depending on the size of the boat, 50 gallons could be a reasonable quantity of water. (Explanations will vary.) 32) 1 car and 13 light trucks; 4 cars and 11 light trucks; 7 cars and 9 light trucks; 10 cars and 7 light trucks; 13 cars and 5 light trucks; 16 cars and 3 light trucks; 19 cars and 1 light truck 33) 1500 34) Does not make sense. Dividing speed by time does not yield distance. Multiplying speed by time yields distance. For example, 10 mi/hr × 2 hr = 20 mi. (Explanations will vary.) 35) Does not make sense. Carpeting covers the area of the floors, not volume. (Indeed, if it covered the volume of the rooms, there wouldn't be any space left for people or furniture.) Cubic feet are a measure of volume, not area. (Explanations will vary.) 36) Label the bags 1-20 and choose one coin from bag 1, two coins from bag 2, three coins from bag 3, and so on. Weigh all the coins you chose together, a total of 210 coins. If all the coins were authentic, they would would weigh 2100 oz, since 210 coins × 10 oz/coin = 2100 oz. However, 1-20 of the coins are counterfeit, and each (11-oz) counterfeit coin will add an extra ounce to the weight. If the actual weight is 2101, there must be one counterfeit coin, and since one coin was chosen from bag 1, bag 1 must have the counterfeit coins. If the actual weight is 2102, bag 2 must have the counterfeits; if the actual weight is 2103, bag 3 must have the counterfeits, etc. In general: (Actual weight, in oz) - 2100 = the number of the bag with the counterfeit coins.

37) D 38) B 19

Answer Key Testname: CHAPTER 2

39) C 40) D 41) C 42) D 43) D 44) D 45) D 46) A 47) A 48) C 49) B 50) A 51) D 52) B 53) A 54) B 55) B 56) A 57) B 58) A 59) C 60) B 61) C 62) A 63) A 64) B 65) D 66) D 67) A 68) B 69) D 70) B 71) D 72) D 73) D 74) C 75) D 76) D 77) C 78) D 79) D 80) C 20

Answer Key Testname: CHAPTER 2

81) A 82) A 83) B 84) D 85) B 86) B 87) B 88) C 89) B 90) C 91) A 92) B 93) B 94) B 95) D 96) C 97) C 98) D 99) B 100) A 101) C 102) D 103) C 104) D 105) D 106) A 107) B 108) A 109) C 110) A 111) B 112) A 113) C 114) B 115) D 116) B 117) C 118) C 119) B 120) D 121) A 122) D 21

Answer Key Testname: CHAPTER 2

123) C 124) A 125) D 126) D 127) D 128) D 129) A 130) D 131) C 132) A 133) B 134) A 135) C 136) A 137) C 138) A 139) B 140) A 141) A 142) D 143) D 144) D 145) B 146) A 147) D 148) C 149) A

Exam

Chapter 3

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 1) Two candidates for governor of a state differ in their accounts of the state's economy during the incumbent's term. The incumbent claims that during his four-year term the economy has improved, citing a rise in the median household income from $33,000 to $34,500. The challenger claims that the economy has declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be right? A) The incumbent is referring to the state economy, while the challenger is referring to the national economy. B) Though the median household income increased, prices increased by a greater percent, meaning that in real terms the median income actually decreased. C) It is not possible for both candidates to be right; one of them is obviously lying.

D) Only those in the middle income group saw their incomes rise, those with lower and higher incomes actually saw their incomes decline during the incumbent's term.

2) Any test for a disease has a certain rate of false positives (percentage of those who don't have the

disease who test positive) and a certain rate of false negatives (percentage of those who do have the disease who test negative). You would like to determine the chance that a person has the disease given that they have tested positive for the disease. Which of the following will you need to know? A) The rate of false positives, the rate of false negatives, the incidence of the disease

B) The rate of false positives, the incidence of the disease C) The rate of false positives, the rate of false negatives D) The rate of false positives, the rate of false negatives, the incidence of the disease, the number of people being tested

3) Which of the statements below suggests an appropriate level of precision? A) Every day I drive a distance of 75.134 miles to work. B) Every day I drive a distance of 75.1341 miles to work. C) Every day I drive a distance of 76 miles to work. D) Every day I drive a distance of 80 miles to work. [to the nearest 10 miles]

4) A researcher looks at the percentage of people having high blood pressure amongst those who

exercise regularly and amongst those who do not exercise regularly. She selects 300 people under 40, of whom 100 exercise regularly and 200 do not. Among those who exercise regularly the rate of high blood pressure is 10% and among those who do not exercise regularly it is 15%. She then selects 300 people over 40, of whom 200 exercise regularly and 100 do not. Among those who exercise regularly the rate of high blood pressure is 30% and among those who do not exercise regularly it is 35%. However when she combines both age groups she finds that among those who exercise regularly the rate of high blood pressure is 23.3% and among those who do not exercise regularly it is 21.7%. Explain how the apparent inconsistency in these results came about. A) Mistakes must have been made in measuring blood pressures.

B) The group that exercises regularly contains a greater proportion of older people than the

group that does not exercise regularly. So when the age groups are combined, the "regular exercise" group has a higher rate of high blood pressure. C) The people in the "regular exercise" group probably started exercising because they have high blood pressure. D) Those that do not exercise regularly must be receiving some other treatment to lower their blood pressure.

5) In 2000 a company increased its workforce by 30%. In 2001 it decreased its workforce by 30%.

How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000? A) It is 9% lower. B) It is 3% lower.

C) It is 9% higher.

D) It is unchanged.

6) Which of the statements below suggests an appropriate level of precision? A) According to his bathroom scales, Enrique's weight is 190 lb [to the nearest ten pounds] B) According to his bathroom scales, Enrique's weight is 194.1134 lb. C) According to his bathroom scales, Enrique's weight is 194 lb. D) According to his bathroom scales, Enrique's weight is 194.113 lb. Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 7) The total number of gallons of gasoline that will be used by American drivers in a year. A) One hundred billion B) Ten trillion

C) One trillion

D) Ten billion

Solve the problem. 8) The area of Jose's apartment is 37% more than the area of Alan's apartment. Determine which of the statement's below is true. A) The area of Jose's apartment is 37% of the area of Alan's apartment.

B) The area of Jose's apartment is 137% of the area of Alan's apartment. C) The area of Jose's apartment is 137% more than the area of Alan's apartment. D) The area of Alan's apartment is 37% less than the area of Jose's apartment.

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 9) The total number of cups of coffee drunk last year by Europeans. A) Ten trillion B) Two trillion

C) Two hundred billion

D) Ten billion

Answer the question. 10) Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that the incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that they have the disease? Find the exact percentage. A) 10% B) 13.4% C) 8.8% D) 95%

10)

11) The average annual precipitation in Tewinville is 70 inches. In 2000, a particularly wet year, the

11)

12) Which of the statements below suggests an appropriate level of precision? A) 8000 people have enrolled for the college for next year. [Number given to the nearest

12)

precipitation was 140 inches. Which of the following statements are correct? More than one statement may be correct. A: In 2000, the precipitation was 200% of normal. B: In 2000, the precipitation was 100% of normal. C: In 2000, the precipitation was 200% above normal. D: In 2000, the precipitation was 100% above normal. A) A and C B) A and D C) B and C D) B and D

thousand] B) 8300 people have enrolled for the college for next year. [Number given to the nearest hundred] C) 8314.1 people have enrolled for the college for next year.

D) 8314 people have enrolled for the college for next year. Solve the problem. 13) The retail cost of a computer is 39% more than its wholesale cost. Determine which of the statement's below is true. A) The wholesale cost of the computer is 61% of the retail price.

B) The retail cost of the computer is 39% of the wholesale price. C) The retail cost of the computer is 139% more than the wholesale price. D) The retail cost of the computer is 139% of the wholesale price.

13)

Answer the question. 14) In Slackville, the unemployment rate was 20% last year and this year it is 30%. Which of the following statements is correct? A) In absolute terms, the unemployment rate this year is 50 percentage points higher than last year and in relative terms it is 10% higher. B) In absolute terms, the unemployment rate this year is 10 percentage points higher than last year and in relative terms it is 33.3% higher. C) In absolute terms, the unemployment rate this year is 10 percentage points higher than last year and in relative terms it is 10% higher. D) In absolute terms, the unemployment rate this year is 10 percentage points higher than last year and in relative terms it is 50% higher. Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 15) The total number of breaths taken in his lifetime by a man who lives to be 80. A) Three hundred million B) Three billion

C) Fifty million

14)

15)

D) Ten billion

Answer the question. 16) Which of the statements below suggests an appropriate level of precision? A) Worldwide there will be 133 million births next year.

16)

B) Worldwide there will be 133,147,763 births next year. C) Worldwide there will be 100 million births next year. [to the nearest one hundred million] D) Worldwide there will be 133.147 million births next year. 17) Suppose that a test for a disease correctly gives positive results for 95% of those having the disease

17)

18) Of those who applied to the college, 60% were accepted and of those accepted, 30% enrolled. What

18)

and correctly gives negative results for 92% of those who don't have the disease. Suppose also that the incidence of the disease is 1%. If a person tests positive for the disease, what can you say about their chance of having the disease? A) It is 95% B) It is quite low C) It is very high D) It is about 50%

percentage of those who applied, enrolled? A) 60% × 30% = 18%

B) 60% - 30% = 30% D) 60% + 30% = 90%

C) 60% × 30% = 1.8%

19) Between 1990 and 2000, the population of Emeryville grew from 20,000 to 25,000 while the

population of Sun City grew from 100,000 to 110,000. Which of the statements below is correct? A) Emeryville had greater absolute growth in population, and also greater relative growth.

B) Sun City had greater absolute growth in population, and also greater relative growth. C) Emeryville had greater absolute growth in population, but Sun City had greater relative growth.

D) Sun City had greater absolute growth in population, but Emeryville had greater relative growth.

19)

20) In 2000 your salary increased by 20% . In 2001 you received a 20% pay cut. After the two changes,

20)

how does your salary compare to your original salary? A) It is higher.

B) It is lower. C) It is unchanged. D) Cannot be determined from the information given Solve the problem. 21) Allison weighs 27% less than she did one year ago. Determine which of the statement's below is true. A) Allison's current weight is 27% of her weight one year ago.

21)

B) Allison's weight one year ago is 127% of her current weight . C) Allison's current weight is 73% of her weight one year ago. D) Allison's current weight is 127% of her weight one year ago. Answer the question. 22) A researcher looks at the percentage of people having high blood pressure amongst those who exercise regularly and amongst those who do not exercise regularly. She selects 300 people under 40, of whom 200 exercise regularly and 100 do not. Among those who exercise regularly the rate of high blood pressure is 10% and among those who do not exercise regularly it is 15%. She then selects 300 people over 40, of whom 100 exercise regularly and 200 do not. Among those who exercise regularly the rate of high blood pressure is 30% and among those who do not exercise regularly it is 35%. However when she combines both age groups she finds that among those who exercise regularly the rate of high blood pressure is 23.3% and among those who do not exercise regularly it is 21.6%. Explain the apparent inconsistency in these results. A) In spite of exercising, people get older.

22)

B) Among those who exercise regularly, younger people have a lower rate of high blood

pressure, and among those who do not exercise regularly younger people have a lower rate of high blood pressure. But looking at both groups combined, young people have a higher rate of high blood pressure. C) Within the under-40 age group the percentage with high blood pressure is lower amongst those who exercise, but within the over-40 age group, the percentage with high blood pressure is higher amongst those who exercise. D) Within each age group the percentage with high blood pressure is lower amongst those who exercise, but when the age groups are combined, the percentage with high blood pressure is higher amongst those who exercise.

Solve the problem. 23) During the sale the price of the sofa was discounted by 30%. Determine which of the statement's below is true. A) The sale price of the sofa is 70% less than the regular price.

B) The sale price of the sofa is 30% of the regular price. C) The regular price of the sofa is 101% of the sale price. D) The sale price of the sofa is 70% of the regular price.

23)

Answer the question. 24) In the 1980s, the population of Pleasanton decreased by 10%. In the 1990s, its population increased by 40%. How does the population of Pleasanton at the end of the 1990s compare with its population in 1980? A) It is 26% higher. B) It is 34% higher.

C) It is 30% higher.

24)

D) It is 50% higher.

25) If your salary is 25% higher than mine, then how does my salary compare to your salary? A) My salary is 75% of yours. B) My salary is 25% less than yours. C) My salary is 125% of yours. D) My salary is 20% less than yours.

25)

26) In 2000, the balance on Martin's credit card increased by 50%. In 2001, the balance increased by

26)

20%. How does the balance at the end of 2001 compare to the balance at the beginning of 2000? A) It is 100% higher. B) It is 70% higher.

C) It is 80% higher.

D) It is 60% higher.

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 27) The weight of a grain of rice. A) 0.0006 ounces B) 0.01 ounces

C) 0.006 ounces

27)

D) 0.000001 ounces

Solve the problem. 28) John is 4 times as heavy as his dog. Determine which of the statement's below is true. A) John weight is 300% of his dog's weight.

28) B) John weighs 300% more than his dog. D) John's dog weighs 300% less than John.

C) John weighs 400% more than his dog.

Answer the question. 29) Which of the statements below suggests an appropriate level of precision? A) My temperature this morning is 37.6° F.

29)

B) My temperature this morning is 37.612° F. C) My temperature this morning is 40° F. [to the nearest 10 degrees] D) My temperature this morning is 37.6127° F. Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 30) The thickness of a compact disc. A) 0.01 inches B) 0.05 inches C) 0.1 inches D) 0.005 inches Solve the problem. 31) Cathy scored 9 times as much as Helen on the test. Determine which of the statement's below is true. A) Cathy's score was 900% more than Helen's score.

B) Cathy's score was 800% of Helen's score. C) Cathy's score was 900% of Helen's score. D) Helen's score was 800% less than Cathy's score. 6

30)

31)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 32) The total number of steps an adult would take in walking from New York to San Francisco. A) One hundred million B) One million

C) Ten million

32)

D) One billion

Answer the question. 33) Your true height is 70.4 inches. A tape measure that can be read to the nearest tenth of an inch gives your height as 70.5 inches. A second tape measure which can be read to the nearest eighth of 3 an inch gives your height as 70 inches. Which of these two measurement is more precise? Which 8

33)

is more accurate? A) The second tape measure gives a more precise reading and also a more accurate reading.

B) The second tape measure gives a more precise reading but the first tape measure gives a more accurate reading. C) The first tape measure gives a more precise reading and also a more accurate reading.

D) The first tape measure gives a more precise reading but the second tape measure gives a more accurate reading.

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 34) The total amount of money spent each year on food by Americans. A) Thirty trillion dollars B) One trillion dollars

C) Ten billion dollars

34)

D) One hundred billion dollars

Answer the question. 35) Your true weight is 62.66 kilograms. A scale that gives weights to the nearest quarter kilogram 3 gives your weight as 62 kilograms. A digital scale that gives weights to the nearest 0.1 kilogram 4

35)

gives your weight as 62.6 kilograms. Which of these two measurement is more precise? Which is more accurate? A) The first scale gives a more precise reading and also a more accurate reading.

B) The first scale gives a more precise reading but the digital scale gives a more accurate reading.

C) The digital scale gives a more precise reading but the first scale gives a more accurate reading.

D) The digital scale gives a more precise reading and also a more accurate reading. 36) Which of the statements below suggests an appropriate level of precision? A) The population of sperm whales worldwide is 817,210. B) The population of sperm whales worldwide is 817,213 C) The population of sperm whales worldwide is 817,200. D) The population of sperm whales worldwide is 800,000.

36)

Solve the problem. 37) The value of her house today is 500% more than when she bought it. Determine which of the statement's below is true. A) The value of her house today is 600% more than when she bought it.

37)

B) The value of her house today is 6 times what it was when she bought it. C) The value of her house today is 5 times what it was when she bought it. D) The value of her house today is 500% of the value when she bought it. Answer the question. 38) Suppose that of the total amount collected in taxes by the U.S. government, 25% of it comes from families with incomes greater than $200,000. If taxes are increased by 5% across the board, which of the following statements will be true? A) 5% of the additional revenue will come from each income group.

38)

B) A family with an income greater than $200,000 will have to pay 25% more in taxes. C) The total amount collected from families with incomes greater than $200,000 will increase by 25%.

D) 25% of the additional revenue collected by the government will come from families with incomes greater than $200,000.

39) Which of the statements below suggests an appropriate level of precision? A) The number of people at the demonstration was 122,600. B) The number of people at the demonstration was 100,000 [to the nearest one hundred

39)

thousand].

C) The number of people at the demonstration was 122,615. D) The number of people at the demonstration was 120,000. 40) A teacher gives the same math exam to two different classes. The second class has more students

than the first. The mean score for the first class is 60% and the mean score for the second class is 70%. What can you say about the mean score for both classes combined? A) It may be higher or lower than 65%, this cannot be determined from the information given.

B) It is higher than 65%. C) It is equal to 65%. D) It is lower than 65%.

40)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Consumer Price Index below to answer the question.

41) Which of the following is greater? Explain why this makes sense.

41)

42) The table below shows the federal hourly minimum wage in various years. Complete the

42)

The minimum wage for 1998 in actual dollars The minimum wage for 1998 in 1995 dollars The minimum wage for 1998 in 2000 dollars The minimum wage for 1998 in 1990 dollars

table by converting each minimum wage from actual dollars to 2001 dollars. In which year was the purchasing power of the minimum wage the highest? If necessary, round values to the nearest cent. Year Actual dollars 2001 dollars 1990 $3.50 1991 $4.25 1996 $4.75 1997 $5.15

Give an appropriate response.

43)

43) The table shows the results of a study examining the effectiveness of home schooling as compared to traditional schooling. The same reading test is given to all students regardless of grade.

10th grade Passed Failed Home school 78 222 Traditional 25 75

Test

12th grade Passed Failed 98 2 287 13

For each age grade, determine the percentage passing the test amongst those schooled at home and among those with traditional schooling. If the two age groups are combined, what percentage pass the test amongst those schooled at home and among those with traditional schooling? Explain the apparent inconsistency in these results, and how the design of the study brought about the inconsistency.

44) The tables below show the results of a study examining the incidence of breast cancer

44)

among women who exercise regularly and those who do not. The 425 women in the study were split into two age groups, those under 40 and those 40 or older. UNDER 40 Breast Cancer Yes No Regular exercise No 2 173 Yes 1 99

OVER 40 Breast Cancer Yes No Regular exercise No 2 48 Yes 3 97

For each age group, determine the percentage of women having breast cancer among those exercise regularly and among those who do not exercise regularly. If the two age groups are combined, what percentage have breast cancer among those who exercise regularly and among those who do not exercise regularly? Explain the apparent inconsistency in these results, and how the design of the study brought about the inconsistency.

45) Due to poor sales, a company eliminated a number of jobs. Twenty-five percent of the 300 men in full-time positions lost their jobs, while 20% of the 300 women in full-time positions lost their jobs. 80% of the 150 men in part-time positions lost their jobs, and 75% of the 600 women in part-time positions lost their jobs. Explain the apparent inconsistency in these results.

45)

Use the Consumer Price Index below to answer the question.

46) Between 1990 and 2000, a college raised its annual tuition fees from $4,490 to $6,740. Find

46)

the relative change in the fees over that period and compare it to the overall rate of inflation as measured by the CPI. Were the tuition increases in line with inflation? If necessary, round values to the nearest tenth.

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 47) An agency wishes to determine the number of unemployed people in a town. They 47) conduct a mini-census by delivering a survey to every household in the town, asking for information about household members. The information is entered into a computer.

48) You use your wrist watch to time your friends running 200 meters.

48)

Use the Consumer Price Index below to answer the question.

49) In 1992, Sue rented out her apartment for $720 per month. In 2000 she charged $800 per

49)

month. Convert the 1992 price to 2000 dollars. In real terms, how does the actual price in 2000 compare to the price in 1992? Explain your reasoning. If necessary, round values to the nearest dollar.

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 50) You estimate the speed of other cars by pulling up behind a car, driving at the same 50) speed, and looking at your speedometer. Use the Consumer Price Index below to answer the question.

51) In 1995, the price of gasoline was 120.5 cents per gallon. In 2000 it was 155.0 cents per

gallon. Find the relative change in the price of gasoline over that period and compare it to the overall rate of inflation as measured by the CPI. In real terms, was gasoline more expensive in 1995 or 2000? If necessary, round values to the nearest tenth.

51)

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 52) The average income of 100 people is calculated by using the incomes which they reported 52) on credit card applications. These incomes are entered onto a computer and a statistical package is used to calculate the average income.

53) The average weight of 100 college-age women, found by asking them their weight during

53)

interviews conducted at their college.

Use the Consumer Price Index below to answer the question.

54) The table below shows the federal hourly minimum wage in various years.

54)

Year Minimum wage 1990 $3.50 1991 $4.25 1996 $4.75 1997 $5.15 What was the relative change in the minimum wage from 1990 to 1997? How does this compare to the overall rate of inflation as measured by the CPI? In which of those two years was the purchasing power of the minimum wage higher? If necessary, round values to the nearest tenth.

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 55) According to police reports, attendance at the last three anti-war rallies was 45,000, 55) 60,000, and 22,300 respectively.

Give an appropriate response. 56) The following table shows the deaths due to the same disease in two cities. Compute the death rates in each city for those with health insurance, those without health insurance, and all residents. Explain the apparent inconsistency in these results. City A Health Insurance No health insurance Total

Population Deaths 750,000 1800 25,000 120 775,000 1920

56)

City B Population Deaths 20,000 42 14,000 49 34,000 91

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 57) You use a tape measure to measure people's heights. 57)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write as a percent. 58) 0.00632 A) 0.000632%

58) B) 0.632%

C) 0.0632%

D) 0.316%

True or false? 59) If I earn 100% more than you, then you must earn 50% less than me. A) True B) False

59)

Use scientific notation to solve the problem. 60) If the speed of light is 3.00 × 108 m/sec, how long does it take light to travel 2.29 × 1011 m, the distance from the sun to Mars? A) 7.6 × 102 min B) 7.6 × 103 sec

Write as a percent. 61) 0.953 A) 0.953%

60)

D) 7.6 × 102 sec

C) 76 sec

61) B) 0.0953%

C) 95.3%

Round to the indicated place value. 62) Round to the nearest hundred: 866.561 A) 800 B) 870

D) 953%

62) C) 900

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 63) If you buy 153 items which weigh 0.027 lb each, what is the total weight of your purchase? 63) A) 4.1 lb B) 4.131 lb C) 4.13 lb D) 4 lb

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 64) (2 × 109 ) × (6 × 10-6 )

A) 1.2 × 103

B) 1.2 × 102

C) 1.2 × 104

64)

D) 1.2 × 10-2

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 65) 1.2 × 10-5 , 4.8 × 10-15 65)

A) 2.5 × 1020

B) 2.5 × 109

C) 2.5 × 101/3

D) 2.5 × 1010

Find the absolute and relative errors. 66) Your credit card applies a finance charge of $27.85. The finance charge should have been $25.52. A) absolute error: -$2.33 B) absolute error: $2.33 relative error: -9.1% relative error: 9.1% C) absolute error: $2.33 D) absolute error: $2.33 relative error: 8.4% relative error: 23.3% Write the number in scientific notation. 67) 5,100,000 A) 5.1 × 105 B) 5.1 × 10-5

67) C) 5.1 × 106

D) 5.1 × 10-6

Write the percentage as a fraction or decimal, as indicated. 68) Write as a fraction. 1 12 % 2

A) 1 4

68)

B) 1 8

C) 5

D) 1

C) 0.000784

D) 0.00784

Write the number in ordinary notation. 69) 7.84 × 10-4

A) 0.0000784

66)

69)

B) -784,000

Solve the problem. 70) Suppose the current cost of gasoline is $3.17 per gallon. Find the current price index using the 1995 price as the reference value. In 1995, the cost of gasoline was 120.5 cents per gallon. A) 196.5 B) 263.1 C) 38 D) 2.6 State the number of significant digits and the implied precision of the given number. 71) 762.7 A) 4 significant digits, precise to the nearest tenth

B) 1 significant digit, precise to the nearest unit C) 4 significant digits, precise to the nearest unit D) 1 significant digit, precise to the nearest tenth

70)

71)

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 72) (1.2 × 102 ) + (2.3 × 101 )

A) 1.43 × 103

B) 1.43 × 102

C) 3.5 × 102

Round to the indicated place value. 73) Round to the nearest tenth: 7.255 A) 7.26 B) 7.2

73) C) 7.4

D) 7.3

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 74) (14 × 108 ) ÷ (2 × 106 )

A) -7.0 × 10-2

72)

D) 3.5 × 101

C) 7.0 × 102

B) 7.0 × 10-2

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 75) 957 employees is % of 766 employees. A) 0.1 B) 80.0 C) 124.9

D) -7.0 × 102

74)

75) D) 1.2

Solve the problem. 76) The appliance store where the Scott family shops offers a 9% discount for paying cash. The Scott family received a discount of $50. What was their total bill before the discount? A) $5 B) $500 C) $6 D) $556 Decide whether the statement is believable, given the precision with which it is stated. 77) There are 381,324,152 flowers in the botanical gardens. A) Believable B) Not believable at that precision

76)

77)

Use the Consumer Price Index below to answer the question.

78) In 1990, the federal minimum hourly wage was $4.25. Convert this to 2000 dollars. If necessary, round values to the nearest cent. A) $5.76 B) $3.23

C) $3.33

D) $5.60

78)

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 79) The total rainfall in Laketown last year was 9.4 inches. This year it was 1.1 inches. 79) A) Absolute change: -8.3 in. B) Absolute change: -8.3 in. Percentage change: -8.8% Percentage change: -88.3% C) Absolute change: -8.3 in. D) Absolute change: 8.3 in. Percentage change: -754.5% Percentage change: 754.5%

State the number of significant digits and the implied precision of the given number. 80) 200.010 A) 6 significant digits, precise to the nearest thousandth

80)

B) 3 significant digits, precise to the nearest thousandth C) 5 significant digits, precise to the nearest hundredth D) 2 significant digits, precise to the nearest hundredth Determine whether the source of error represents random or systematic error. 81) Anne counts the number of cars passing an intersection in a 15-minute period. Sometimes she makes errors in counting. A) Random error B) Systematic error Write as a percent. 82) 2.9 A) 0.29%

81)

82) B) 290%

C) 0.0029%

D) 29%

Solve the problem. 83) The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. Test positive Disease 109 No disease 1,032 Total 1,141

Test negative 15 8,844 8,859

Total 124 9,876 10,000

What percentage of those that tested negative actually have the disease? A) 12.1% B) 99.8% C) 11.4%

D) 0.2%

83)

84) The table below shows the result of a polygraph test conducted on 2000 college students. Students

84)

were asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds student lying Has cheated 78 Has not cheated 202 Total 280

Test finds student truthful 13 1,707 1,720

Total 91 1,909 2000

What percentage of those that were telling the truth were found to be lying? A) 10.6% B) 89.4% C) 14.3%

D) 72.1%

Use scientific notation to solve the problem. 85) How many liters of oil are needed to supply the electrical energy needs of an average U.S. home for 4 weeks? Assume that the energy released by burning one liter of oil is 1.2 × 107 joules and that

85)

the electrical energy used daily in an average U.S. home is 5 × 107 joules. Round your answer to the nearest tenth of a liter. A) 1 liters B) 16.7 liters C) 6.7 liters D) 116.7 liters

Answer the question. 86) Suppose you are constructing a scale model solar system using a scale ratio of 1 to 10 billion. In your scale model what will be the diameter of Jupiter (in meters)? The diameter of Jupiter is 143,000 km. A) 0.0143 m B) 0.00143 m C) 0.000143m D) 0.143 m Solve the problem. 87) A store manager paid $124 for an item and set the selling price at $176.08. What was the percent markup? A) 42% B) 29% C) 44% D) 43% Write the number in scientific notation. 88) The population of a small country is 5,533,000 . A) 5.533 × 10-5 B) 5.533 × 105

87)

88) C) 5.533 × 106

D) 5.533 × 104

C) 0.004

D) -40,000

Write the number in ordinary notation. 89) 4 × 10-4

A) 0.00004

86)

89)

B) 0.0004

Use the Consumer Price Index below to answer the question.

90) Suppose you needed $45,000 to maintain a particular standard of living in 1986. How much

90)

would you have needed in 2000 to maintain the same standard of living? If necessary, round values to the nearest thousandth. A) $66,000 B) $71,000 C) $29,000 D) $75,000

Write as a percent. 91) 7 9

A) 7.8%

91) B) 777.8%

C) 77.8%

Round to the indicated place value. 92) Round to the nearest hundredth: 13.1838 A) 13.184 B) 13.19

D) 70.0%

92) C) 13.183

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 93) $978 is % of $1,763. A) 180.3 B) 0.1 C) 0.6

D) 13.18

93) D) 55.5

Use scientific notation to solve the problem. 94) The distance from the earth to the sun is 92,900,000 miles. How long would it take a rocket, traveling at 2.9 x 103 miles per hour, to reach the sun?

A) 3.2 × 102 hr

C) 3.2 × 104 hr

B) 3.2 hr

D) 3.2 × 103 hr

95) If you could generate energy by fusing the hydrogen in ordinary tap water, how much water

would you need to meet the energy needs of the United States for 42 years? Assume that the energy released by fusion of hydrogen in one liter of water is 7 × 1013 joules and that the U.S.

annual energy consumption is 1 × 1020 joules. Give your answer in scientific notation. A) 1.4 × 107 liters B) 6 × 101.5 liters C) 6 × 107 liters D) 6 × 10-7 liters

94)

95)

Round to the indicated place value. 96) Round to the nearest thousandth: 8.33177 A) 8.332 B) 8.3318

96) C) 8.333

D) 8.331

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 97) 400 million, 8 trillion 97) A) 5 × 10-4 B) 5 × 10-5 C) 5 × 10-7 D) 0.5 × 102/3

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 98) Terry and Ricky went on a 40-mile canoe trip with their class. On the first day they traveled 16 miles. What percent of the total distance was that? A) 300% B) 40% C) 3% D) 0.4% Round to the indicated place value. 99) Round to the nearest hundredth: 0.759 A) 0.76 B) 0.77

98)

99) C) 0.8

D) 0.75

Use the Consumer Price Index below to answer the question.

100) A meal in a restaurant cost $44 in 2000. What was its price in 1992 dollars? If necessary, round values to the nearest dollar. A) $36 B) $34

C) $35

100)

D) $54

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 101) The average amount spent on food last year by the residents of your town was $3,200 per person. 101) The population of your town is 50,360. What was the total amount spent on food last year by the residents of your town? A) $160,000,000 B) $161,152,000 C) $161,000,000 D) $161,200,000

Solve the problem. 102) Suppose it cost $16.28 to fill a gas tank in 2000. How much would it have cost to fill the same tank in 1,995? Use the table below: YEAR GASOLINE PRICE (cents per gallon) 1955 29.1 1965 31.2 1975 56.7 1985 119.6 1995 120.5 2000 155.0 2010 284.0 A) $11.51 B) $20.94 C) $12.66 D) $14.06 Write the number in scientific notation. 103) 0.08 A) 8 × 10-2 B) -8 × 102

103) C) 8 × 10-1

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 104) The weight of the child is 8 kilos while the weight of her father is 87.5 kilos. 87.5 kilos is what percent of 8 kilos? A) 1,093.8 B) 0.9 C) 9.1

D) 8 × 10-3

104) D) 10,938.0

Carry out the indicated operation and give your answer with the specified number of significant digits. 105) (7.6 × 105 ) ÷ (1.1 × 10-5 ); 2 significant digits

A) 7 × 1010

102)

B) 6.9 × 100

C) 6.91 × 1010

105)

D) 6.9 × 1010

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 106) 946 people voted for the incumbent candidate out of 1,783 voters. What percent voted for the incumbent? A) 53.1% B) 0.5% C) 188.5% D) 0.1% State the number of significant digits and the implied precision of the given number. 107) 8,400.0 A) 2 significant digits, precise to the nearest 100

106)

107)

B) 3 significant digits, precise to the nearest tenth C) 5 significant digits, precise to the nearest 100 D) 5 significant digits, precise to the nearest tenth Round to the indicated place value. 108) Round to the nearest tenth: 1.8861 A) 1.9 B) 1.89

108) C) 1.8

D) 2.0

Solve the problem. 109) The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. Test positive Disease 117 No disease 1,060 Total 1,177

Test negative 15 8,808 8,823

109)

Total 132 9,868 10,000

What percentage of those that don't have the disease tested negative? A) 88.1% B) 99.8% C) 89.3%

D) 98.7%

Use scientific notation to solve the problem. 110) A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels 1.86 × 105 miles per second.

A) 6.0 × 105 miles C) 6.0 × 1012 miles

110)

B) 6.0 × 1014 miles D) 6.0 × 107 miles

Determine ratio of A to B. Round as indicated. 111) A = $93,000 is the average cost of a home in Town A and B = $217,000 is the average cost of a home in Town B. (Round to the nearest hundredth when necessary.) A) 0.43 B) 4.29 C) 0.04 D) 2.33 True or false? 112) It is possible for one person's weight to be 350% more than another person's weight. A) True B) False

111)

112)

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 113) The population of Placerville grew from 4,560 a decade ago to 6,890 today. 113) A) Absolute change: 2,330 B) Absolute change: 2,330 Percentage change: 33.8% Percentage change: 51.1% C) Absolute change: 33.8% D) Absolute change: -2,330 Percentage change: 2,330 Percentage change: 51.1% Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 114) 1048, 1016 114)

A) 32

B) 103

C) 1032

Write the percentage as a fraction or decimal, as indicated. 115) Write as a fraction. 3.125% A) 1 B) 5 32 16

D) 1048 - 1016

115) C) 1

D) 1

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 116) $664.24 is % of $52.86. A) 8.0 B) 12,566.0 C) 0.8

116) D) 1,256.6

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 117) (7 × 107 ) - (3 × 106)

A) 6.7 × 106

B) 6.7 × 107

C) 4 × 101

Solve the problem. 118) The table below shows the result of a polygraph test conducted on 2000 college students. Students were asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds student lying Has cheated 83 Has not cheated 211 Total 294

Test finds student truthful 12 1,694 1,706

117)

D) 4 × 107

118)

Total 95 1,905 2000

What percentage of those that were found to be lying were actually telling the truth? A) 87.4% B) 88.9% C) 12.6% D) 71.8%

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 119) 1 trillion, 1 hundred 119) A) 106 B) 1012 - 102 C) 1014 D) 1010

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 120) 3.5 cases is % of 21.1 cases. A) 0.2 B) 602.9 C) 6.0

120) D) 16.6

Write the number in ordinary notation. 121) 3.0 × 104

A) 300,000

121)

B) 3,000

C) 120

D) 30,000

Answer the question. 122) Suppose you are constructing a scale model solar system using a scale ratio of 1 to 200 billion. In your scale model what will be the distance from Saturn to the Sun (in meters)? The distance from Saturn to the Sun is 1427 million km. A) 14.27 m B) 0.7135 m C) 0.007135 m D) 7.135 m Write the number in scientific notation. 123) The hard drive of the computer has a capacity of 30 gigabytes. (The prefix giga means 1 billion). A) 3 × 1010 bytes B) 30 × 109 bytes C) 3 × 109 bytes

122)

123) D) 3 × 1013 bytes

Determine ratio of A to B. Round as indicated. 124) A = 22.9% is the divorce rate in City A B = 28.9% is the divorce rate in City B (Round to the nearest hundredth when necessary.) A) 7.92 B) 1.26

124) C) 0.79

D) 0.08

True or false? 125) Given that Sue's weight increased from 120 lb to 132 lb and that Mark's weight increased from 150 lb to 165 lb, we can say that in absolute terms, Mark's weight increased more, but that in relative terms, Sue's weight increased more. A) True B) False Answer the question. 126) Find the scale ratio for a map if 6 inches on the map represents 7 miles on the ground. A) 1 : 443,520 B) 1 : 10,560 C) 1 : 73,920 D) 1 : 6160

125)

126)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 127) A city has a deficit of $45.8 million. How much is this per person if the population of the city is 127) 133,800? A) $342 per person B) $342.3 per person

C) $300 per person

D) $340 per person

Decide whether the statement is believable, given the precision with which it is stated. 128) A mountain's peak is 24,900 feet above sea level. A) Believable B) Not believable at that precision Find the absolute and relative errors. 129) The true distance from your home to your office is 31.3 miles but your odometer reads 32.3 miles. A) absolute error: 1 miles B) absolute error: -1 miles relative error: 3.2% relative error: -3.2% C) absolute error: 1 miles D) absolute error: 1 miles relative error: 3.1% relative error: 0.3% True or false? 130) If 35% of the students in Mr. Harris's class speak Spanish and 6% speak French, then 41% must speak either Spanish or French A) True B) False Write the number in ordinary notation. 131) 2.938 × 10-6

A) 0.0000002938

129)

130)

131)

B) 0.00002938

C) 0.000002938

D) -2,938,000

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 132) (4 × 10-4) ÷ (8 × 10-2)

A) 2.0 × 10-2

128)

B) 5.0 × 105

C) 5.0 × 10-3

D) 2.0 × 106

132)

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 133) The unemployment rate in Midtown a decade ago was 20%. This year it was 30%. 133) A) Absolute change: 10 percentage points B) Absolute change: 50 percentage points Percentage change: 33.3 % Percentage change: 10% C) Absolute change: -10 percentage points D) Absolute change: 10 percentage points Percentage change: 33.3 % Percentage change: 50%

Write the number in scientific notation. 134) 0.006 × 107

A) 6 × 1010

134) C) 6 × 104

B) 6 × 10<5

D) 0.6 × 105

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 135) (8.5 × 1029) ÷ (1.7 × 10-8 )

A) 5 × 1021

B) 8.5 × 1037

C) 8.5 × 1021

Write the percentage as a fraction or decimal, as indicated. 136) Write as a decimal. 300% A) 0.3 B) 3.01

D) 5 × 1037

136) C) 3.0

D) 30

Write as a percent. 137) 1 7

A) 1.42857143%

135)

137) B) 70%

C) 142.857143%

D) 14.2857143%

Restate the fact as indicated. 138) The national debt was about $6.9 trillion at the end of 2003. Express this quantity as the number of dollars per person. Assume a U.S. population of 280 million. A) About $2464.29 per person B) About $246,428.57 per person

C) About $24,642.86 per person

138)

D) About $246.43 per person

State the number of significant digits and the implied precision of the given number. 139) 9.000327 minutes A) 4 significant digits, precise to the nearest 0.0001 minute

139)

B) 4 significant digits, precise to the nearest 0.000001 minute C) 7 significant digits, precise to the nearest 0.000001 minute D) 7 significant digits, precise to the nearest 0.0001 minute Write the number in scientific notation. 140) 5,494 A) 5.494 × 104 B) 5.494 × 10-3

140) C) 5.494 × 103

D) 5.494 × 101

Write the percentage as a fraction or decimal, as indicated. 141) Write as a fraction. 56% A) 7 B) 28 25 5 Write as a percent. 142) 76.711 A) 0.76711%

141) C) 28

D) 14

C) 7,671.1%

D) 7.6711%

C) 17.996

D) 18.01

142) B) 76.711%

Round to the indicated place value. 143) Round to the nearest hundredth: 17.99552 A) 18.00 B) 17.9955

143)

Determine whether the source of error represents random or systematic error. 144) Athlete's are timed in the 100-m dash by a person with a stop watch. There is some error involved in stopping the watch at the correct instant. A) Systematic error B) Random error

144)

Answer the question. 145) Find the scale ratio for a map if 1 centimeter on the map represents 100 kilometers on the ground. A) 1 : 100,000 B) 1 : 10,000 C) 1 : 10,000,000 D) 1 : 1,000,000

145)

Round to the indicated place value. 146) Round to the nearest ten thousandth: 17.83469 A) 17.83 B) 17.8346

146) C) 17.835

Write the percentage as a fraction or decimal, as indicated. 147) Write as a decimal. 38% A) 0.38 B) 0.038

D) 17.8347

147) C) 3.8

D) 0.27

Find the absolute and relative errors. 148) The length of the piece of fabric is 21 inches but you measure it as 19.1 inches. A) absolute error: 1.9 inches B) absolute error: -1.9 inches relative error: 9% relative error: -19% C) absolute error: -1.9 inches D) absolute error: -1.9 inches relative error: -9% relative error: -9.9% Solve for the percentage in the problem. Round to the nearest tenth of a percent. 149) % of 56 clients is 381 clients. A) 1.5 B) 68.0 C) 680.4

148)

149) D) 0.1

Round to the indicated place value. 150) Round to the nearest thousandth: 16.6145 A) 16.61 B) 16.614

150) C) 16.615

D) 16.616

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 151) Last year the Mayor of the town of Little Heath had an approval rating of 82%. This year his 151) approval rating had fallen to 21%. A) Absolute change: 61 percentage points B) Absolute change: -61 percentage points Percentage change: 290.5% Percentage change: -74.4% C) Absolute change: -61 percentage points D) Absolute change: -61 percentage points Percentage change: -7.4% Percentage change: -290.5%

Use scientific notation to solve the problem. 152) Suppose that we could somehow capture all the energy released by the Sun in just one second. For how many years could U.S. energy needs be met by this energy? Assume that the annual energy generation of the Sun is 1 × 1034 joules and that U.S. annual energy consumption is 1 × 1020 joules. Give your answer in scientific notation. A) 1 × 1014 years

B) 3.17 × 101.3 years D) 7.61 × 106 years

C) 3.17 × 106 years Write as a percent. 153) 5 2 3

A) 283.333333%

153) B) 56.6666667%

C) 5.66666667%

D) 566.666667%

Carry out the indicated operation and give your answer with the specified number of significant digits. 154) 441 ÷ 0.0385; 1 significant digit A) 10,000 B) 11,000 C) 11,454.5 D) 11,455 Write the number in ordinary notation. 155) 2 × 105

A) 20,000

154)

155)

B) 20,000,000

C) 2,000,000

Write the percentage as a fraction or decimal, as indicated. 156) Write as a fraction. 1,500%

A) 30

152)

D) 200,000

156)

B) 150

C) 15

D) 15 2

Solve the problem. 157) A hardware store had monthly sales of $72,400 and spent 8% of it on legal fees. How much was spent on legal fees? A) $57,920 B) $90,500 C) $5,792 D) $905,000

157)

Write the number in scientific notation. 158) 3,600 million A) 3.6 × 103 B) 36 × 108

158) C) 3.6 × 1010

D) 3.6 × 109

Write the number in ordinary notation. 159) 3.0484 × 10-7

159)

A) 0.000000030484 C) 0.0000030484

B) 0.00000030484 D) -304,840,000

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 160) At a certain college, the percentage of male students decreased from 66% in 1970 to 52% this year. 160) A) Absolute change: -14 percentage points Percentage change: -21.2% B) Absolute change: 14 percentage points Percentage change: 26.9% C) Absolute change: -14 percentage points Percentage change: -26.9% D) Absolute change: -21.2 percentage points Percentage change: -14%

Use scientific notation to solve the problem.

161) The earth is approximately 92,900,000 miles from the sun. If 1 mile = 1.61 × 103 m, what is the distance to the sun in meters? A) 5.7 × 1010 m B) 5.7 × 10-10 m

C) 1.50 × 1010 m

D) 1.50 × 1011 m

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 162) Terry has saved $552 at the bank. He wants to save $2,940 for a trip to California. What percent of his goal has been reached? A) 5.3% B) 1.9% C) 53% D) 18.8% Round to the indicated place value. 163) Round to the nearest whole number: 6.7 A) 6 B) 7

162)

163) C) 8

Solve the problem. 164) The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election? A) 43.2% B) 45% C) 64.8% D) 34% Carry out the indicated operation and give your answer with the specified number of significant digits. 165) (2.2 × 10-10) ÷ (5.936 × 10-3); 3 significant digits

A) 4 × 10-8

161)

B) 3.7 × 10-8

C) 3.706 × 10-8

D) 3.71 × 10-8

164)

165)

True or false? 166) If the value of my home has quadrupled since I bought it, that means its value has increased by 400%. A) True B) False

166)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 167) Subtract the weight 3.2 lb from 149 lb. 167) A) -145.8 lb B) 150 lb C) 146 lb D) 145.8 lb

Determine ratio of A to B. Round as indicated. 168) A = 250 and B = 360 (Do not round.) A) 1 B) 36 36 25

168) C) 1 25

Round to the indicated place value. 169) Round to the nearest whole number: 710.785 A) 710.8 B) 711

D) 25 36

169) C) 710

Find the absolute and relative errors. 170) Your weight is 108 pounds but the scale indicates that it is 103 pounds. A) absolute error: 5 pounds B) absolute error: -5 pounds relative error: 4.6% relative error: -4.6% C) absolute error: -5 pounds D) absolute error: -5 pounds relative error: -50% relative error: -4.9%

170)

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 171) Yesterday the total number of gallons of gasoline used by people driving cars in the United States 171) was 7 × 1010.

A) Yes

B) No

Solve the problem. 172) The table below shows a housing index that can be used to compare housing prices in different cities. CITY INDEX Juneau, AK 100 Palo Alto, CA 365 Denver, CO 87 Spokane, WA 78 Boston, MA 182 Manhattan, NY 495 Suppose you see a house valued at $720,000 in Palo Alto. Find the price of a comparable house in Denver. A) $154,455 B) $137,293 C) $171,616 D) $3,020,690

172)

Write the percentage as a fraction or decimal, as indicated. 173) Write as a decimal. 0.02% A) 0.0012 B) 0.02

173) C) 0.002

D) 0.0002

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 174) Last year the total amount spent by Americans on food was about 1011 dollars. 174)

A) No

B) Yes

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 175) You drive from your house to the store, a distance of 1.78 miles, then you drive another 42 miles 175) to work. What is the total distance that you drive? A) 40 miles B) 44 miles C) 43.78 miles D) 43.8 miles

Determine whether the source of error represents random or systematic error. 176) You time how long you spend working out each day. Your watch is running slow and loses one minute each hour. A) Random error B) Systematic error Determine ratio of A to B. Round as indicated. 177) A = 62.9 is the average number of points scored in a college basketball game. B = 52.5 is the average number of points scored in a high school basketball game. (Round to the nearest hundredth when necessary.) A) 0.12 B) 1.2 C) 0.83 D) 11.98

176)

177)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 178) One million, one millionth 178) A) 106 - 10-6 B) 10-1 C) 1012 D) 1011 Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 179) The value of Anna's house increased from $190,000 when she bought it 20 years ago to $1.14 179) million today. A) Absolute change: $950,000 B) Absolute change: $950,000 Percentage change: 500% Percentage change: 50% C) Absolute change: $-950,000 D) Absolute change: $950,000 Percentage change: 500% Percentage change: 83.3%

Solve the problem. 180) Suppose it cost $4.96 to fill a gas tank in 1965. How much would it cost to fill the same tank in 1,975? Use the table below. YEAR GASOLINE PRICE (cents per gallon) 1955 29.1 1965 31.2 1975 56.7 1985 119.6 1995 120.5 2000 155.0 2010 284.0 A) $10.02 B) $9.01

C) $12.88

180)

D) $11.27

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 181) (5 × 10-2) ÷ (20 × 104)

181)

Write the number in ordinary notation. 182) 6.517 × 104

182)

A) 2.5 × 10-7

A) 260.68

C) -2.5 × 105

B) -2.5 × 10-7

B) 651,700

C) 65,170

D) 2.5 × 105

D) 6,517

True or false? 183) If somebody tells you that their exam score was 70%, up 80% from the last exam, you would conclude that they must be lying or bad at math, because that is impossible. A) True B) False Write as a percent. 184) 32 40

A) 80%

183)

184) B) 80

C) 800%

D) 8%

True or false? 185) It is possible for one person's weight to be 143% less than another person's weight. A) True B) False

185)

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary. 186) The population density in country A is 120 people per square mile while in country B, it is 521 186) people per square mile. A) Absolute difference: -401 people per square mile Relative difference: -334.2% B) Absolute difference: -401 people per square mile Relative difference: -7.7% C) Absolute difference: 401 people per square mile Relative difference: 334.2% D) Absolute difference: -401 people per square mile Relative difference: -77%

Round to the indicated place value. 187) Round to the nearest ten: 44.2 A) 40

187) B) 39

C) 41

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 188) In the next hour, roughly 109 people will die worldwide. 188)

A) No

B) Yes

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 189) Two years ago I earned $76,000. Last year I earned $41,000. 189) A) Absolute change: $35,000 B) Absolute change: $-35,000 Percentage change: 46.1% Percentage change: -85.4% C) Absolute change: $-35,000 D) Absolute change: $35,000 Percentage change: -46.1% Percentage change: 85.4%

Determine whether the source of error represents random or systematic error. 190) A survey is conducted on smoking amongst teenagers. When questioned by adults, teenagers tend to underreport how much they smoke. A) Random error B) Systematic error Answer the question. 191) Suppose you are constructing a scale model solar system using a scale ratio of 1 to 100 billion. In your scale model what will be the distance from Neptune to the Sun (in meters)? The distance from Neptune to the Sun is 4497 million km. A) 44.97 m B) 0.4497 m C) 4.497 m D) 0.04497 m

190)

191)

Use scientific notation to solve the problem.

192) Assume that the volume of the earth is 5 × 1014 cubic meters and the volume of a bacterium is 2.5 × 10-16 cubic meters. If the earth could be filled with bacteria, how many would it contain? A) 2.0 × 1030 bacteria B) 5.0 × 10-31 bacteria

D) 5.0 × 1031 bacteria

C) 2.0 × 10-30 bacteria 32

192)

Solve the problem. 193) Find the gasoline price index for 1,985 using the 1955 price as the reference value. Use the table below.

193)

YEAR GASOLINE PRICE (cents per gallon) 1955 29.1 1965 31.2 1975 56.7 1985 119.6 1995 120.5 2000 155.0 2010 284.0

A) 24.3

B) 41.1

C) 369.9

D) 411

Answer the question. 194) Find the scale ratio for a map if 1 inch on the map represents 10 miles on the ground. A) 1 : 63,360 B) 1 : 52,800 C) 1 : 10 D) 1 : 633,600

194)

Determine whether the source of error represents random or systematic error. 195) A government census fails to include homeless people. A) Random error B) Systematic error

195)

Answer the question.

196) The distance from the Earth to the Sun is about 1.5 × 108 km, while the distance from the Earth to

196)

the moon is about 3.8 × 105 km. If a scale model of the solar system is constructed so that the distance from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon? A) 39, 474 m B) 39.5 m C) 6.36 m D) 0.25 m

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 197) (15 × 10-2 ) ÷ (5 × 101 )

A) 6.0 × 10-1

B) 3.0 × 10-3

C) 6.0 × 10-3

D) 3.0 × 10-1

197)

Use the Consumer Price Index below to answer the question.

198) Suppose you needed $49,000 to maintain a particular standard of living in 2000. How much

198)

Answer the question. 199) Find the scale ratio for a map if 3 centimeters on the map represents 0.6 kilometer on the ground. A) 1 : 200,000 B) 1 : 2,000 C) 1 : 60,000 D) 1 : 20,000

199)

would you have needed in 1990 to maintain the same standard of living? If necessary, round values to the nearest thousandth. A) $37,000 B) $38,000 C) $36,000 D) $65,000

Solve the problem. 200) The regular selling price of an item is $55. For a special year-end sale the price is at a markdown of 20%. Find the discount sale price. A) $66.00 B) $45.83 C) $44.00 D) $11.00

201) Find the gasoline price index for a year in which the cost of gasoline was $1.44 per gallon. Use the

200)

201)

1965 price as the reference value. In 1965, the cost of gasoline was 31.2 cents per gallon. A) 112.8 B) 21.7 C) 461.5 D) 4.6

Restate the fact as indicated. 202) The population of the United States in 2000 was roughly 280 million. Express this as the number of people per square mile. The land area of the United States is roughly 3,536,000 square miles. A) 790 people per square mile B) 8 people per square mile

C) 79 people per square mile

202)

D) 0.8 people per square mile

Decide whether the statement is believable, given the precision with which it is stated. 203) Last year, the company made $127.2 in profits. A) Believable B) Not believable at that precision

203)

Use scientific notation to solve the problem.

204) A computer can do one calculation in 1.4 × 10-7 seconds. How long would it take the computer to do a trillion (1012) calculations? A) 1.4 × 106 sec B) 1.4 × 1012 sec

C) 1.4 × 10-7 sec

204)

D) 1.4 × 105 sec

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 205) (5 × 105 ) × (2 × 102) A) 1.0 × 1010 B) 1.0 × 107 C) 1.0 × 109 D) 1.0 × 108

205)

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 206) % of 105 cartons is 18.3 cartons. A) 0.1 B) 573.8 C) 17.4

206) D) 0.2

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 207) The book contains 106 letters. 207)

A) Yes

B) No

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 208) $15.99 is % of $279.04. A) 1,745.1 B) 174.5 C) 57.0

208) D) 5.7

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 209) In the last election, in a certain city the percentage of eligible voters who voted in the local election 209) was 68.1%. This year, the percentage fell to 50.8%. A) Absolute change: -17.3 percentage points Percentage change: -34.1% B) Absolute change: 17.3 percentage points Percentage change: -25.4% C) Absolute change: 17.3 percentage points Percentage change: 34.1% D) Absolute change: -17.3 percentage points Percentage change: -25.4% Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 210) You have covered 57.6 miles of a 2,200 mile journey. How much further do you have to go? 210) A) 2,142.4 miles B) 2,140 miles C) 2,100 miles D) 2,142 miles

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 211) Best's Computers claims that of its 5,140 items in inventory, 4,895 items are IBM PC, while the rest are Apple. What percent of total inventory is Apple? Round to the nearest tenth of a percent. A) 4.8% B) 1.0% C) 21.0% D) 95.2%

211)

Determine whether the source of error represents random or systematic error. 212) A study is conducted to assess the effectiveness of vaccinations. If a person has been vaccinated against the measles, and the doctor knows this, the doctor is less likely to diagnose an illness as measles. A) Random error B) Systematic error Answer the question. 213) Find the scale ratio for a map if 4 centimeters on the map represents 10 kilometers on the ground. A) 1 : 250,000 B) 1 : 25,000 C) 1 : 2500 D) 1 : 1,000,000 Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 214) Last week, Brian earned $285 while Lucy earned $563. $285 is what percentage of $563? A) 27.8% B) 49.4% C) 50.6%

D) 50.4%

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 216) Tech Support spent $77,980 this year on delivery costs alone. If total sales were $268,000, what percent of total sales was spent on delivery costs? Round to the nearest tenth of a percent. A) 2.9% B) 29.1% C) 3.4% D) 34.0% Solve the problem. 217) In a local election, 25,100 people voted. This was an increase of 6% over the last election. How many people voted in the last election? A) 26,606 people B) 23,679 people C) 23,594 people D) 26,702 people

213)

214)

Solve the problem. 215) Computer sales for a certain company have reached $40 million per year and are growing at 12% annually. At this growth rate, what will the amount of sales be next year? Round to the nearest tenth of a million. A) $44.8 million B) $48.3 million C) $36.2 million D) $4.8 million

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 218) % of 6 gross is 0.02 gross. A) 3.3 B) 33.3 C) 300.0

212)

215)

216)

217)

218) D) 0.3

Solve the problem. 219) The table below shows the result of a polygraph test conducted on 2000 college students. Students were asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds student lying Has cheated 84 Has not cheated 197 Total 281

Test finds student truthful 11 1,708 1,719

219)

Total 95 1,905 2000

What percentage of those that were lying were found to be truthful? A) 0.6% B) 11.6% C) 10.3%

D) 29.9%

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 220) (3.8 × 1040) ÷ (1.9 × 1010)

220)

Write the number in ordinary notation. 221) 5.638 × 10-5

221)

A) 3.8 × 1030

A) 0.000005638

B) 2 × 104

C) 2 × 1030

C) 0.00005638

B) -563,800

D) 2 × 1050

D) 0.0005638

Solve the problem. 222) The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. Test positive Disease 108 No disease 1,267 Total 1,375

Test negative 17 8,608 8,625

222)

Total 125 9,875 10,000

What percentage of those that tested positive actually have the disease? A) 1.3% B) 86.4% C) 1.1%

D) 7.9%

Determine ratio of A to B. Round as indicated. 223) A = 36 square meters is the area of a circle with diameter 12 meters. B = 144 square meters is the area of a square with sides of length <12 meters. (Do not round.) A) 4 B) C) 6 D) 4 6

223)

Use the Consumer Price Index below to answer the question.

224) A book cost $33 in 1987. What was its price in 1998 dollars? If necessary, round values to the nearest dollar. A) $23

B) $52

C) $45

224)

D) $47

Solve the problem. 225) Brand X copier advertises that its copiers run 23% longer between service calls than its competitor. If Brand X copiers run 41,600 copies between services, how many copies would the competitor run? A) 33,821 copies B) 51,168 copies C) 23,503 copies D) 32,032 copies

225)

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 226) My age in seconds is about 5 × 109 . 226)

A) Yes

B) No

Write the percentage as a fraction or decimal, as indicated. 227) Write as a decimal. 935% A) 0.935 B) 9.35

227) C) 9.36

D) 93.5

Decide whether the statement is believable, given the precision with which it is stated. 228) Using a meter stick, I measured the length of the kitchen to within 0.0843 centimeters. A) Believable B) Not believable at that precision Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 229) Maria's company has 966 employees, Ruth's company has 778 employees. 966 is what percent of 778 ? A) 0.1 B) 80.5 C) 1.2 D) 124.2

228)

229)

Write the number in scientific notation. 230) 270,000 A) 2.7 × 105 B) 2.7 × 10-5

230) C) 2.7 × 10-4

D) 2.7 × 104

Solve the problem. 231) In a local election, 31,900 people voted. This was a decrease of 7% over the last election. How many people voted in the last election? A) 34,133 people B) 29,813 people C) 29,667 people D) 34,301 people

231)

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary. 232) Last year the total revenue for Clearline phone company was $19.6 million while the revenue for 232) its competitor, the Speakmore was $10.6 million. A) Absolute difference: $9 million B) Absolute difference: $9 million Relative difference: 45.9% Relative difference: 84.9% C) Absolute difference: $-9 million D) Absolute difference: $9 million Relative difference: -45.9% Relative difference: 8.5%

Write the number in scientific notation. 233) A beam of light can travel from my house to yours in 900 nanoseconds. (the prefix nano means one billionth). A) 9 × 10-9 B) -9 × 107 C) 9 × 10-6 D) 9 × 10-7 Write as a percent. 234) 9 A) 0.9%

233)

234) B) 450%

C) 0.09%

D) 900%

True or false? 235) If you score 60% on the midterm math exam and 80% on the final exam, your overall score will be greater than 70%. Assume that the final counts for 60% of the grade and that the midterm counts for 40% of the grade. A) True B) False

235)

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary. 236) In a certain country, the life expectancy for men is 70.1 years while the life expectancy for women 236) is 75.1 years. A) Absolute difference: -5 years B) Absolute difference: -5 years Relative difference: -6.7% Relative difference: -0.7% C) Absolute difference: -5 years D) Absolute difference: 5 years Relative difference: -7.1% Relative difference: 7.1%

Carry out the indicated operation and give your answer with the specified number of significant digits. 237) 3,762 × 20.42; 2 significant digits A) 77,000 B) 80,000 C) 76,820.04 D) 76,800

237)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 238) 5.6 × 108 , 1.4 × 10-4 238)

A) 4 × 1012

B) 4 × 104

C) 4 × 102

D) 4.2 × 1012

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 239) In his lifetime my grandfather spent 5 × 104 hours watching television. 239)

A) No

B) Yes

Write the percentage as a fraction or decimal, as indicated. 240) Write as a fraction. 0.05% A) 1 B) 1 2000 4000

240) C) 1

200

D) 1

1000

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 241) Find your speed by dividing the distance you traveled, 262 kilometers, by the time, 2.2 hours. 241) A) 119 kilometers per hour B) 119.1 kilometers per hour

C) 120 kilometers per hour

D) 100 kilometers per hour

Determine ratio of A to B. Round as indicated. 242) A = 4 and B = 24 (Do not round.) A) 2 B) 6 3

242) C) 4

D) 1 6

243) A = 3.1 million is the population of City A

243)

B = 1.2 million is the population of City B (Round to the nearest hundredth when necessary.) A) 2.58 B) 25.83

C) 0.26

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 244) % of 3,134 sales is 23 sales. A) 7.3 B) 17.3 C) 13,626.1

D) 0.39

244) D) 0.7

Solve the problem. 245) Suppose the current cost of gasoline is $3.16 per gallon. Find the current price index using the 1975 price as the reference value. In 1975, the cost of gasoline was 56.7 cents per gallon. A) 5.6 B) 259.3 C) 17.9 D) 557.3

245)

Write as a percent. 246) 0.08 A) 0.8%

246) B) 0.008%

C) 80%

D) 8%

Use scientific notation to solve the problem. 247) The national debt of a small country is $7,020,000,000 and the population is 2,443,000. What is the amount of debt per person? A) $2.87 B) $28.70 C) $2.87 × 106 D) $2.87 × 103

247)

Use the Consumer Price Index below to answer the question.

248) What was the purchasing power of $1 in 1987 in terms of 1990 dollars? If necessary, round values to the nearest cent. A) $1.15

B) $1.10

C) $1.26

248)

D) $0.87

Find the absolute and relative errors. 249) The length of the room is 13 feet but you measure it to be 13 feet and 7 inches. A) absolute error: 7 inches B) absolute error: -7 inches relative error: 5.4% relative error: -4.5% C) absolute error: 7 inches D) absolute error: 7 inches relative error: 4.3% relative error: 4.5%

249)

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 250) In her lifetime my grandmother saw about 6 × 107 hours of commercials on television. 250)

A) No

B) Yes

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 251) 1 billion, 1 thousand 251) A) 103 B) 106 C) 1012 D) 109 - 103

Write the number in scientific notation. 252) 0.000001 A) 9.97 × 10-7 B) -9.97 × 107

252) C) 9.97 × 10-6

D) 9.97 × 10-8

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 253) 3 × 10-8, 3 × 10-32 253)

A) 10-24

B) 1040

C) 101/4

D) 1024

True or false? 254) In Fremont in 1990, the mayor's approval rating was 80%. In 1998, his approval rating was only 64%. True or false? in absolute terms his approval rating decreased by 16 percentage points whereas in relative terms, it decreased by 20%. A) True B) False Restate the fact as indicated. 255) Worldwide there are approximately 132 million births per year. Express this quantity in births per second. A) 4.2 births per second B) 101 births per second

C) 251 births per second

254)

255)

D) 63,300 births per second

Solve the problem. 256) The table below shows a housing index that can be used to compare housing prices in different cities. CITY INDEX Juneau, AK 100 Palo Alto, CA 365 Denver, CO 87 Spokane, WA 78 Boston, MA 182 Manhattan, NY 495 Suppose you see a house valued at $180,000 in Spokane. Find the price of a comparable house in Juneau. A) $140,400 B) $230,769 C) $253,846 D) $207,692

256)

Use the Consumer Price Index below to answer the question.

257) Find the inflation rate from 1990 to 1991. If necessary, round values to the nearest tenth. A) 1.0% B) 4.2% C) 4.0% D) 4.6% Write the number in scientific notation. 258) 211.1 A) 2.111 × 10-1 B) 2.111 × 102

258) C) 2.111 × 10-2

Round to the indicated place value. 259) Round to the nearest thousandth: 1.6843 A) 1.685 B) 1.684

D) 2.111 × 101

259) C) 1.68

D) 1.67

Solve the problem. 260) Midtown Antiques collects 4% sales tax on all sales. If total sales including tax are $1,317.24, find the portion that is the tax amount. A) $40.66 B) $52.69 C) $1,266.58 D) $50.66 Carry out the indicated operation and give your answer with the specified number of significant digits. 261) 23.5 × 0.139; 3 significant digits A) 3.3 B) 3.27 C) 3.267 D) 3 Write the number in ordinary notation. 262) 8.0815 × 106

A) 808,150

257)

260)

261)

262)

B) 80,815,000

C) 484.89

D) 8,081,500

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 263) It would take me about 1 × 106 seconds to walk across the United States (from New York to 263) California). A) No

B) Yes

Write the number in ordinary notation. 264) 5.08 × 107

A) 5,080,000

264)

B) 508,000,000

C) 355.6

D) 50,800,000

Solve the problem. 265) Find the gasoline price index for 1,985 using the 2000 price as the reference value. Use the table below.

265)

YEAR GASOLINE PRICE (cents per gallon) 1955 29.1 1965 31.2 1975 56.7 1985 119.6 1995 120.5 2000 155.0 2010 284.0

A) 77.2

B) 84.9

C) 7.7

D) 129.6

Determine whether the source of error represents random or systematic error. 266) When scientists estimate the height of a mountain there is a certain amount of error involved in measuring distances and angles. A) Random error B) Systematic error

266)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 267) At the beginning of last year, the population of your city was 224,000. By the end of the year it had 267) increased by 3,675 people. What was the population at the end of the year? A) 228,000 B) 227,700 C) 227,675 D) 230,000

Find the absolute and relative errors. 268) It took you one hour and 6 minutes to drive home, you estimated the time to be one hour and 20 minutes. A) absolute error: 14 minutes B) absolute error: -14 minutes relative error: 21.2% relative error: -21.2% C) absolute error: 14 minutes D) absolute error: 14 minutes relative error: 17.5% relative error: 2.1%

268)

Decide whether the statement is believable, given the precision with which it is stated. 269) A business projects next year's profits to be $9,500,000. A) Believable B) Not believable at that precision

269)

True or false? 270) If my salary increases by 5% each year, in 20 years, I will earn exactly twice as much as I do now. A) True B) False

270)

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 271) 91.1 yards is % of 9 yards. A) 10,122.0 B) 1.0 C) 1,012.2

271) D) 9.9

Solve the problem. 272) The table below shows the result of a polygraph test conducted on 2000 college students. Students were asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds student lying Has cheated 83 Has not cheated 210 Total 293

Test finds student truthful 14 1,693 1,707

272)

Total 97 1,903 2000

What percentage of those that were found to be truthful were actually lying ? A) 0.8% B) 71.7% C) 11%

D) 14.4%

State the number of significant digits and the implied precision of the given number. 273) 9.100 × 106

273)

A) 4 significant digits, precise to the nearest 1,000 B) 7 significant digits, precise to the nearest unit C) 2 significant digits, precise to the nearest 1,000 D) 4 significant digits, precise to the nearest thousandth Round to the indicated place value. 274) Round to the nearest tenth: 1.58 A) 1.5 B) 2

274) C) 1.6

D) 1.7

State the number of significant digits and the implied precision of the given number. 275) 0.0075 meter A) 2 significant digits, precise to the nearest 0.001 meter

275)

B) 2 significant digits, precise to the nearest 0.0001 meter C) 4 significant digits, precise to the nearest 0.0001 meter D) 4 significant digits, precise to the nearest 0.001 meter Write the percentage as a fraction or decimal, as indicated. 276) Write as a decimal. 61.8% A) 0.0618 B) 0.618

276) C) 6.18

D) 0.508

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 277) Students at East Central High School earned $596 selling car washes. They want to make $3,080 for a club trip. What percent of their goal has been reached? A) 1.9% B) 19.4% C) 5.2% D) 52%

277)

Carry out the indicated operation and give your answer with the specified number of significant digits. 278) 792 ÷ 0.00211; 3 significant digits A) 375,355.45 B) 375,355 C) 375,400 D) 375,000

278)

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible, it does not make sense. 279) Last year my heart beat 4 × 107 times. 279)

A) Yes

B) No

Write the number in scientific notation. 280) A company produces 278,000 small appliances in one year. A) 2.78 × 106 B) 2.78 × 105 C) 27.8 × 104

280) D) 2.78 × 10-5

Solve the problem. 281) The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. Test positive Disease 112 No disease 1,024 Total 1,136

Test negative 16 8,848 8,864

281)

Total 128 9,872 10,000

What percentage of those that have the disease tested positive? A) 11.4% B) 87.5% C) 89.6%

D) 9.9%

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary. 282) In Jose's hometown, there are 210,000 people whose first language is English and 130,000 whose 282) first language is Spanish . A) Absolute difference: 80,000 B) Absolute difference: -80,000 Relative difference: 6.2% Relative difference: -38.1% C) Absolute difference: 80,000 D) Absolute difference: 80,000 Relative difference: 38.1% Relative difference: 61.5%

Restate the fact as indicated. 283) The speed of light is approximately 5,866,000,000,000 miles per year. Express this speed in miles per second. A) 3100.2 miles per second B) 186,009.6 miles per second

C) 4,460,000 miles per second

283)

D) 11,160,578.4 miles per second

Determine ratio of A to B. Round as indicated. 284) A = 24 and B = 4 (Do not round.) A) 6 B) 1 6

284) C) 2 3

D) 3 2

Restate the fact as indicated.

285) In a given year, the U.S.annual energy consumption is roughly 1 × 1020 Joules. Express this as

285)

energy consumption per person per second. Assume that the U.S. population during this year is roughly 280 million. . A) 11,324.9 Joules per person per second B) 3.6 × 1011 Joules per person per second

C) 190.3 Joules per person per second

D) 680,000 Joules per person per second

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 286) 1012, 1036 286)

A) 1 3

B) 101/3

C) 10-24

State the number of significant digits and the implied precision of the given number. 287) 19,000 A) 5 significant digits, precise to the nearest unit

D) 1012 - 1036

287)

B) 2 significant digits, precise to the nearest 10,000 C) 2 significant digits, precise to the nearest 1,000 D) 5 significant digits, precise to the nearest 1,000 Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary. 288) In 1960, in the town of Thornton the percentage of 50 year old women that had never been 288) married was 11.7%. Last year, the percentage of 50 year old women that had never been married was 26.7%. A) Absolute change: -15 percentage points Percentage change: -56.2% B) Absolute change: 15 percentage points Percentage change: 128.2% C) Absolute change: 128.2 percentage points Percentage change: 15% D) Absolute change: 15 percentage points Percentage change: 56.2% Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary. 289) In the college there are 1,290 male students and 1,030 female students. 289) A) Absolute difference: 260 B) Absolute difference: 260 Relative difference: 20.2% Relative difference: 2.5% C) Absolute difference: -260 D) Absolute difference: 260 Relative difference: -20.2% Relative difference: 25.2%

State the number of significant digits and the implied precision of the given number. 290) 70,008 people A) 2 significant digits, precise to the nearest person

B) 1 significant digit, precise to the nearest 10,000 people C) 2 significant digits, precise to the nearest 10,000 people D) 5 significant digits, precise to the nearest person

290)

Answer Key Testname: CHAPTER 3

1) B 2) A 3) C 4) B 5) A 6) C 7) A 8) B 9) C 10) C 11) B 12) D 13) D 14) D 15) A 16) A 17) B 18) A 19) D 20) B 21) C 22) D 23) D 24) A 25) D 26) C 27) A 28) B 29) A 30) B 31) C 32) C 33) D 34) B 35) D 36) D 37) B 38) D 39) D 40) B 41) The minimum wage for 1998 in 2000 dollars. For the minimum wage to have the same purchasing power in 2000 as in 1998, it must increase in line with inflation. So the 1998 minimum wage in 2000 dollars will be greater than the 1998 minimum wage in 1998 dollars, 1995 dollars, or 1990 dollars. 49

Answer Key Testname: CHAPTER 3

42)

Year Actual dollars 2001 dollars 1990 $3.50 $4.74 1991 $4.25 $5.53 1996 $4.75 $5.36 1997 $5.15 $5.68 The purchasing power of the minimum wage the highest in 1997.

43) Home schooled 10th grade 26.0% 12th grade 98.0% AGE GROUPS COMBINED 44.0%%

Traditional 25.0% 95.7% 78.0%

Within each age group, the percentage passing the test is higher for students who are home schooled, yet when the age groups are combined, the percentage passing the test is higher amongst those with traditional schooling. The group of home schoolers is comprised of mostly 10th graders, while the group of traditional students is mostly 12th graders, who would be expected to do better on the test than 10th graders.

44) No regular exercise UNDER 40 1.1% OVER 40 4% AGE GROUPS COMBINED 1.8%

Regular exercise 1% 3% 4%

Within each age group, the percentage with breast cancer is lower amongst those who exercise regularly, yet when the age groups are combined, the percentage with breast cancer is higher amongst those who exercise regularly. Possible answer: The 225 women who do not exercise regularly were unequally divided among the two age groups, 175 in the younger group and 50 in the older group, while the 200 women who do exercise regularly were equally divided into the two age groups. The greater number of younger women, among whom we would expect a lower incidence of breast cancer, virtually guaranteed that the combined rate for the group who do not exercise regularly would be lower. 45) Within each category, the percentage of men fired was greater than the percentage of women fired; yet the overall firing rate was higher for women (56.7%) than for men (43.3%). These results arises because the percentage of part-time workers fired was much higher than the percentage of full-time workers fired and among the female workers there were far more part-time than full-time workers. 46) Relative change in cost = 50.1% Overall rate of inflation between 1990 and 2000 was 31.8% The rate of increase in tuition fees was greater than the rate of inflation. 47) Answers may vary. Possible answer Sources of random error: errors made by people filling out the surveys errors made entering the data into the computer Systematic error: some people won't be counted because they won't respond to the survey - undocumented immigrants especially are unlikely to respond. Certain groups will be excluded from the survey - homeless people and prisoners for example

Answer Key Testname: CHAPTER 3

48) Answers may vary. Possible answer

Sources of random error: Inaccurate reading of your wrist watch Systematic error: If you wrist watch is running too fast or too slow this could introduce systematic error, tending to make all the measurements too high or too low. 49) The 1992 price in 2000 dollars is $884. So a price of $884 per month in 2000 would be equivalent to a price of $720 per month in 1992. But the actual 2000 price, $800, is less than this. So, in real terms, the 2000 price is lower than the 1992 price.

50) Answers may vary. Possible answer

Sources of random error: You may not be driving at exactly the same speed as the other car, your speed may be slightly lower or higher Systematic error: If your speedometer is not accurate, it may be systematically over or understating speeds of other cars. 51) Relative change in cost between 1995 and 2000 = 28.6% Overall rate of inflation between 1995 and 2000 = 13.0% In real terms, gasoline was more expensive in 2000. 52) Answers may vary. Possible answer Possible source of random error: Errors in entering the data Possible source of systematic error: On credit card applications people tend to report their income as higher than it actually is, in order to be accepted for a credit card. 53) Answers may vary. Possible answer Sources of random error: women may not know their weight exactly there may have been weight gain or loss since the last time they weighed themselves the scales they used to weigh themselves may not be accurate, this is random error as some scales used may read too high while others may read too low Systematic error: women perceiving themselves to be overweight may report their weight as lower than it actually is 54) The minimum wage increased by 47.1% from 1990 to 1997. During the same period, inflation was 22.8%. In relative terms, the minimum wage increased by more than inflation so the purchasing power of the minimum wage was higher in 1997 than in 1990. 55) Answers may vary. Possible answer Sources of random error: Difficulties in exactly measuring the size of a large crowd which is constantly moving and fluctuating in size, will result in random error. Systematic error: Police may tend to consistently underreport attendance at rallies for political reasons.

Answer Key Testname: CHAPTER 3

56) Death Rates Health Insurance. No health insurance Total

City A

City B

0.24% 0.48% 0.25%

0.21% 0.35% 0.27%

The rate for both those with health insurance and those without health insurance is higher in City A than in City B; yet the overall rate is higher in City B than in City A. These results arises because the percentage of deaths among people without health insurance is higher and there is a much higher percentage of such people in City B. 57) Answers may vary. Possible answer Sources of random error: Inaccurate reading of the tape measure will be a source of random error, as you could equally well overestimate or underestimate a height Systematic error: If the tape measure is not completely accurate this will be a source of systematic error, tending to make all readings too low or too high.

58) B 59) A 60) D 61) C 62) C 63) A 64) C 65) B 66) B 67) C 68) B 69) C 70) B 71) A 72) B 73) D 74) C 75) C 76) D 77) B 78) D 79) B 80) A 81) A 82) B 83) D 84) A 85) D 86) A 52

Answer Key Testname: CHAPTER 3

87) A 88) C 89) B 90) B 91) C 92) D 93) D 94) C 95) C 96) A 97) B 98) B 99) A 100) A 101) A 102) C 103) A 104) A 105) D 106) A 107) D 108) A 109) C 110) C 111) A 112) A 113) B 114) C 115) A 116) D 117) B 118) D 119) D 120) D 121) D 122) D 123) A 124) C 125) B 126) C 127) A 128) A 53

Answer Key Testname: CHAPTER 3

129) A 130) B 131) C 132) C 133) D 134) C 135) D 136) C 137) D 138) C 139) C 140) C 141) D 142) C 143) A 144) B 145) C 146) D 147) A 148) C 149) C 150) C 151) B 152) C 153) D 154) A 155) D 156) C 157) C 158) D 159) B 160) A 161) D 162) D 163) B 164) B 165) D 166) B 167) C 168) D 169) B 170) B 54

Answer Key Testname: CHAPTER 3

171) B 172) C 173) D 174) A 175) B 176) B 177) B 178) C 179) A 180) B 181) A 182) C 183) B 184) A 185) B 186) D 187) A 188) A 189) C 190) B 191) A 192) A 193) D 194) D 195) B 196) D 197) B 198) A 199) D 200) C 201) C 202) C 203) A 204) D 205) D 206) C 207) A 208) D 209) D 210) C 211) A 212) B 55

Answer Key Testname: CHAPTER 3

213) A 214) C 215) A 216) B 217) B 218) D 219) B 220) C 221) C 222) D 223) B 224) D 225) A 226) B 227) B 228) B 229) D 230) A 231) D 232) B 233) D 234) D 235) A 236) A 237) A 238) A 239) B 240) A 241) C 242) D 243) A 244) D 245) D 246) D 247) D 248) A 249) D 250) A 251) B 252) A 253) D 254) A 56

Answer Key Testname: CHAPTER 3

255) A 256) B 257) B 258) B 259) B 260) D 261) B 262) D 263) A 264) D 265) A 266) A 267) A 268) A 269) A 270) B 271) C 272) A 273) A 274) C 275) B 276) B 277) B 278) D 279) A 280) B 281) B 282) D 283) B 284) A 285) A 286) C 287) C 288) B 289) D 290) D

Exam Name___________________________________

Chapter 4

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Which of the following will contribute to an increased federal debt? A) Raising taxes B) Decreasing Social Security benefits

C) Increasing receipts

D) Increasing international aid

2) Which of the following will not contribute to maintaining a balanced federal budget? A) Reducing discretionary spending B) Balancing yearly receipts and outlays C) Large tax increases D) Increasing Social Security benefits

3) Which of the following will allow the federal debt to be retired? A) Zero gross debt B) Zero net surplus C) Zero gross deficit D) Zero net deficit

4) Which of the following will contribute to an increased federal debt? A) Increasing international aid B) Increasing receipts C) Decreasing Social Security benefits D) Raising taxes

5) What type of spending is easiest for the government to control? A) Entitlement spending B) Interest payments on the debt C) Medicare D) Discretionary spending

6) Which of the following is not a way the government borrows money from the public? A) Selling Treasury notes B) Selling bonds to investors C) Raising taxes D) All of the above

7) Which of the following is not a way the government borrows money from the public? A) Raising taxes B) Selling Treasury notes C) Selling bonds to investors D) All of the above

8) Which of the following will allow the federal debt to be retired? A) Zero net deficit B) Zero net surplus C) Zero gross deficit D) Zero gross debt

9) Which of the following will not contribute to maintaining a balanced federal budget? A) Reducing discretionary spending B) Large tax increases C) Increasing Social Security benefits D) Balancing yearly receipts and outlays

Solve the problem. 10) Suppose that you need a loan of $80,000. Find the total cost of all the monthly payments for each of the loan options listed below. Assume that the loans are fixed rate. Round the total cost of each loan to the nearest dollar. Option 1: a 30-year loan at an APR of 7% Option 2: a 15-year loan at an APR of 6.5% A) Option 1: $196,610 B) Option 1: $245,608 Option 2: $131,442 Option 2: $186,056 C) Option 1: $191,606 D) Option 1: $184,614 Option 2: $125,440 Option 2: $119,442 Provide an appropriate response. 11) What type of spending is easiest for the government to control? A) Interest payments on the debt B) Entitlement spending

C) Medicare

10)

11)

D) Discretionary spending

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether the statement makes sense. Explain your reasoning. 12) I have a fixed-rate 30-year mortgage of $120,000 at 4.5%. I inherited some money recently. If I pay off my mortgage in 20 years instead of 30, the total amount of interest I will end up paying will be less.

13) Sheila is in the 22% tax bracket, so a $1000 charitable contribution will reduce her total tax

12)

13)

bill by 0.22 × $1000 = $220.

Solve the problem. 14) Assume you have a balance of $1400 on a credit card with an APR of 18%, or 1.5% per month. You start making monthly payments of $500, but at the same time you charge an additional $180 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. The following table shows how you can calculate your monthly balance.

Month Payment Expenses 0 1 $500 $180 2 $500 $180 3 $500 $180

Interest 1.5% × $1400 = $21.00

14)

New Balance $1400 $1400 - $500 + $180 + $21.00 = $1101.00

Complete and extend the table to show your balance at the end of each month until the debt is paid off.

Decide whether the statement makes sense. Explain your reasoning. 15) Paul has about $2200 available for all his personal expenses combined. He figures that he can easily afford to pay $1100 in rent.

15)

16) When I bought government bonds, I was effectively lending money to the government.

16)

17) Raul is planning to invest his money for one year only. He chose an account paying

17)

18) I have a 30-year mortgage and have been paying it off for 6 years now so I should have

18)

19) Niyas is starting a college fund for his 4-year old daughter. He will invest money in a

19)

20) Sandi has a credit card balance of $7000. The credit card company charges interest of

20)

21) Sue opened a savings account and deposited $10,000. On the same day Pat opened an

21)

22) I am young and I'm going to invest my money for at least 6 years. I am going to put all

22)

23) In 2005, the federal deficit was about 9 trillion dollars.

23)

24) If I pay off my mortgage in 8 years instead of 16, I will have to pay about twice as much

24)

25) My mortgage payment is $1400 per month so I will have a tax deduction of

25)

26) Gabe said "For years there has been no money in the Social Security trust fund, just a

26)

simple interest at 5% per year which was clearly a better deal than an account paying a 4.6% APR with interest compounded annually.

paid off about one fifth of the principal by now.

savings account and the money will remain in the account for at least 15 years. The bank told him that an account offering an APR of 5% compounded annually was a better deal than an account offering simple interest at 6% per year.

APR = 18%, compounded daily. She's broke. She figures if she skips making any payments for three months, she'll end up owing an extra $315 at the end of the three months. That's because 18% APR is equivalent to 1.5% monthly and 1.5% of $7000 is $105, and 3 times $105 is $315.

account at a different bank and also deposited $10,000. Both accounts had the same APR and both were paying compound interest but after two years Sue had more in her account than Pat did. Neither person made any additional deposits or withdrawals from their account during those two years.

my money into stocks. The return is higher than for other investments and over such a time period, there is no risk of losing any of the principal. Historically there has never been a 6-year period in which the Dow ended lower than it started.

per month since I will be paying the mortgage off in half the time.

12 × $1400 = $16,800.

bunch of IOUs". Kim said "That's impossible, if that were true, how come the government has been able to pay out Social Security benefits all these years?" Who is making more sense?

For the loan described, calculate the monthly payment and the portions of the payments that go to principal and to interest during the first 3 months. Use a table. 27) Calculate the monthly payment and the portions of the payments that go to the principal 27) and to interest during the first 3 months for a home mortgage of $144,397 with a fixed APR of 8.0% for 30 years.

Decide whether the statement makes sense. Explain your reasoning. 28) I was offered a 30-year mortgage at a fixed rate of 6% or an adjustable rate mortgage that starts at 5% for the first year. The ARM has no rate cap, but I will take that one anyway because it doesn't look like interest rates will be going up any time soon.

28)

29) My annual income after tax is only $25,000. I need to cut back on my nonessential

29)

30) By 2040 projected Social Security payments will be about $900 billion more than

30)

31) The government has been borrowing from the Social Security trust fund for many years.

31)

spending. Something has to go - either the mango smoothies, the movies, or the vacation. I figure it's the vacation that is making the biggest dent in my budget. I take a vacation once a year which costs about $1100. I go to the movies once a week and spend a total of $15 and I have a mango smoothie every day at my favorite cafe. It costs $4.50 plus tax.

collections from Social Security taxes. The government will then need to redeem $900 billion in IOUs from the Social Security trust fund. However, it should be fairly easy for the government to find the $900 billion by cutting discretionary spending.

This will cause a problem when it has to pay out more in Social Security benefits than it collects in Social Security taxes. Sally, who graduated college in 2005, says that it won't happen in her lifetime but that it might happen in her children's lifetime.

Solve the problem. 32) The table below shows the expenses and payments for 4 months on a credit card account with an initial balance of $500. Assume that the interest rate is 1.7% per month (20.4% APR) and that interest for a given month is based on the balance for the previous month. Complete the table. Month 0 1 2 3 4

Payment $200 $100 $300 $250

Expenses Interest $120 1.7% × $500 = $8.50 $310 $60 $180

Balance $500 $428.50

Decide whether the statement makes sense. Explain your reasoning. 33) Bill is in the 12% tax bracket so the tax he owes will be 12% of his taxable income.

34) Juan won't have to pay any taxes this year. The profit from his business was less than the amount of the standard deduction.

32)

33) 34)

35) Paul figures that at today's prices he can live on $15,000 per year. Currently, banks are

35)

36) Before the government borrows money from its own trust funds such as the Social

36)

37) When I bought government bonds, I was effectively lending money to the government.

37)

38) In 2005, the federal deficit was about 9 trillion dollars.

38)

offering an APR of 3%. So he says "if I build a retirement fund that gives me $500,000 by the time I retire, then if the APR remained at 3% for ever, and if I lived for ever, I could live on the interest alone for ever. That's because 3% of $500,000 is $15,000."

Security trust fund to finance a deficit, it first tries to cover the deficit by borrowing from the public .

For the loan described, calculate the monthly payment and the portions of the payments that go to principal and to interest during the first 3 months. Use a table. 39) Calculate the monthly payment and the portions of the payments that go to the principal 39) and to interest during the first 3 months for a student loan of $46,029 with a fixed APR of 7.0% for 12 years.

Decide whether the statement makes sense. Explain your reasoning. 40) The government has been borrowing from the Social Security trust fund for many years. This will cause a problem when it has to pay out more in Social Security benefits than it collects in Social Security taxes. Sally, who graduated college in 2005, says that it won't happen in her lifetime but that it might happen in her children's lifetime.

40)

41) The two accounts were offering the same APR, and both accounts had the same annual

41)

42) I am young and I am looking for high-return investments even if that means higher risk.

42)

43) Jose's car gets about 20 miles to the gallon. He is thinking of buying a new fuel-efficient

43)

44) By 2040 projected Social Security payments will be about $900 billion more than

44)

percentage yield, but one account compounded interest daily while the other compounded interest weekly.

That's why I am putting most of my money into stocks.

car which gets 40 miles to the gallon and which costs $25,000. He reasons in this way: " I drive about 300 miles per week. Gas costs about $3.50 per gallon. That means I'll save $ 1365 per year on gas. That means that if gas remains at $3.50 per gallon it will be about 18 years before the car has paid for itself. I don't think I can justify buying the new car. "

45) Gabe said "For years there has been no money in the Social Security trust fund, just a

45)

46) My share of the federal government's debt is about the same as my annual net income.

46)

47) I will be retiring soon so I need low-risk investments. I'm going to put most of my money

47)

48) Before the government borrows money from its own trust funds such as the Social

48)

49) We will never be able to send our daughter to college. In order to have $100,000 in 20

49)

50) Sam is in the 12% tax bracket, so a $500 tax credit will reduce his total tax bill by

50)

51) Steve is planning to open a savings account either at Quarterly Bank or at Daily Bank.

51)

52) Apartments in a new building can either be bought or rented. Gale calculated that it

52)

53) If two accounts offer the same APR, the account which compounds interest weekly will be

53)

54)

55) My share of the federal government's debt is about the same as my annual net income.

55)

56) Maria saved $720 in taxes after donating $3000 to charity. So Maria's sister also donated $

56)

57) Jeremy hasn't paid off his credit card debt but he knows that it's important to start saving.

57)

bunch of IOUs". Kim said "That's impossible, if that were true, how come the government has been able to pay out Social Security benefits all these years?" Who is making more sense?

into bonds. The return may not be as high as for stocks but as least there is no chance of losing any of the principal.

Security trust fund to finance a deficit, it first tries to cover the deficit by borrowing from the public .

years we would have to save at least $500 each month, That's more than we can afford.

0.12 × $500 = $60.

Quarterly Bank is offering an APR of 4.5% compounded quarterly, which is clearly the better deal since Daily Bank is offering an APR of 4.5% but with daily compounding.

would be cheaper for her to buy. Gale's brother did the same calculations for himself for the same apartment and found that it would be cheaper to rent.

a better deal than the account which compounds interest monthly.

3000 to charity thinking that she would save $720 but she only saved $360.

He decides to invest some money in a savings account and to continue making just the minimum payments each month on his credit card. The interest rate on his credit card is 21.5% per month.

58) The bank paid an annual interest rate (APR) of 7% but at the end of the year my account

58)

balance had grown by only 6.9%

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation for the unknown. 59) x2 = 49

A) x = 7

59) B) x = 49 2

C) x = ± 49 2

D) x = ±7

Assume you have a balance of $3200 on your credit card that you want to pay off. Calculate your monthly payment and total payment under the given conditions. Assume you make no additional charges to the card. 60) The credit card APR is 19% and you want to pay off the balance in 3 years. 60) A) $176.46; $6,352.54 B) $100.46; $3,616.51

C) $140.92; $5,073.22

D) $117.30; $4,222.77

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 61) Wendy buys a $1 lottery ticket every day and takes 2 yoga classes per week which cost $16 each. A) 95% B) 22% C) 3% D) 14% Provide an appropriate response. 62) ________ outlays are expenses that will be paid automatically unless Congress acts to change them. A) Primary B) Discretionary

C) Mandatory

D) None of the above

61)

62)

Determine whether the spending pattern described is at, above, or below the national average. Assume that any salaries or wages are after tax.

63) A couple over the age of 65 with a fixed monthly salary of $4500 spends $720 per month on transportation. A) above average

B) at average

C) below average

Use the given stock table to answer the question. 64) How does the share price for company ABC compare to the profit per share that it earned in the past year? 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s ABC 0.63 2.5 28 4156 XYZ 0.21 1.2 13 9175

High 25.68 18.17

A) price = 2.5 × earnings C) price = 25.04 × earnings

Low Close 24.87 25.04 17.26 17.39

64)

Net Chg -0.35 +0.09

B) price = 28 × earnings D) earnings = 28 × price

Provide an appropriate response. 65) What is the compound interest formula for interest paid more than once a year?

A) A = P 1 + APR

63)

B) A = P 1 + APR

65)

C) A = P x (1 + APR)nY

D) A = P x (1 + APR)Y

Assume you have a balance of $3200 on your credit card that you want to pay off. Calculate your monthly payment and total payment under the given conditions. Assume you make no additional charges to the card. 66) The credit card APR is 21% and you want to pay off the balance in 2 years. 66) A) $164.43; $3,946.42 B) $247.51; $5,940.18

C) $140.80; $3,051.17

D) $197.60; $4,277.35

Provide an appropriate response. 67) True or False? If net income is negative, the budget has a surplus. A) True B) False

68) True or False? A mortgage lender will typically require a down payment of 10% to 20% of the purchase price. A) False

67)

68)

B) True

Solve the problem. 69) You have money in an account at an APR of 4% compounded annually. To the nearest year, how long will it take for your money to triple? A) 39 years B) 28 years C) 17 years D) 22 years

69)

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 70) Kelsey earned $62,383 in wages. Conner earned $62,383, all in dividends and long-term capital 70) gains. Calculate the overall tax rate for each, including both FICA and income taxes. Assume they are both single and take the standard deduction. Note that long-term capital gains and dividends are taxed at 0% on income less than $40,000 for single taxpayers or $80,000 for married couples filing jointly, 15% on additional income up to $441,500 for single taxpayers or $496,600 for married couples filing jointly, 20% on income above $441,500 for single taxpayers or $496,600 for married couples filing jointly. A) Kelsey: 18.4% B) Kelsey: 10.8% C) Kelsey: 10.9% D) Kelsey: 16.9% Conner: 5.4% Conner: 5.4% Conner: 11.8% Conner: 9.3%

Answer the question. 71) You could take a 15-week, three-credit college course, which requires 11 hours per week of your time and costs $600 per credit-hour in tuition. Or during those hours you could have a job paying $14 per hour. What is the net cost of the class compared to working? A) $1954 B) $4110 C) $2910 D) $754

71)

Solve.

72) Determine how much of the total loan payment applies toward principal and how much applies

72)

toward interest for a home mortgage of $139,855 with a fixed APR of 4.7% for 20 years. A) $139,855 pays off the principal and $76,135.75 represents interest payments.

B) $139,855 pays off the principal and $76,262.88 represents interest payments. C) $139,855 pays off the principal and $76,099.42 represents interest payments. D) $139,855 pays off the principal and $76,186.61 represents interest payments. Determine whether the spending pattern described is at, above, or below the national average. Assume that any salaries or wages are after tax.

73) A couple under the age of 30 has a combined household income of $3200 per month and spends $ 440 per month on transportation. A) above average

B) below average

Evaluate or simplify the following the expression. 74) 65 ÷ 6 2

A) 18

73)

C) at average

74)

B) 1,296

C) 216

D) 1 216

Solve the problem. 75) Suppose your after-tax income is $36,871. Your annual expenses are $30,418 for rent, $6,831 for food and household expenses, $1,384 for interest on credit cards, and $8,359 for entertainment, travel, and other. You expect to get a 25% raise next year. Will this affect the outcome? A) Yes, a raise would create a surplus. B) No, a raise would still create a deficit.

76) Suppose you start saving today for a $40,000 down payment that you plan to make on a house in

20 years. Assume that you make no deposits into the account after your initial deposit. The account has daily compounding and an APR of 5%. How much would you need to deposit now to reach your $40,000 goal in 20 years? A) $19,994.49 B) $5694.38 C) $14,716.19 D) $14,384.59

75)

76)

Find the annual percentage yield (APY). 78) A bank offers an APR of 2.5% compounded daily. A) 102.53% B) 2.60%

78) C) 5.00%

D) 2.53%

Solve the problem. 79) Suppose a government decided to pay off its $8 trillion debt with a one-time charge distributed equally among all workers. Assuming the country's total work force is 127 million people, how much would each worker be charged? A) About $63,000 per worker. B) About $15,875,000 per worker.

C) About $6,000 per worker.

79)

D) About $1,588,000 per worker.

Answer the question. 80) You put $304 per month in an investment plan that pays an APR of 3% compounded monthly. How much money will you have after 17 years? Compare this amount to the total amount of deposits made over the time period. A) $80,796.30; this is $3,276.30 more than the total amount of the deposits.

80)

B) $80,744.87; this is $29,064.87 more than the total amount of the deposits. C) $80,770.57; this is $18,754.57 more than the total amount of the deposits. D) $68,654.99; this is $18,754.57 more than the total amount of the deposits. Calculate the amount of interest you'll have at the end of the indicated period. 81) You invest $8,000 in an account that pays simple interest of 2% for 7 years. A) $1,120.00 B) $160.00 C) $1,005.96

81) D) $1,337.93

Solve the problem. 82) In a recent year, the total receipts for the US federal government were estimated to be $2288 billion. The total outlays were estimated to be $2613 billion. The table below shows the makeup of federal government receipts that year - the percentage of total receipts coming from each category.

82)

Approximate makeup of federal government receipts Category Portion of total receipts Social Security, Medicare, and other social insurance receipts 37% Individual income taxes 44% Corporate income taxes 12% Excise taxes 3% Other 4% How much income came from corporate income taxes that year? A) $265 billion B) $275 billion C) $314 billion

D) $280 billion

Calculate the balance under the given assumptions. 83) Find the savings plan balance after 11 years with an APR of 3% and monthly payments of $353. A) $3,655.10 B) $46,855.26 C) $55,123.83 D) $4,300.12

83)

Assume you have a balance of $3200 on your credit card that you want to pay off. Calculate your monthly payment and total payment under the given conditions. Assume you make no additional charges to the card. 84) The credit card APR is 18% and you want to pay off the balance in 4 years. 84) A) $94.00; $4,512.00 B) $112.91; $5,419.89

C) $130.64; $6,270.75

D) $80.51; $3,864.62

Provide an appropriate response. 85) A ______ represents money that is borrowed (or taken from savings) during a single year. A) deduction B) debt

C) deficit

85)

D) None of the above

Solve the equation for the unknown quantity. 86) 10n - 10 = 20 A) 3 B) 24

86) C) 20

D) 12

Solve the problem. 87) You have money in an account at an APR of 7% compounded weekly. To the nearest year, how long will it take for your money to double? A) 8 years B) 6 years C) 10 years D) 14 years Provide an appropriate response. 88) True or False? The bank that pays the highest annual percentage rate (APR) is never the best deal, no matter what. A) False B) True

87)

88)

Use the given stock table to answer the question. 89) How much profit per share did company XYZ earn in the past year? 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s ABC 0.63 2.5 21 4156 XYZ 0.21 1.2 13 9175

A) $1.21

High 25.68 18.17

B) $1.45

Low Close 24.87 25.35 17.26 17.75

89) Net Chg +0.22 +0.09

C) $1.16

Solve the equation for the unknown quantity. 90) t - 9 = 11 A) 2 B) -2

D) $1.37

90) C) 20

D) -20

Solve the problem. 91) You need a $127,469 loan. Compute the monthly payment for each of the loan options listed below. Assume that the loans are fixed rate. Option 1: a 30 year-loan at an APR of 7.15% Option 2: a 15-year loan at 6.75% A) Option 1: $875.69 B) Option 1: $860.93 Option 2: $1,166.56 Option 2: $1,127.99 C) Option 1: $879.75 D) Option 1: $848.24 Option 2: $1,179.11 Option 2: $1,093.79 Solve the equation for the unknown. 92) (x - 2)3 = 27

A) x = -4

91)

92) B) x = 4

C) x = -5

D) x = 5

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 93) Kevin is married, but he and his wife filed separately. His gross salary was $30,852, and he 93) earned $559 in interest. He had $1,279 in itemized deductions and received a tax credit $5950 for his two children. Find his taxable income. A) $18,861 B) $12,611 C) $2,263.32 D) $17,582

Evaluate or simplify the following the expression. 94) 42 × 4 -2

A) 4

94)

B) 16

C) 1

D) 8

Solve the problem. 95) Budget Summary for the Wonderful Widget Company (all amounts in thousands of dollars) 2014 2015 2016 2017 Total Receipts $854 $908 $950 $990 Outlays Operating 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus/Deficit -146 -174 -246 -207 Debt (accumulated) -146 -320 -566 -773

95)

Assume that for 2018, total receipts are $1,073,815, operating expenses are $577,523, employee benefits are $210,252, security costs are$129,122, and interest on debt is $63,000. Calculate the year-end surplus or deficit. A) $769,544.00 B) $93,918.00 C) $219,918.00 D) $898,666.00

Assume you have a balance of $3200 on your credit card that you want to pay off. Calculate your monthly payment and total payment under the given conditions. Assume you make no additional charges to the card. 96) The credit card APR is 18% and you want to pay off the balance in 1 year. 96) A) $251.22; $3,014.66 B) $293.38; $3,520.51

C) $441.55; $5,298.61

D) $352.53; $4,230.33

Provide an appropriate response. 97) ______, or income, represent money that has been collected. A) Net income B) Outlays

C) Receipts

97)

D) None of the above

Compute the total and annual returns on the described investment. 98) Seven years after paying $7,275 for shares in a new company, you sell the shares for $11,030. A) Total Return: 49.03% B) Total Return: 51.62% Annual Return: 5.82% Annual Return: 6.13% C) Total Return: 41.29% D) Total Return: 54.20% Annual Return: 4.90% Annual Return: 6.43%

98)

Solve.

99) Calculate the monthly payment for a student loan of $122,834 at a fixed APR of 7.6% for 30 years. A) $1,301.48 B) $1,040.93 C) $743.31 D) $867.30 Find the annual percentage yield (APY). 100) A bank offers an APR of 2.5% compounded quarterly. A) 5.05% B) 1.25% C) 2.52%

99)

100) D) 2.5%

Solve the problem. 101) Suppose your after-tax income is $36,423. Your annual expenses are $30,204 for rent, $6,357 for food and household expenses, $1,275 for interest on credit cards, and $8,251 for entertainment, travel, and other. Do you have a surplus or deficit? A) Deficit B) Surplus

101)

Use the given stock table to answer the question. 103) How does the share price for company XYZ compare to the profit per share that it earned in the past year? 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s ABC 0.63 2.5 19 4156 XYZ 0.21 1.2 14 9175

High 25.68 18.17

A) earnings = 14 × price C) price = 14 × earnings

Low Close 24.87 25.46 17.26 17.51

103)

Net Chg +0.29 +0.09

B) price = 1.2 × earnings D) price = 17.51 × earnings

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 104) Elena spends $5 per day on a coffee at the neighborhood cafe and $350 per month on food. A) 43% B) 10% C) 521% D) 6%

104)

Find the monthly interest payments in the situation described. Assume that monthly interest rates are 1/12 of annual interest rates. 105) Ashton maintains an average balance of $1300 on his credit card which carries an annual interest 105) rate of 24%. A) $260 B) $3120 C) $312 D) $26

Solve the equation for the unknown quantity. 106) 8x + 8 = 7x + 17 A) 5 B) 11 3

106) C) 3 5

D) 9

Evaluate or simplify the following the expression. 107) 3 -4

107)

A) - 81

B) 81

C) 1

D) 1

A) 7

B) 10

C) 25

D) 3

108) 52

108)

Provide an appropriate response. 109) A plan in which payments are made at the beginning of each period is called a(n) ________. A) future annuity B) annuity due

C) ordinary annuity

109)

D) None of the above

110) True or False? If you buy an item (such as property or stock) at one price and later sell it at a lower price, the profit is called a capital gain. A) False

110)

B) True

111) True or False? Long-term capital gains are profits on items sold within 12 months of their purchase. A) True

111)

B) False

Solve the problem. 112) You want to have a $80,000 college fund in 15 years. How much will you have to deposit now in an account with an APR of 6% and monthly compounding? A) $31,920.49 B) $34,567.93 C) $29,894.03 D) $32,598.59 Prorate the given expenses to find the monthly cost. 113) Keiko pays $300 per month for food, a semiannual health insurance premium of $1400, and an annual car insurance premium of $550. Round your answer to the nearest dollar. A) $579 B) $625 C) $304 D) $462 Provide an appropriate response. 114) The ______ is the actual percentage by which a balance increases in 1 year. A) APR B) APY

C) AARP

112)

113)

114)

D) None of the above

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 115) $14,000 deposit at an APR of 4% with semiannual compounding for 12 years 115) A) $22,518.12 B) $20,720.00 C) $17,755.39 D) $22,414.45

Solve.

116) Tim is in the 35% marginal tax bracket and claims the standard deduction. How much will his tax bill be reduced if he qualifies for a $563 tax credit? A) $1,099.50 B) $563

C) $197.05

116)

D) $760.05

Solve the problem. 117) Budget Summary for the Wonderful Widget Company (all amounts in thousands of dollars) 2014 2015 2016 2017 Total Receipts $854 $908 $950 $990 Outlays Operating 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus/Deficit -146 -174 -246 -207 Debt (accumulated) -146 -320 -566 -773

117)

Assume that for 2018, total receipts are $1,044,961, operating expenses are $609,251, employee benefits are $154,234, security costs are $128,496, and interest on debt is $63,000. Calculate the year-end accumulated debt. A) -$557,020.00 B) $8,440.00 C) -$120,056.00 D) -$683,020.00

Provide an appropriate response. 118) The relative change in the investment value is the ______. A) annual return B) complete return

C) total return

118)

D) None of the above

The expenses and income of an individual are given in table form. Find the net monthly cash flow (it could be positive or negative). Assume salaries and wages are after taxes, that 1 month = 4 weeks, and that 1 year = 12 months. Round your answer to the nearest dollar.

119)

119) Income Part-time job: $1000 /month Student loan: $6500/year Scholarship: $5400/year

A) $258

Expenses Rent: $600/month Groceries: $75/week Tuition and fees: $3800 twice a year Entertainment: $180/month B) $595 C) $278

D) $503

Answer the question. 120) You intend to create a college fund for your baby. If you can get an APR of 5.0% with monthly compounding and want the fund to have a value of $111,840 after 18 years, how much should you deposit monthly? A) $272.23 B) $352.30 C) $5,996.17 D) $320.27

120)

Solve.

121) Calculate the monthly payment for a home mortgage of $137,000 with a fixed APR of 3.1% for 30

121)

years.

A) $4,751.80

B) $1,153.80

C) $585.01

D) $353.92

Solve the problem.

122)

122) Mutual Fund Listing (MFABC) 1-Day Net Change 1-Day Return NAV $10.94 ^$0.02 ^0.36% YTD 1-YR 5-Yr 10-Yr Fund 1.74% 2.57% 2.96% 4.81% TOTAL RETURNS (%) 5 and 10 year returns are annualized Suppose you invest $7000 in this fund today. How many shares will you buy? Round to three decimal places. A) 1,562.857 shares B) 7,658.000 shares

C) 63.985 shares

D) 639.854 shares

Calculate the balance under the given assumptions. 123) Find the savings plan balance after 34 months with an APR of 3% and monthly payments of $302. A) $10,703.07 B) $3,641.64 C) $3,095.39 D) $9,097.61

123)

Calculate the amount of interest you'll have at the end of the indicated period. 124) You invest $20,000 in an account that pays simple interest of 2% for 1 year. A) $400 B) $40 C) $600

124) D) $20,400

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 125) Carmen and James are married and filed jointly. Their combined wages were $125,217. They 125) earned a net of $2,388 from a rental property they own, and they received $1,746 in interest. They contributed $4,110 to their tax-deferred retirement plans, and their itemized deductions total $14,237. Find their adjusted gross income. A) $147,698 B) $125,241 C) $111,004 D) $121,749

Provide an appropriate response. 126) _______ is interest paid both on the original principal and on all interest that has been added to the original principal. A) Basic interest B) Simple interest

C) Compound interest

126)

D) None of the above

Determine whether the spending pattern described is at, above, or below the national average. Assume that any salaries or wages are after tax.

127) A single 48-year old man with a monthly salary of $4800 spends $450 on food. A) at average B) above average C) below average

127)

128)

128) Income Salary: $30,000/year Jewelry sales: $250/month

A) -$238

Expenses House payments: $1500/month Groceries: $100/week Household expenses: $320/month Car insurance: $400 semiannually Donations: $420/year Miscellaneous: $700/month B) -$272 C)

D) -$502

Prorate the given expenses to find the monthly cost. 129) Linda enrolls for 10 credit-hours for each of two semesters at a cost of $500 per credit-hour (tuition and fees). In addition, textbooks cost $300 per semester. Round your answer to the nearest dollar. A) $133 B) $442 C) $1325 D) $883

129)

Solve.

130) You are in the 35% tax bracket. An apartment rents for $1,400 per month. Your monthly mortgage

130)

payments would be $1,600, of which an average of $1,300 per month goes toward interest during the first year. Determine whether renting or buying is cheaper (in terms of monthly payments) during the first year. Assume you are itemizing deductions in all cases. A) Renting is cheaper; $1,400 per month for renting versus $1,600 per month for buying

B) Renting is cheaper; $1,400 per month for renting versus $1150 per month for buying C) Buying is cheaper; $1,145 per month for buying versus $1,400 per month for renting D) Buying is cheaper; $1,300 per month for buying versus $1,400 per month for renting Provide an appropriate response. 131) True or False? A progressive income tax means that people with a higher age pay at a higher tax rate. A) False B) True

131)

Solve.

132) Jim is in the 35% tax bracket and itemizes his deductions. How much will his tax bill be reduced if he makes a $3,574 contribution to charity? A) $4,824.90 B) -$2,323.10

C) $1,250.90

132)

D) $3,574

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 133) Your deductible expenditures are $16,544 for interest on a home mortgage, $7,249 for 133) contributions to charity, and $1,595 for state income taxes. Your filing status entitles you to a standard deduction of $25,100. Should you itemize your deductions rather than claiming the standard deduction? If so, what is the difference? A) Yes, $50,488

B) Yes, -$2,902 C) Yes, $288 D) No, you are better off with the standard deduction.

Solve the problem.

134)

134) Mutual Fund Listing (MFABC) 1-Day Net Change 1-Day Return NAV $29.11 ^$0.00 ^0.00% YTD 1-YR 5-Yr 10-Yr Fund 2.53% 5.68% -3.96% -1.07% TOTAL RETURNS (%) 5 and 10 year returns are annualized Suppose you had invested $2,000 in this fund 5 years ago. How much would your investment be worth now? A) $2,109.31 B) $2,266.13 C) $1,759.48 D) $1,895.27

135) In 2011, a country's government projected total receipts of $2590 billion ($2.590 trillion) and a

135)

deficit of $223 billion for 2013. If outlays turn out to be higher than expected by 7% while receipts turn out to be lower by 7%, what would the 2013 surplus or deficit be? A) $571 billion deficit B) $215 billion deficit

C) $601 billion deficit

D) $155 billion deficit

Answer the question. 136) Many insurance companies carry a deductible provision that states how much of a claim you must pay out of pocket before the insurance company pays the remaining expenses. Suppose you have a car insurance policy with a $800 deductible provision (per claim) for collisions. During a two-year period, you file claims for $650 and $1200. The annual premium for the policy is $450. Determine how much you would pay with and without the insurance policy. A) With policy $2500, without policy $1850 B) With policy $1900, without policy $1850

C) With policy $2350, without policy $1850

136)

D) With policy $1950, without policy $2000

Provide an appropriate response. 137) A savings plan in which payments are made at the end of each month is called a(n)_____? A) future annuity B) annuity due

C) ordinary annuity

137)

D) None of the above

Answer the question. 138) You currently drive 288 miles per week in a car that gets 24 miles per gallon of gas. You are considering buying a new fuel-efficient car for $15,000 (after trade-in on your current car) that gets 48 miles per gallon. Insurance premiums for the new and old car are $800 and $600 per year, respectively. You anticipate spending $1000 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car? By how much? A) the new car is $3540 less expensive B) the old car is $3540 less expensive

C) the new car is $5540 less expensive

D) the old car is $5540 less expensive

138)

Compute the total and annual returns on the described investment. 139) Five years after paying $12,646 for shares in a new company, you sell the shares for $5,306. A) Total Return: -58.04% B) Total Return: -46.43% Annual Return: -15.95% Annual Return: -12.76% C) Total Return: -60.94% D) Total Return: -55.14% Annual Return: -16.74% Annual Return: -15.15% Provide an appropriate response. 140) True or False? A credit check is one example of a closing cost when taking out a mortgage loan. A) False B) True Solve the problem. 141) Suppose your after-tax income is $44,243. Your annual expenses are $25,098 for rent, $5,828 for food and household expenses, $1,276 for interest on credit cards, and $7,731 for entertainment, travel, and other. You expect to get a 25% raise next year. Could you afford $5,411 in tuition and fees without going into debt? A) Yes B) No

142) The average cost of a 4-year college education is projected to be $100,000 in 17 years. How much

139)

140)

141)

142)

money should be invested now at 4%, compounded quarterly, to provide $100,000 in 17 years? A) $50,833.10 B) $84,437.75 C) $100,000.00 D) $25,840.04

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 143) Carla earned wages of $52,597, received $1,886 in interest from a savings account, and contributed 143) $3,444 to a tax deferred retirement plan. Itemizing, she had deductions totaling $7,020. Find her gross income. A) $39,969 B) $51,039 C) $57,927 D) $54,483

144) You are married filing jointly and have a taxable income of $287,772. You make monthly

144)

contributions of $1,009 to a tax-deferred savings plan. Calculate the effect on annual take-home pay of the tax-deferred contribution. If necessary, round values to the nearest dollar. A) Take-home pay will be $3,875 less per year with tax-deferred plan

B) Take-home pay will be $3,875 more per year with tax-deferred plan C) Take-home pay will be $2,906 more per year with tax-deferred plan D) Take-home pay will be $2,906 less per year with tax-deferred plan Solve the equation for the unknown quantity. 145) 6r + 3 = 39 A) 30 B) 6

145) C) 3

146) 5x - 7 = 63 - 9x A) -5

D) 34 146)

C) - 35 2

B) 5

D) - 14

Determine whether the spending pattern described is at, above, or below the national average. Assume that any salaries or wages are after tax.

147) A couple in their forties with a combined household income of $56,000 per year spends $400 per month on health care. A) above average

B) at average

C) below average

Find the annual percentage yield (APY). 148) A bank offers an APR of 3.2% compounded monthly. A) 0.27% B) 3.25% C) 0.53%

148) D) 6.49%

Provide an appropriate response. 149) A(n) ________ deduction is the addition of all individual deductions to which you are entitled. A) standard B) complete

C) itemized

D) None of the above

147)

149)

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 150) Kyle is single and earned wages of $33,354. He received $310 in interest from a savings account. 150) He contributed $571 to a tax-deferred retirement plan. He had $477 in itemized deductions from charitable contributions. Calculate his adjusted gross income. A) $33,093 B) $32,616 C) $34,235 D) $33,758

Solve the equation for the unknown quantity. 151) x + 18 = 5 A) 18 B) -13 5

151) C)

D) 23

Calculate the balance under the given assumptions. 152) Find the savings plan balance after 13 months with an APR of 3% and monthly payments of $520. A) $6,319.81 B) $6,862.34 C) $5,832.99 D) $5,371.84 Solve the problem. 153) Consider an account with an APR of 4%. Find the APY with quarterly compounding, monthly compounding, and daily compounding. A) 13.06%, 14.07%, 14.08% B) 19.06%, 19.07%, 19.08%

C) 1.00%, 0.33%, 4.16%

152)

153)

D) 4.06%, 4.07%, 4.08%

You need a loan of $100,000 to buy a condo. Calculate your monthly payments and total closing costs for each choice. 154) Choice 1: 30-year fixed rate at 4% with closing costs of $1,478 and no points 154) Choice 2: 20-year fixed rate at 3.5% with closing costs of $1,478 and 2 points A) Choice 1: $543.49; $1,478 B) Choice 1: $421.10; $1,478 Choice 2: $474.36; $3,278 Choice 2: $586.19; $2,956 C) Choice 1: $605.98; $1,478 D) Choice 1: $477.42; $1,478 Choice 2: $449.04; $3,228 Choice 2: $579.96; $3,478 Provide an appropriate response. 155) True or False? If net income is negative, the budget has a surplus. A) True B) False

155)

Solve the problem. 156) Suppose your after-tax income is $40,666. Your annual expenses are $25,992 for rent, $6,452 for food and household expenses, $1,262 for interest on credit cards, and $7,655 for entertainment, travel, and other. You expect to get a 25% raise next year. Could you afford $3,862 in tuition and fees without going into debt? A) No B) Yes

157) Calculate the annual interest for a $1,000 Treasury bond with a current yield of 4.2% that is quoted at 117.5 points. A) $37.80

B) $49.35

C) $33.60

157)

D) $59.22

Provide an appropriate response. 158) The lump sum deposit that would give you the same end result as regular payments into a savings plan is called the _____ of the savings plan. A) total value B) present value

C) future value

156)

158)

D) None of the above

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 159) Jenny earned wages of $89,704, received $5,054 in interest from a savings account, and contributed 159) $6,027 to a tax deferred retirement plan. She had deductions totaling $13,175. Find her taxable income. A) $82,208 B) $75,958 C) $9,864.96 D) $76,181

Compute the total and annual returns on the described investment. 160) Four years after buying 600 shares of XYZ stock for $40 per share, you sell the stock for $1,000. A) Total Return: -100.62% B) Total Return: -81.46% Annual Return: -57.56% Annual Return: -46.60% C) Total Return: -86.25% D) Total Return: -95.83% Annual Return: -49.34% Annual Return: -54.82%

160)

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 161) Matt is single and earned wages of $32,257. He received $434 in interest from a savings account. 161) He contributed $453 to a tax-deferred retirement plan. He had $463 in itemized deductions from charitable contributions. Calculate his taxable income. A) $25,425 B) $19,688 C) $37,194 D) $27,725 Determine whether the spending pattern described is at, above, or below the national average. Assume that any salaries or wages are after tax.

162) A single 42-year old man with a monthly salary of $3700 spends $180 on health care. A) below average B) above average C) at average

162)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 163) $11,000 deposit at an APR of 3% with daily compounding for 9 years 163) A) $2,970.00 B) $10,088.86 C) $14,409.61 D) $11,036.73

Use the given stock table to answer the question. 164) Based on the fact that stocks historically trade at an average P/E ratio of about 12-14, does the stock price of company XYZ seem cheap, about right, or expensive right now? 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s ABC 0.63 2.5 26 4156 XYZ 0.21 1.2 13 9175

A) expensive

High 25.68 18.17

Low Close 24.87 25.13 17.26 17.75

164)

Net Chg -0.19 +0.09

B) about right

C) cheap

Solve.

165) Determine the total payment over the term of a student loan of $199,773 at a fixed APR of 8.3% for 20 years. A) $410,143.57

B) $409,954.50

C) $410,308.97

D) $410,033.29

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 166) Julio goes to a concert once every two weeks at an average ticket price $60; he spends $800 per year on car insurance. A) 390% B) 195% C) 16% D) 90% Provide an appropriate response. 167) If you sell a stock for more than you paid for it, you have a __________. A) capital gain B) return

C) dividend

165)

166)

167)

D) None of the above

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 168) Bill earned wages of $47,532, received $1,760 in interest from a savings account, and contributed 168) $3,194 to a tax deferred retirement plan. Itemizing, he had deductions totaling $7,323. Find his adjusted gross income. A) $34,725 B) $52,486 C) $46,098 D) $59,809

Solve the problem. 169) Calculate the current yield for a $100 Treasury bond with a coupon rate of 6.4% that has a market value of $75. A) 7.68% B) 6.40% C) 9.39% D) 8.53%

169)

Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period. 170) A $9,642 deposit in an account with an APR of 6.5% compounded continuously for 4 years. 170) A) $12,404.11 B) $12,505.00 C) $12,974.28 D) $12,478.89

Calculate the amount of interest you'll have at the end of the indicated period. 171) You invest $700 in an account that pays simple interest of 4% for 5 year(s). A) $140.00 B) $560.00 C) $14.00

171) D) $35.00

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 172) Jeff earned wages of $48,342, received $1,810 in interest from a savings account, and contributed 172) $4,026 to a tax deferred retirement plan. Itemizing, he had deductions totaling $7,300. Find his taxable income. A) $54,178 B) $41,628 C) $38,826 D) $33,576

Solve the problem. 173) In a recent year, the total receipts for the US federal government were estimated to be $2288 billion. The total outlays were estimated to be $2613 billion. The table below shows the makeup of federal government receipts that year - the percentage of total receipts coming from each category.

173)

Approximate makeup of federal government receipts Category Portion of total receipts Social Security, Medicare, and other social insurance receipts 37% Individual income taxes 44% Corporate income taxes 12% Excise taxes 3% Other 4% How much income came from individual income taxes that year? A) $965 billion B) $1 trillion C) $1.1 trillion

D) $847 billion

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 174) Your deductible expenditures $4,625 for contributions to charity and $702 for state income taxes. 174) Your filing status entitles you to a standard deduction of $12,550. Should you itemize your deductions rather than claiming the standard deduction? If so, what is the difference? A) No, you are better off with the standard deduction.

B) Yes, $5,327 C) Yes, $7,223 D) Yes, $8,627 For the given principal, interest rate, and time period, determine the amount of interest that would be earned in an account paying simple interest. Also determine the amount of interest that would be earned in an account paying compound interest with interest compounded annually. Determine how much more interest would be earned in the account paying compound interest. Round to the nearest cent. 175) Principal: $5,539 Rate: 4% Years: 10 175) A) $5,983.47 B) $350.68 C) $3,767.87 D) $444.47

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 176) $20,000 is invested at an APR of 2.9% for 10 years. 176) A) $25,220.00 B) $25,868.33 C) $25,800.00 D) $26,618.51

Provide an appropriate response. 177) ______, or income, represent money that has been collected. A) Net income B) Receipts

C) Outlays

177)

D) None of the above

Answer the question. 178) Assume that you have a health insurance plan with the following provisions: · Office visits require a copayment of $25 · Emergency room visits have a $250 deductible (you pay the first $250) · Surgical operations have a $1000 deductible (you pay the first $1000) · You pay a monthly premium of $600

178)

During a one-year period, your family has the following expenses: Expense Total cost (before insurance) Feb 18: Emergency room $740 Mar 13: Office visit $100 Apr 14: Surgery $8200 May 12: Office visit $120 Nov 23: Emergency room $1120 Determine your health-care expenses for the year with and without the insurance policy. A) With policy $15260,without policy $10,820

B) With policy $8660,without policy $10,880 C) With policy $2150,without policy $10,280 D) With policy $8750,without policy $10,280 Solve the problem. 179) Suppose the government has a unified net income of $50 billion, but was supposed to deposit $175 billion in the Social Security trust fund. What was the on-budget surplus or deficit? A) $125 billion deficit B) $225 billion surplus

C) $125 billion surplus

179)

D) $225 billion deficit

Calculate the amount of interest you'll have at the end of the indicated period. 180) You invest $60,200 in an account that pays simple interest of 4% for 3 year(s). A) $722.40 B) $5,016.67 C) $7,224.00

180) D) $80,266.67

Solve the problem. 181) Suppose your after-tax income is $37,498. Your annual expenses are $31,763 for rent, $6,264 for food and household expenses, $1,328 for interest on credit cards, and $7,976 for entertainment, travel, and other. Do you have a surplus or deficit? A) Deficit B) Surplus

181)

Solve.

182) Calculate the monthly payment for a home mortgage of $408,000 with a fixed APR of 3.0% for 15

182)

years.

A) $27,747.17

B) $2,817.57

C) $3,415.71

D) $1,025.01

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 183) $7,660 deposit at an APR of 4% with semiannual compounding for 5 years 183) A) $9,337.50 B) $9,319.56 C) $9,192.00 D) $8,457.26 Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 184) Caitlin is single and earned wages of $32,660. She received $340 in interest from a savings 184) account. She contributed $587 to a tax-deferred retirement plan. She had $528 in itemized deductions from charitable contributions. Calculate her gross income. A) $31,885 B) $33,000 C) $32,413 D) $33,587

Solve the problem. 185) Anna deposits $2500 in a savings account that compounds interest annually at an APR of 6% . Dave deposits $2600 in a savings account that compounds interest daily at an APR of 5.7%. After 10 years, who has more in their savings account and how much more do they have? A) Anna has $175.26 more than Dave. B) Dave has $120.17 more than Anna.

C) Anna has $113.05 more than Dave.

185)

D) Dave has $125.86 more than Anna.

Solve the equation for the unknown quantity. 186) 5z + 13 = 4z + 2 A) 15 B) -15

186) C) -11

D) 11

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 187) George spends $15 per week at the movies and $650 per month on rent. A) 13% B) 10% C) 1% D) 120%

187)

Solve the problem. 188) You have a choice between a 30-year fixed rate loan at 5% and an ARM with a first-year rate of 2.5%. The ARM rate rises to 6.5% at the start of the third year. Neglecting compounding and changes in principal, estimate your monthly savings with the ARM during the first year on a $ 150,000 loan. A) $302.50 B) $312.50 C) $332.50 D) $362.50 Answer the question. 189) You currently drive 288 miles per week in a car that gets 24 miles per gallon of gas. A new fuel-efficient car costs $15,000 (after trade-in on your current car) and gets 48 miles per gallon. Insurance premiums for the new and old car are $800 and $600 per year, respectively. You anticipate spending $1000 per year on repairs for the old car and having no repairs on the new car. Assuming that gas remains at $3.50 per gallon, estimate the number of years after which the costs of owning the new and old cars are equal. A) 6.7 years B) 7.3 years C) 5.7 years D) 7.9 years

188)

189)

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 190) Jim earned wages of $86,003, received $5,151 in interest from a savings account, and contributed 190) $6,116 to a tax deferred retirement plan. Itemizing, he had deductions totaling $8,778. Find his adjusted gross income. A) $80,988 B) $85,038 C) $72,210 D) $97,270

Solve the equation for the unknown quantity. 191) 6x - 12 = 2x - 4 A) -2 B) 1

191) C) -1

Solve the problem. 192) In 2013, the United States publicly held debt was $17 trillion. Use the loan payment formula to determine the annual payments needed to pay this debt off in 12 years. Assume an annual interest rate of 4%. A) $1798 billion B) $1811 billion C) $1836 billion D) $1824 billion

192)

Solve the equation for the unknown. 193) p1/3 = 5

A) p = 1 125

193) B) p = 1 15

C) p = 125

D) p = 15

Provide an appropriate response. 194) _________ loans differ from installment loans in that you are not required to pay off your balance in any set period of time. A) Auto B) Credit card

C) Mortgage

194)

D) None of the above

195) True or False? If you deposit $7,000 in an in investment account today, it can double in value to

195)

$14,000 in just a couple decades even at a relatively low interest rate (4%). A) False B) True

Solve the problem. 196) You need a $156,099 loan. Compute the monthly payment for each of the loan options listed below. Assume that the loans are fixed rate. Option 1: a 30 year-loan at an APR of 7.25% Option 2: a 15-year loan at 6.8% A) Option 1: $1,087.69 B) Option 1: $1,064.87 Option 2: $1,448.20 Option 2: $1,385.67 C) Option 1: $1,082.77 D) Option 1: $1,049.49 Option 2: $1,432.85 Option 2: $1,343.84

197) Suppose that the federal debt increases at an annual rate of 1% per year. Use the compound

interest formula to determine the size of the debt in 25 years. Assume that the current size of the debt is $17 trillion. A) $22.9 trillion B) $19.4 trillion C) $21.8 trillion D) $24.7 trillion

196)

197)

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 198) Andy earned $57,751 from wages as an engineer. Determine his overall tax rate on his gross 198) income, including both FICA and income taxes. Assume he is single and takes the standard deduction. If necessary, round values to the nearest tenth. A) 22.3% B) 9.4% C) 17.5% D) 33.0%

Evaluate or simplify the following the expression. 199) 251/2

A) 10

199) C) 25 2

B) 20

D) 5

Provide an appropriate response. 200) A ______ gives you a share of ownership in a company. A) cash B) bond

C) stock

200)

D) None of the above

Find the monthly interest payments in the situation described. Assume that monthly interest rates are 1/12 of annual interest rates. 201) Derek bought a new car for $35,000. He made a down payment of $18,000 and financed the 201) balance through the car dealer. He was unable to make the first monthly payments. Until he makes a payment he is paying 2.5% interest per month on the balance. A) $5100 B) $425 C) $875 D) $10,500

Solve the equation for the unknown quantity. 202) 6x = 12

A) 6

202) C) 1 2

B) 72

D) 2

Solve.

203) Determine the total payment over the term of a student loan of $51,658 at a fixed APR of 8% for 13 years. A) $83,330.37

B) $83,251.79

C) $83,283.23

D) $83,229.32

203)

Provide an appropriate response. 204) ________ outlays are expenses that will be paid automatically unless Congress acts to change them. A) Primary B) Mandatory

C) Discretionary

204)

D) None of the above

205) The average annual percentage yield (APY) that would give the same overall growth is the ______. A) complete return

205)

B) total return D) None of the above

C) annual return

206) True or False? The gross debt represents money the government must repay to individuals and institutions that bought Treasury issues. A) False

206)

B) True

Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period. 207) A $6,000 deposit in an account with an APR of 3.3% compounded continuously for 7 years. 207) A) $7,559.16 B) $1,905.79 C) $6,201.30 D) $7,531.01 Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 208) Kelly earned wages of $95,446, received $4,550 in interest from a savings account, and 208) contributed $6,078 to a tax deferred retirement plan. Itemizing, she had deductions totaling $8,803. Find her gross income. A) $106,074 B) $81,065 C) $99,996 D) $93,918

Solve the problem. 209) You want to have a $50,000 college fund in 10 years. How much will you have to deposit now in an account with an APR of 4.4% and quarterly compounding? A) $32,227.74 B) $32,506.11 C) $32,891.26 D) $32,279.28

209)

210) In a recent year, the total receipts for the US federal government were $2154 billion. The total

210)

211) $644 is deposited into a savings account at 3% interest, compounded monthly. To the nearest year,

211)

outlays were $2472 billion. The deficit was $318 billion. What would the deficit have been, if there had been a 0.5% decrease in total receipts? A) $337 billion B) $333 billion C) $323 billion D) $329 billion

how long will it take for the account balance to reach $1,000,000? A) 172 years B) 221 years C) 245 years

D) 343 years

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 212) $2,000 deposit at an APR of 3% with monthly compounding for 2 years 212) A) $2,010.01 B) $1,698.81 C) $3,125.00 D) $2,123.51 Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 213) You are single and have a taxable income of $58,594. You make monthly contributions of $518 to 213) a tax-deferred savings plan. Calculate the effect on annual take-home pay of the tax-deferred contribution. If necessary, round values to the nearest dollar. A) Take-home pay will be $1,368 more per year with tax-deferred plan

B) Take-home pay will be $746 less per year with tax-deferred plan C) Take-home pay will be $746 more per year with tax-deferred plan D) Take-home pay will be $1,368 less per year with tax-deferred plan 214) Mark earned $27,803 from wages as a mechanic and made $1,517 in interest. Calculate his FICA tax. If necessary, round values to the nearest cent. A) $2,148.93 B) $2,111.76

C) $2,242.98

214)

D) $2,126.93

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 215) $8,000 is invested at an APR of 2.8% for 4 years. 215) A) $8,934.34 B) $8,690.99 C) $896.00 D) $225.50

Solve the problem. 216) Calculate the annual interest for a $1,000 Treasury bond with a current yield of 5.8% that is quoted at 108 points. A) $62.64 B) $52.20 C) $46.40 D) $75.17

216)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 217) $1,800 deposit at an APR of 4% with quarterly compounding for 5 years 217) A) $1,891.82 B) $2,189.98 C) $2,160.00 D) $2,196.34

Provide an appropriate response. 218) True or False? Early in an installment loan term, the portion going toward interest is relatively low and the portion going toward principal is relatively high. As the term proceeds, the portion going toward interest gradually increases and the portion going toward principal gradually decreases. A) True B) False

218)

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 220) $1,250 is invested at an APR of 1.9% for 8 years. 220) A) $1,453.13 B) $1,440.00 C) $1,426.03 D) $1,416.25 For the given principal, interest rate, and time period, determine the amount of interest that would be earned in an account paying simple interest. Also determine the amount of interest that would be earned in an account paying compound interest with interest compounded annually. Determine how much more interest would be earned in the account paying compound interest. Round to the nearest cent. 221) Principal: $1,000 Rate: 3% Years: 19 221) A) $162.43 B) $1,183.51 C) $613.51 D) $183.51

You need a loan of $100,000 to buy a condo. Calculate your monthly payments and total closing costs for each choice. 222) Choice 1: 30-year fixed rate at 4.5% with closing costs of $1,499 and no points 222) Choice 2: 20-year fixed rate at 4% with closing costs of $1,499 and 4 points A) Choice 1: $496.67; $1,499 B) Choice 1: $516.61; $1,499 Choice 2: $595.94; $5,299 Choice 2: $615.99; $2,998 C) Choice 1: $506.69; $1,499 D) Choice 1: $510.04; $1,499 Choice 2: $605.98; $5,499 Choice 2: $609.07; $5,249 Provide an appropriate response. 223) True or False? With tax-deferred savings, you never have to pay tax on the earnings. A) True B) False Solve the problem. 224) Budget Summary for the Wonderful Widget Company (all amounts in thousands of dollars) 2014 2015 2016 2017 Total Receipts $854 $908 $950 $990 Outlays Operating 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus/Deficit -146 -174 -246 -207 Debt (accumulated) -146 -320 -566 -773

223)

224)

Assume that for 2018, total receipts are $1,037,920, operating expenses are $609,157, employee benefits are $246,407, security costs are$134,747, and interest on debt is $63,000. Calculate the year-end surplus or deficit. A) $738,170.00 B) $872,917.00 C) -$15,391.00 D) $110,609.00

Answer the question. 225) Suppose you are 25 years old and would like to retire at age 65. Furthermore, you would like to have a retirement fund from which you can draw an income of $253,279 per year-forever! How can you do it? Assume a constant APR of 5% compounded monthly. A) Deposit $2,944.91 per month. B) Deposit $2,543.61 per month.

C) Deposit $3,988.59 per month.

D) Deposit $3,319.47 per month.

Solve the equation for the unknown. 226) v3 = 8

A) v = 2.7

225)

226) B) v = 2

C) v = 512

D) v = 24

Solve the problem. 227) Suppose a government decided to pay off its $5 trillion debt with a one-time charge distributed equally among all workers. Assuming the country's total work force is 127 million people, how much would each worker be charged? A) About $2,540,000 per worker. B) About $25,400,000 per worker.

C) About $39,000 per worker.

D) About $4,000 per worker.

227)

228) Budget Summary for the Wonderful Widget Company (all amounts in thousands of dollars) Total Receipts Outlays Operating Employee Benefits Security Interest on Debt Total Outlays Surplus/Deficit Debt (accumulated)

2014 $854

2015 $908

2016 $950

2017 $990

525 200 275 0 1000 -146 -146

550 220 300 12 1082 -174 -320

600 250 320 26 1196 -246 -566

600 250 300 47 1197 -207 -773

228)

Assume that for 2018, total receipts are $1,071,977, operating expenses are $564,288, employee benefits are $207,332, security costs are $139,281, and interest on debt is $63,000. Calculate the year-end accumulated debt. A) -$548,924.00 B) C) $144,302.00 D) -$674,924.00

Provide an appropriate response. 229) All of your income for the year including wages, tips, profits from a business, interest or dividends from investments is called your _____ income. A) adjusted gross B) taxable

C) gross

229)

D) None of the above

Solve the problem. 230) You need a $84,713 loan. Compute the monthly payment for each of the loan options listed below. Assume that the loans are fixed rate. Option 1: a 30 year-loan at an APR of 8% Option 2: a 15-year loan at 7.5% A) Option 1: $633.11 B) Option 1: $630.61 Option 2: $818.68 Option 2: $810.48 C) Option 1: $613.91 D) Option 1: $621.59 Option 2: $763.03 Option 2: $785.30

231) $106 is deposited into a savings account at 4% interest, compounded weekly. To the nearest year, how long will it take for the account balance to reach $440? A) 36 years B) 32 years C) 25 years

230)

231)

D) 50 years

232) In a recent year, the total receipts for the US federal government were $2154 billion. The total

232)

outlays were $2472 billion. The deficit was $318 billion. What would the deficit have been, if there had been a 0.5% increase in total receipts? A) $315 billion B) $311 billion C) $307 billion D) $301 billion

Provide an appropriate response. 233) The ________ in financial formulas is the balance upon which interest is paid. A) principal B) power

C) percentage

D) None of the above

233)

Solve the problem. 234) In a recent year, the total receipts for the US federal government were estimated to be $2288 billion. The total outlays were estimated to be $2613 billion. The table below shows the makeup of federal government outlays in that year- the percentage of total outlays spent in each category.

234)

Approximate makeup of federal government outlays Category Portion of outlays Social security 21% Defense and homeland security 20% Non-defense discretionary 18% Medicare 13% Medicaid, government pensions, and other mandatory spending 20% Interest on debt 8% How much was spent on Medicare that year? A) $357 billion B) $349 billion

C) $340 billion

D) $280 billion

235) In a recent year, the total receipts for the US federal government were $2154 billion. The total

235)

236) You just put $2,483 in a CD that is expected to earn 6% compounded quarterly, and $7,390 in a

236)

outlays were $2472 billion. The deficit was $318 billion. What would the deficit have been, if there had been a 2% decrease in total outlays? A) $269 billion B) $265 billion C) $361 billion D) $259 billion

savings account that is expected to earn 4% compounded semiannually. Determine when, to the nearest year, the values of your two investments will be the same. A) 38 years B) 71 years C) 55 years D) 22 years

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 237) $5,500 deposit at an APR of 5% with monthly compounding for 6 years 237) A) $44,459.93 B) $7,419.60 C) $5,638.94 D) $5,935.68

Solve the problem. 238) Budget Summary for the Wonderful Widget Company (all amounts in thousands of dollars) 2014 2015 2016 2017 Total Receipts $854 $908 $950 $990 Outlays Operating 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus/Deficit -146 -174 -246 -207 Debt (accumulated) -146 -320 -566 -773 Assume that for 2018, total receipts are $1,078,240, operating expenses are $581,794, employee benefits are $166,136, security costs are$124,931, and interest on debt is $63,000. Calculate the outlays for 2018. A) $935,861.00 B) $1,889,170.00 C) $934,792.00 D) $2,014,101.00

238)

Answer the question. 239) You must decide whether to buy a new car for $20,000 or lease the same car over a three-year period. Under the terms of the lease, you make a down payment of $2000 and have monthly payments of $200. At the end of three years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $10,000. Assume you sell the new car at the end of three years at the same residual value. Compare the cost of leasing and buying the car. A) Buy $10,000, lease $9200 B) Buy $11,000, lease $9200

C) Buy $10,000, lease $9400

D) Buy $10,000, lease $8900

Solve the problem. 240) In 2011, a country's government projected total receipts of $2590 billion ($2.590 trillion) and a deficit of $223 billion for 2013. If outlays turn out to be higher than expected by 9% while receipts turn out to be lower by 8%, what would the 2013 surplus or deficit be? A) $683 billion deficit B) $237 billion deficit

C) $681 billion deficit

C) A = P × APR

241)

D) A = P - APR × Y

242) True or False? A discount broker offers advice based on in-depth research. A) True B) False Use the given stock table to answer the question. 243) Based on the fact that stocks historically trade at an average P/E ratio of about 12-14, does the stock price of company ABC seem cheap, about right, or expensive right now? Yld Vol Stock Div % P/E 100s ABC 0.63 2.5 28 4156 XYZ 0.21 1.2 13 9175

A) about right

240)

D) $235 billion deficit

Provide an appropriate response. 241) What is the general form of the compound interest formula for interest paid once a year? A) A = P × APRY B) A = P × (1 + APR)Y

52-Week High Low 33.16 16.74 27.83 12.07

239)

High 25.68 18.17

B) expensive

Low Close 24.87 25.04 17.26 17.39

243)

Net Chg -0.35 +0.09

C) cheap

Solve the problem. 244) Suppose you start saving today for a $11,000 down payment that you plan to make on a condo in 6 years. Assume that you make no deposits into the account after your initial deposit. The account has monthly compounding and an APR of 3.6%. How much would you need to deposit now to reach your $11,000 goal in 6 years? A) $8865.95 B) $8871.66 C) $8721.15 D) $8896.81

245) Suppose your after-tax income is $36,521. Your annual expenses are $31,810 for rent, $5,526 for food and household expenses, $1,249 for interest on credit cards, and $7,842 for entertainment, travel, and other. You expect to get a 25% raise next year. Will this affect the outcome? A) Yes, a raise would create a surplus. B) No, a raise would still create a deficit.

242)

244)

245)

246) Calculate the current yield for a $1,000 Treasury bond with a coupon rate of 4% that has a market value of $850. A) 4.24%

B) 5.18%

C) 4.00%

246)

D) 4.71%

Compute the total and annual returns on the described investment. 247) Five years after buying 200 shares of XYZ stock for $25 per share, you sell the stock for $20,000. A) Total Return: 255.00% B) Total Return: 270.00% Annual Return: 27.16% Annual Return: 28.76% C) Total Return: 315.00% D) Total Return: 300.00% Annual Return: 33.55% Annual Return: 31.95%

247)

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 248) Tom and Toni are married and file jointly. Their combined wages were $129,949. They earned a 248) net of $1,837 from a rental property they own, and they received $1,542 in interest. They contributed $3,351 to their tax-deferred retirement plans, and their itemized deductions total $10,783. Find their taxable income. A) $111,177 B) $104,877 C) $119,194 D) $117,427

Answer the question. 249) You have a choice between going to an in-state college where you would pay $6000 per year for tuition and an out-of-state college where the tuition is $9000 per year. The cost of living is higher at the in-state college, where you can expect to pay $950 per month in rent, compared to $500 per month at the other college. You will pay $1900 per year to travel back and forth from the out-of-state college. Assuming all other factors are equal, which is the less expensive choice on an annual basis? Find the cost of each college for one year. A) In-state $17,700, out-of-state $15,000 B) In-state $17,400, out-of-state $16,900

C) In-state $17,700, out-of-state $16,900

249)

D) In-state $17,400, out-of-state $15,000

Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period. 250) A $30,313 deposit in an account with an APR of 3.6% compounded continuously for 10 years. 250) A) $43,378.60 B) $42,338.77 C) $43,174.41 D) $43,448.51

Solve the problem. 251) Suppose that the federal debt increases at an annual rate of 1.5% per year. Use the compound interest formula to determine the size of the debt in 50 years. Assume that the current size of the debt is $17 trillion. A) $33.3 trillion B) $36.3 trillion C) $35.8 trillion D) $39.3 trillion

252) In a recent year, the total receipts for the US federal government were estimated to be $2288

251)

252)

billion. The total outlays were estimated to be $2613 billion. The table below shows the makeup of federal government outlays in that year- the percentage of total outlays spent in each category. Approximate makeup of federal government outlays Category Portion of outlays Social security 21% Defense and homeland security 20% Non-defense discretionary 18% Medicare 13% Medicaid, government pensions, and other mandatory spending 20% Interest on debt 8% How much was spent on non-defense discretionary outlays that year? A) $523 billion B) $388 billion C) $479 billion

Calculate the amount of interest you'll have at the end of the indicated period. 253) You invest $11,000 in an account that pays simple interest of 2% for 15 years. A) $1,003.20 B) $2,053.14 C) $220.00

D) $470 billion

253) D) $3,300.00

Solve.

254) Calculate the monthly payment for a student loan of $62,204 at a fixed APR of 8% for 15 years. A) $594.45 B) $713.59 C) $892.45 D) $509.41 Provide an appropriate response. 255) For any loan, the ______ is the amount of money owed at any particular time. A) principal B) installment

C) interest

255)

D) None of the above

Find the annual percentage yield (APY). 256) A bank offers an APR of 3.25% compounded semiannually. A) 6.55% B) 1.63% C) 3.28%

256) D) 3.25%

Evaluate or simplify the following the expression. 257) 361/2 ÷ 36-1/2

A) 36

254)

257) C) 6

B) -1

Solve the equation for the unknown quantity. 258) y/20 + 6 = 10 A) -82 B) -80

D) 18

258) C) 80

D) 82

Solve the problem. 259) Suppose the government has a unified net income of -$230 billion, but was supposed to deposit $210 billion in the Social Security trust fund. What was the on-budget surplus or deficit? A) $20 billion surplus B) $440 billion surplus

C) $20 billion deficit

259)

D) $440 billion deficit

Provide an appropriate response. 260) A ______ represents money that is borrowed (or taken from savings) during a single year. A) debt B) deduction

C) deficit

260)

D) None of the above

Solve the problem. 261) You need a $119,100 loan. Compute the monthly payment for each of the loan options listed below. Assume that the loans are fixed rate. Option 1: a 30 year-loan at an APR of 8% Option 2: a 15-year loan at 7% A) Option 1: $873.91 B) Option 1: $886.60 Option 2: $1,070.50 Option 2: $1,106.34 C) Option 1: $890.10 D) Option 1: $863.10 Option 2: $1,118.00 Option 2: $1,038.76

261)

262) Suppose you have a student loan of $100,000 with an APR of 7% for 25 years. If you decide you

262)

263) Suppose that you want to have a $96,180 retirement fund after 35 years. How much will you need

263)

would like to pay off the loan in 10 years instead of 25, how much more will you have to pay each month? A) $464.30 B) $454.30 C) $478.30 D) $470.30

to deposit now if you can obtain an APR of 6%, compounded daily? Assume that no additional deposits are to be made to the account. A) $7,398.93 B) $22,434.78 C) $90,578.92 D) $11,779.89

Evaluate or simplify the following the expression. 264) 22 × 2 6

A) 256

264)

B) 48

C) 68

D) 4096

Solve the problem. 265) In 2013, the United States publicly held debt was $17 trillion. Use the loan payment formula to determine the annual payments needed to pay this debt off in 25 years. Assume an annual interest rate of 5%. A) $1216 billion B) $1206 billion C) $1196 billion D) $1247 billion Provide an appropriate response. 266) True or False? There is high risk for investing money in federally insured bank accounts. A) False B) Ture

265)

266)

Solve.

267) Calculate the monthly payment for a loan of $15,000 at a fixed APR of 8% over a period of 4 years. A) $100.00 B) $428.46 C) $25.00 D) $366.19

267)

Solve.

269) Genevieve is in the 32% tax bracket. George is in the 35% tax bracket. They each itemize their

269)

deductions and they each donate $7,971 to charity. Compute their true costs for charitable donations. A) Genevieve: $5,420.28 B) Genevieve: $2,550.72 George: $5,181.15 George: $2,789.85 C) Genevieve: $5,181.15 D) Genevieve: $2,789.85 George: $5,420.28 George: $2,550.72

Provide an appropriate response. 270) A _______ represents a promise of future cash. A) stock

270) B) return D) None of the above

C) bond

Calculate the balance under the given assumptions. 271) Find the savings plan balance after 3 months with an APR of 4% and monthly payments of $199. A) $509.14 B) $2,571.14 C) $2,185.47 D) $598.99 Prorate the given expenses to find the monthly cost. 272) Sarah takes courses on a quarter system. Three times a year, she takes 15 credits at a tuition rate of $260 per credit; her fees are $190 per quarter and her room in a shared house costs $130 per week. Round your answer to the nearest dollar. A) $1586 B) $1153 C) $904 D) $2251

271)

272)

Provide an appropriate response. 273) True or False? A loan that you pay off with equal regular payments is called an installment loan. A) False B) True

273)

274) ________ is interest paid only on the original principal, and not on any interest added at later

274)

dates.

A) Compound Interest C) Simple interest

B) Basic interest D) None of the above

Solve the problem. 275) Budget Summary for the Wonderful Widget Company (all amounts in thousands of dollars) 2014 2015 2016 2017 Total Receipts $854 $908 $950 $990 Outlays Operating 525 550 600 600 Employee Benefits 200 220 250 250 Security 275 300 320 300 Interest on Debt 0 12 26 47 Total Outlays 1000 1082 1196 1197 Surplus/Deficit -146 -174 -246 -207 Debt (accumulated) -146 -320 -566 -773

275)

Assume that for 2018, total receipts are $1,054,068, operating expenses are $511,646, employee benefits are $220,513, security costs are$124,078, and interest on debt is $63,000. Calculate the outlays for 2018. A) $917,315.00 B) $1,973,305.00 C) $1,849,227.00 D) $919,237.00

Evaluate or simplify the following the expression. 276) 512-1/3

A) 1 4,096

276)

B) 1 24

C) 1 8

D) -8

Solve.

277) Determine the total payment over the term of a home mortgage of $120,000 with a fixed APR of 4% for 30 years. A) $206,243.41

B) $141,509.43

C) $205,623.11

D) $210,352.85

Answer the question. 278) Stephen sets up an IRA with an APR of 5% compounded monthly at age 26. At the end of each month, he deposits $88 in the account. How much will the IRA contain when he reaches 65? Compare that amount to the total amount of deposits made over the time period. A) $90,313.11; this is $55,113.11 more than the total amount of the deposits.

B) $126,725.71; this is $85,541.71 more than the total amount of the deposits. C) $90,696.72; this is $68,598.02 more than the total amount of the deposits. D) $2,411.24; this is $123.24 more than the total amount of the deposits.

277)

278)

Solve the equation for the unknown. 279) x2 - 5 = 20

A) x = ± 5

279) B) x = ± 4

C) x = 4

D) x = 5

Solve.

280) Mike and Carrie are in the 24% marginal tax bracket and claim the standard deduction. How much will their tax bill be reduced if they qualify for a $565 tax credit? A) $765.00 B) $565 C) $135.60

D) $700.60

Solve the equation for the unknown. 281) v3 + 4 = 129

A) v = 1,953,125

280)

281) B) v = 5

C) v = 41.7

D) v = 375

Solve.

282) Denise is in the 12% tax bracket and claims the standard deduction. How much will her tax bill be reduced if she makes a $4,760 contribution to charity? A) $571.20 B) $4,760 C) $0

282)

D) $5,331.20

You need a loan of $100,000 to buy a condo. Calculate your monthly payments and total closing costs for each choice. 283) Choice 1: 30-year fixed rate at 4.25% with closing costs of $1,320 and 1 points 283) Choice 2: 20-year fixed rate at 3.75% with closing costs of $1,320 and 3 points A) Choice 1: $497.36; $2,320 B) Choice 1: $481.74; $2,320 Choice 2: $602.49; $4,320 Choice 2: $542.26; $1,320 C) Choice 1: $501.43; $3,120 D) Choice 1: $491.94; $2,320 Choice 2: $463.16; $5,120 Choice 2: $592.89; $4,320 Determine whether the spending pattern described is at, above, or below the national average. Assume that any salaries or wages are after tax.

284) A single 48-year old man with a monthly salary of $4800 spends $1200 on rent. A) at average B) above average C) below average

284)

Solve the problem. 285) You need a loan of $180,000 to buy a home. You have a choice between a 30-year fixed rate loan at 4% and an ARM with a first-year rate of 2%. Suppose that the ARM rate rises to 7% at the start of the third year. Neglecting compounding and changes in principal, estimate how much extra you will be paying per month during the third year of the ARM over what you would have paid if you had taken the fixed rate loan. A) $420 B) $440 C) $450 D) $430 Provide an appropriate response. 286) True or False? The gross debt represents money the government must repay to individuals and institutions that bought Treasury issues. A) True B) False

285)

286)

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 287) $18,000 is invested at an APR of 3% for 5 years. 287) A) $20,259.16 B) $541.50 C) $2,700.00 D) $20,866.93

Use the given stock table to answer the question. 288) How much profit per share did company ABC earn in the past year? 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s ABC 0.63 2.5 24 4156 XYZ 0.21 1.2 14 9175

A) $1.27

High 25.68 18.17

B) $1.05

Low Close 24.87 25.22 17.26 17.51

C) $1.15

288) Net Chg +0.16 +0.09

D) $1.02

Solve the equation for the unknown. 289) (t/2)2 = 16

A) t = 8

289) B) t = ±8

C) t = 16

D) t = 512

Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 290) Abbey earned $79,545 in wages. Kathryn earned $79,545, all in dividends and long-term capital 290) gains. Calculate the total tax owed by each, including both FICA and income taxes. Assume they are both single and take the standard deduction. Note that long-term capital gains and dividends are taxed at 0% on income less than $40,000 for single taxpayers or $80,000 for married couples filing jointly, 15% on additional income up to $441,500 for single taxpayers or $496,600 for married couples filing jointly, 20% on income above $441,500 for single taxpayers or $496,600 for married couples filing jointly. A) Abbey: $16,573 B) Abbey: $10,487 Kathryn: $5,932 Kathryn: $5,932 C) Abbey: $11,909 D) Abbey: $15,616 Kathryn: $9,932 Kathryn: $8,635

Solve the problem. 291) In a recent year, the total receipts for the US federal government were $2154 billion. The total outlays were $2472 billion. The deficit was $318 billion. What would the deficit have been, if there had been a 0.5% increase in total outlays? A) $320 billion B) $326 billion C) $330 billion D) $307 billion

292) Kerry invests $286 in a savings account that earns 4.2% compounded annually. Andy invests $286 in a savings account that earns 6% compounded annually. How much is in each of their accounts after 10 years and after 20 years? A) Kerry: $397.47; $552.39 B) Kerry: $431.56; $651.21 Andy: $455.84; $726.54 Andy: $512.18; $917.24 C) Kerry: $468.57; $468.57 D) Kerry: $414.17; $624.96 Andy: $575.49; $575.49 Andy: $483.19; $865.32

291)

292)

Solve.

293) Determine how much of the total loan payment applies toward principal and how much applies

293)

toward interest for a student loan of $70,998 at a fixed APR of 5% for 18 years. A) $70,998 pays off the principal and $36,816.23 represents interest payments.

B) $70,998 pays off the principal and $36,796.49 represents interest payments. C) $70,998 pays off the principal and $36,843.86 represents interest payments. D) $70,998 pays off the principal and $36,885.30 represents interest payments. Solve the problem. Refer to the table if necessary. Table 4E.1 2021 Marginal Tax Rates and Standard deductions, by Filing Status Married Married Filing Head of Tax Rate Single Filing Jointly separately Household 10% up to $9950 up to $19,900 up to $9950 up to $14,200 12% up to $40,525 upto $81,050 up to $40,525 up to $54,200 22% up to $86,375 up to $172,750 up to $86,375 up to $86,350 24% up to $164,925 up to $329,850 up to $164,925 up to $164,900 32% up to $209,425 up to $418,850 up to $209,425 up to $209,400 35% up to $523,600 up to $628,300 up to $314,150 up to $523,600 37% above $523,600 above $628,300 above $314,150 above $523,600 Standard $12,550 $25,100 $12,550 $18,800 Deduction *Each higher marginal rate begins where the prior one leaves off. For example, for a single person, the 12% rate applies to income above $9950 (because that is where the 10% rate ends) but below $40,525. 294) Stephen earned $72,007 from wages as an accountant and made $2,337 in interest. Find how much 294) he paid in FICA and income taxes. Assume he is single and takes the standard deduction. If necessary, round values to the nearest dollar. A) $10,188 B) $19,103 C) $14,852 D) $17,627

Answer Key Testname: CHAPTER 4

1) D 2) D 3) A 4) A 5) D 6) C 7) A 8) D 9) C 10) C 11) D 12) Yes, the statement makes sense. With a shorter-term loan, the total amount of interest paid will be less. 13) Yes, the statement makes sense. 14) Month Payment Expenses Interest New Balance 0 $1400 1 $500 $180 $21.00 $1101.00 2 $500 $180 $16.52 $797.52 3 $500 $180 $11.96 $489.48 4 $500 $180 $7.34 $176.82 A partial 5th payment will pay off the loan.

15) The average person spends about 33% of their budget on housing. If Paul spends $1100 in rent he will be spending

50% of his budget on rent. This is a large proportion of his income and he wouldn't have much left over for other expenses. 16) Yes, this statement makes sense. 17) Yes, the statement makes sense. If his money is invested for one year only, compounding the interest annually offers no advantage over simple interest and Raul should choose the account with the higher interest rate. In a year his money would grow 5% in the simple interest account or 4.6% in the compound interest account. 18) No, the statement does not make sense. After 6 years, less than one fifth of the principal will have been paid. Early payments on a mortgage tend to be almost entirely interest. As time goes by, a larger portion of the payments goes towards principal. 19) Yes, the statement makes sense. Over such a long time period, the compounding of interest will more than compensate for the lower interest rate and the account offering an APR of 5% compounded annually will be the better deal. 20) No, the statement does not make sense. The extra amount she will end up owing after three months will be more than $315. She is neglecting that the interest is compounded daily. Also at the end of each month she will be charged a late fee which will be added to the balance. Interest will then accrue on the late fees as well. 21) Yes, this is possible. Sue's bank must be compounding the interest more frequently which means that she gets a higher annual percentage yield than Pat. 22) No, the statement does not make sense. Historically, there have been 6-year periods in which the Dow ended lower than it started, for example the period January 2000 to January 2006. Even if the Dow had never before ended lower than it started over a 6-year period, there is no guarantee that this couldn't happen in the future. 23) No, this statement does not make sense. The federal debt was about 9 trillion dollars at the end of 2005, but the deficit for the year 2005 was about $319 billion.

Answer Key Testname: CHAPTER 4

24) No, the statement does not make sense. The monthly payments will be higher but much less than twice as much. With

a shorter-term loan, the total amount of interest paid over the term will be less. So the total amount of all payments will be much less if the loan is paid off in 8 years instead of 16. 25) No, the statement does not make sense. Only the part of the mortgage payment that goes towards interest can be deducted, not the whole of the mortgage payment. 26) Gabe is right. The government has been able to pay Social Security benefits these last years because currently it collects more in Social Security taxes than it pays out in Social Security benefits. It is supposed to invest the excess into the Social Security trust fund but the government has to date borrowed every penny that it ever deposited into the fund. Payment Toward End of... Interest Principal New Principal 27) Month 1 $962.65 $96.89 $144,300.11 Month 2 $962.00 $97.53 $144,202.58 Month 3 $961.35 $98.18 $144,104.40 28) No, the statement does not make sense. It is hard to predict what will happen to interest rates over a 30-year period. It is very risky to take an ARM that has no rate cap. 29) In fact it is the mango smoothies that are making the biggest dent in this person's budget. They are costing roughly $5 × 365 = $1825 per year, more than the vacation which costs $1100. The movies cost only $15 × 52 = $780 per year. 30) If these projections are correct, it is true that the government will need to redeem about $900 billion in 2040. However, it won't be able to accomplish this simply by cutting discretionary spending, the amount is much too large. 31) It is true that there will be a problem when the government has to pay out more in Social Security benefits than it collects in Social Security taxes. However this will probably happen in Sally's lifetime. 2040 is the year when intermediate projections say that the Social Security trust fund will go bankrupt.

32) Month 0 1 2 3 4

Payment $200 $100 $300 $250

Expenses Interest $120 $8.50 $310 $7.28 $60 $10.98 $180 $7.08

Balance $500 $428.50 $645.78 $416.76 $353.84

33) No, the statement does not make sense. Bill will not pay 15% on the whole of his taxable income.

He will pay 10% on the first part of his income (the exact threshold varies from year to year) and 15% on the remaining amount. 34) No, the statement does not make sense. It is true that Juan won't have to pay any income tax, but he will have to pay FICA tax. The FICA tax is paid on the whole income (15.3% for self-employed people) without any deductions or exemptions. 35) No, the statement does not make sense. Due to inflation, the buying power of $15,000 will decrease over time. As the years go by, the amount that Paul needs to live on per year will increase, and $15,000 per year will no longer be enough. 36) No, this statement does not make sense. The government first tries to cover the deficit by borrowing from its trust funds before it borrows money from the public. 37) Yes, this statement makes sense. 38) No, this statement does not make sense. The federal debt was about 9 trillion dollars at the end of 2005, but the deficit for the year 2005 was about $319 billion.

Answer Key Testname: CHAPTER 4

Payment Toward End of... Interest Principal New Principal 39) Month 1 $268.50 $204.85 $45,824.15 Month 2 $267.31 $206.05 $45,618.10 Month 3 $266.11 $207.25 $45,410.86 40) It is true that there will be a problem when the government has to pay out more in Social Security benefits than it collects in Social Security taxes. However this will probably happen in Sally's lifetime. 2040 is the year when intermediate projections say that the Social Security trust fund will go bankrupt. 41) No, the statement does not make sense. If both accounts are paying the same APR, the account which compounds interest daily will have a higher annual percentage yield than the account which compounds weekly. 42) Yes, the statement makes sense. Stocks are high-risk investments which offer the potential of higher returns along with the possibility of losing part or all of your principal. 43) No, the statement does not make sense. Jose is not taking into consideration the savings on repairs that he would have to make on his old car. He probably won't have to spend money on repairs for the new car for quite some time. He is also not taking into consideration the trade-in value of his old car. 44) If these projections are correct, it is true that the government will need to redeem about $900 billion in 2040. However, it won't be able to accomplish this simply by cutting discretionary spending, the amount is much too large. 45) Gabe is right. The government has been able to pay Social Security benefits these last years because currently it collects more in Social Security taxes than it pays out in Social Security benefits. It is supposed to invest the excess into the Social Security trust fund but the government has to date borrowed every penny that it ever deposited into the fund. 46) This is possible. At the end of 2005, the federal debt was about $9 trillion. If this were divided among the roughly 300 million citizens of the United States, each person's share would be about $30,000. 47) No, the statement does not make sense. It is true that bonds are less risky than stocks, however with bonds there is still a chance of losing part or all of the principal. 48) No, this statement does not make sense. The government first tries to cover the deficit by borrowing from its trust funds before it borrows money from the public. 49) No, the statement does not make sense. The monthly payment required in order to end up with $100,000 in 20 years would be much less than $500 even if the APR were fairly low. For example, using an APR of 5%, a monthly payment of $243 would be sufficient to build a college fund of $100,000 in 20 years. 50) No, the statement does not make sense. This is a tax credit not a tax deduction. A tax credit of $500 will reduce Sam's total tax bill by the full $500. 51) No, the statement does not make sense. The yield will be higher at Daily Bank since the interest is compounded more frequently - more frequent compounding means a higher yield. 52) Yes, the statement makes sense. The interest part of the monthly mortgage payment is tax deductible. The amount of savings from this tax deduction depends on the person's tax bracket. Gale must be in a higher tax bracket than her brother which means that she has more of a tax saving from the mortgage deduction. This means that it is more worthwhile for her to buy than it is for her brother. 53) Yes, the statement makes sense. If both accounts are paying the same APR, the account which compounds interest more frequently will have a higher annual percentage yield. 54) No, the statement does not make sense. When interest is compounded, the annual return cannot be obtained by dividing the total return by the number of years. An APY of 7% for 10 years would have given an accumulated amount of P(1 + 0.07)10 which comes to 1.97P, a total return of 97% not 70%. In fact, the annual return corresponding to a total return of 70% over 10 years would be 1.7 1/10 - 1 which comes to 5.4%. 55) This is possible. At the end of 2005, the federal debt was about $9 trillion. If this were divided among the roughly 300 million citizens of the United States, each person's share would be about $30,000.

Answer Key Testname: CHAPTER 4

56) Yes, the statement makes sense. Maria and her sister must be in different tax brackets. Maria must be in the 24% tax

bracket so the tax deduction of $3000 saves her 0.24 × $3000 = $720. Her sister must be in the 12% tax bracket so she saves only 0.12 × $3000 = $360. 57) No, the statement does not make sense. It is more important for Jeremy to pay off his credit card debt before investing any money in a savings account. The interest rate on his savings account is likely to be much less than 21.5% per month. He will save more by using the money to pay off part of his credit card debt and reducing his interest payments on his credit card. 58) No, the statement does not makes sense. The annual percentage yield would be equal to 7% if the interest were compounded annually or more than 7% if the interest were compounded more frequently. The annual percentage yield cannot be less than the APR of 7%.

59) D 60) D 61) B 62) C 63) B 64) B 65) A 66) A 67) B 68) B 69) B 70) A 71) B 72) A 73) B 74) C 75) A 76) C 77) C 78) D 79) A 80) C 81) A 82) B 83) C 84) A 85) C 86) A 87) C 88) A 89) D 90) C 91) B 54

Answer Key Testname: CHAPTER 4

92) D 93) A 94) C 95) B 96) B 97) C 98) B 99) D 100) C 101) A 102) C 103) C 104) A 105) D 106) D 107) D 108) C 109) B 110) A 111) B 112) D 113) A 114) B 115) A 116) B 117) D 118) C 119) C 120) D 121) C 122) D 123) A 124) A 125) B 126) C 127) C 128) B 129) D 130) C 131) A 132) C 133) C 55

Answer Key Testname: CHAPTER 4

134) B 135) C 136) C 137) C 138) D 139) A 140) B 141) A 142) A 143) D 144) C 145) B 146) B 147) A 148) B 149) A 150) A 151) B 152) B 153) D 154) D 155) B 156) B 157) B 158) B 159) A 160) D 161) B 162) C 163) C 164) B 165) D 166) B 167) A 168) C 169) D 170) B 171) A 172) D 173) B 174) A 175) D 56

Answer Key Testname: CHAPTER 4

176) D 177) B 178) D 179) A 180) C 181) A 182) B 183) A 184) B 185) B 186) C 187) B 188) B 189) D 190) B 191) D 192) B 193) C 194) B 195) B 196) B 197) C 198) C 199) D 200) C 201) B 202) D 203) B 204) B 205) C 206) A 207) A 208) C 209) D 210) D 211) C 212) D 213) A 214) D 215) A 216) A 217) D 57

Answer Key Testname: CHAPTER 4

218) B 219) B 220) A 221) D 222) C 223) B 224) C 225) D 226) B 227) C 228) D 229) C 230) D 231) A 232) C 233) A 234) C 235) A 236) C 237) B 238) A 239) A 240) A 241) B 242) B 243) B 244) A 245) A 246) D 247) D 248) B 249) B 250) D 251) C 252) D 253) D 254) A 255) A 256) C 257) A 258) C 259) D 58

Answer Key Testname: CHAPTER 4

260) C 261) A 262) B 263) D 264) A 265) B 266) A 267) D 268) D 269) A 270) C 271) D 272) A 273) B 274) C 275) D 276) C 277) A 278) B 279) A 280) B 281) B 282) C 283) D 284) C 285) C 286) B 287) D 288) B 289) B 290) A 291) C 292) B 293) A 294) C

Exam

Chapter 5

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau. Annual Growth Rate (Percentage)

Use the graph to answer the question. 1) How does world population in 1978 compare to world population in 1977? A) It is 1.75% greater B) It is 1.75 million greater

C) It is 1.75% less

D) It is the same

The graph below shows estimated world population for the period 4000 BC - 2000 AD. Note that the logarithm of the world population and not actual population is plotted on the vertical axis. This means, for example, that when the graph reaches 7 on the vertical scale, world population is 107 and when the graph reaches 9 on the vertical scale, world population is 109 .

Log World Population

Year Use the graph to answer the question. 2) Describe the general trend in world population during the period 2000 BC to the year 1 AD.

A) World population increases at a faster and faster rate. B) World population is constant. C) World population increases at a slower and slower rate. D) World population increases at a constant rate. In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 3) Do Super-Slimmer Shakes increase weight loss? 3) A) Observational study

B) Experiment without blinding C) Case-control study D) Experiment with single blinding E) Experiment with double blinding Answer as requested. 4) Which of the following is likely a coincidence? A) Higher annual rainfall in states with fewer homicides

B) Higher incidence of skin cancer in regions with more sunshine C) Higher real estate prices in cities with more employment opportunities D) More crime in neighborhoods with fewer streetlights

Answer the question. 5) Which of the following describes the process by which scientists examine each others' research? A) Peer review B) Participation review

C) Interpretation

D) Considering the conclusion

The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau. Annual Growth Rate (Percentage)

Use the graph to answer the question. 6) In which year during the period 1960-2010 is estimated world population the greatest? A) 1970 B) 1960 C) 1963 D) 2010

Choose the best wording for the question in the study. 7) A recent magazine article determined that the Gemini is the most popular car on the road. A TV journalist decided to check the accuracy of the article by conducting a survey. Which of the following survey questions will give the journalist the most accurate results? A) What kind of car do you recall seeing most often on the highway?

B) What do you think is the most popular car on the road? C) What kind of car do you drive? D) Do you agree that the Gemini is the most popular car on the road? Answer the question. 8) Which of the following describes a study in which the patients do not know whether they are receiving the treatment or the placebo but the experimenters do know? A) Single-blind experiment B) Case-control study

C) Double-blind experiment

D) Observational study

The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau. Annual Growth Rate (Percentage)

Use the graph to answer the question. 9) In which year(s) during the period 1960-2010 is world population growing at the fastest rate? A) 1963-1964 B) 1984 C) 1970 D) 2010

Answer the question. 10) Which of the following quantities of interest would be the most difficult to measure? A) The best looking team member

10)

B) The team member with the longest hair C) The team member with the highest salary D) The average height of a volleyball team 11) Which of the following describes a study in which neither the participants nor the experimenters know which participants are in the control group? A) Single-blind experiment

11)

B) Case-control study D) Observational study

C) Double-blind experiment

Choose the best wording for the question in the study. 12) In a survey to assess attitudes toward genetically modified foods, which of the following survey questions will give the most accurate results? A) How do you feel about allowing untested genetically modified foods to be sold in stores?

B) Do you agree with increasing the production of genetically modified foods which could be

harmful to the environment? C) Do you agree with increasing the production of genetically modified foods to increase the world food supply? D) How do you feel about genetically modified foods?

12)

Answer as requested. 13) Which of the following is likely the result of some common underlying cause rather than a direct cause? A) The more cash I take out at the ATM, the more my account balance decreases.

13)

B) The more items sold, the greater the revenue. C) When the NASDAQ rises, the Dow Jones Industrial Average also tends to rise. D) People who eat a lot of dessert tend to be heavier than those who don't. Answer the question. 14) Double blinding is used in an experiment to avoid which of the following problems? A) If improvement is observed in a patient, it is difficult to know whether this is due to the treatment or the placebo effect B) If the researcher knows that the patient received the treatment, the researcher may also experience health changes C) If an experimenter knows whether the patient has received the treatment or the placebo, this may influence how he or she questions the patient D) If the patient knows that he received the placebo and not the treatment he may be angry and fail to tell the truth

14)

In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 15) How do lawyers' salaries compare to doctors' salaries? 15) A) Experiment with double blinding

B) Observational study C) Experiment without blinding D) Experiment with single blinding E) Case-control study Answer the question. 16) Which of the following describes a study in which the researchers do not attempt to change the characteristics of those being studied? A) Double-blind experiment B) Case-control study

C) Single-blind experiment

16)

D) Observational study

17) Which of the following is not an argument against using blinding in an experiment? A) The experiment is done on plants, not people B) It would be impossible to conceal from the participants whether they are receiving the treatment or the placebo C) The experiment involves animals, not people

D) The participants in the experiment don't believe in the placebo effect

17)

Choose the best wording for the question in the study. 18) A researcher wants to determine the level of support for the war. Which of the following questions would produce the most accurate results? A) How do you feel about the war?

18)

B) Do you support the troops? C) Do you agree that the troops should be brought home to safety now? D) Do you agree that it is important to defend our country against terrorism? Answer as requested. 19) In studying the relationship between abortion and breast cancer, researchers have identified a hormone that they believe explains how having an abortion can lead to breast cancer. This explanation is an example of which of the guidelines for establishing causality? A) An experiment to establish causality between abortion and breast cancer.

19)

B) Evidence that larger amounts of the suspected cause produce larger amounts of the effect. C) A physical model demonstrating how abortion can cause breast cancer D) Verification that breast cancer rates differ among groups that differ only in the presence or absence of the suspected cause (abortion).

20) Which of the following pairs of variables is likely to have no correlation? A) The unemployment rate and the number of home foreclosures B) The amount of rainfall and the height of the grass C) The annual rainfall in Tempe, Arizona and the annual cost of tuition at Yale University D) The amount of time studying math and grade on a math test

20)

Log World Population

Year Use the graph to answer the question. 21) How does world population in the year 1000 AD compare with world population in the year 2000 BC?

21)

A) The 1000 AD population is roughly ten million larger than the 2000 BC population. B) The 1000 AD population is roughly ten times as large as the 2000 BC population. C) The 1000 AD population is roughly one million larger than the 2000 BC population. D) The 1000 AD population is roughly 14% larger than the 2000 BC population. Answer the question. 22) Which of the following study results implies that there is a problem with the quality of education at Rydell High? A) 30% of the senior class scored above average on the writing portion of a national aptitude test. B) 25% of the senior class scored below average on the math portion of a national aptitude test.

22)

C) 53% of the senior class was accepted for admission to Valley State College in the fall. D) 83% of the seniors who applied for admission to Valley State College were accepted. 23) Which of the following describes the bias that occurs when researchers select their sample in such a way that it is unlikely to be representative of the population? A) Availability bias B) Double-blind bias

C) Selection bias

D) Participation bias

23)

Choose the best wording for the question in the study. 24) Proposition EZ proposes to raise the state sales tax by one quarter of a percent. The proceeds will be earmarked for music education in the public schools. If you want to determine whether or not it will pass, which of the following survey questions will give you the most accurate results? A) Do you believe that music education is important?

24)

B) Are you planning to vote for Proposition EZ which will raise state sales taxes and support

music education? C) Will you vote for proposition EZ which will raise the amount of state sales tax that you pay every year? D) Do you know which proposition will raise state sales tax and fund music education?

Answer the question. 25) Which of the following describes a study in which the participants naturally form groups by choice? A) Observational study B) Single-blind experiment

C) Double-blind experiment

25)

D) Case-control study

26) A researcher wishes to determine the percentage of voters in a town who favor stronger

26)

environmental laws. Which of the following would be the most representative sample? A) A sample of listeners who call in to a radio talk show

B) A random sample of college students C) A sample consisting of every 10th person leaving an organic food store D) A sample selected randomly from the phone book 27) In a study to determine the most popular automobile on the road, which of the following is the

27)

most representative sample? A) A random sample of the cars driving on the highway

B) A random sample of the cars parked at a local high school C) A random sample of the cars parked at an airport D) A random sample of the cars that drive by your house Answer as requested. 28) Suppose that there is perfect positive correlation between the number of hours studied for a test and score on the test. Which of the following statements must be true? More than one statement may be true. A: If we know the number of hours a given student studied, we will be able to perfectly predict their test score. B: If Anne studied twice as long as Manuel, she will score twice as much. C: If Lu Yi studied ten hours more than Andrea, Lu Yi will score ten points more than Andrea. D: All data points lie perfectly on a horizontal line. A) B and C B) All statements are true

C) A

D) A and D

28)

29) Which of the following is not a guideline for establishing causality? A) If possible, test the suspected cause with an experiment. B) Find a physical model that explains how the cause produces the effect. C) Consider only the suspected cause, ignoring other potential causes. D) Seek evidence that larger amounts of the cause produce larger amounts of the effect.

29)

In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 30) Does the new medication relieve depression? 30) A) Experiment with single blinding

B) Experiment without blinding C) Experiment with double blinding D) Observational study E) Case-control study The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau. Annual Growth Rate (Percentage)

Use the graph to answer the question. 31) Describe the trend in world population during the period 1976-1978 A) It remains constant B) It increases at a steady rate

C) It increases at a faster and faster rate

D) It decreases at a steady rate

31)

B) Experiment with double blinding C) Experiment without blinding D) Case-control study E) Experiment with single blinding Answer the question. 33) Which of the following quantities of interest would be the most difficult to measure? A) The crop with the largest tomatoes B) The levels of pesticides in a tomato crop

C) The largest crop of tomatoes

33)

D) The best tasting tomato crop

In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 34) Can acupuncture relieve anxiety? [The level of anxiety at any given time will be determined by 34) interviewing the patient. The interviewer will be a person other than the acupuncturist.] A) Experiment with single blinding

B) Experiment with double blinding C) Case-control study D) Experiment without blinding E) Observational study Choose the best wording for the question in the study. 35) A researcher wishes to determine the level of support for a new environmental law. Which of the following questions will produce the most accurate results? A) How do you feel about this latest new environmental law?

35)

B) Are you in favor of the new environmental law which will improve the quality of our air? C) Are you in favor of the new environmental law which will cost taxpayers ten million dollars?

D) How do you feel about the new environmental law? In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 36) Are short women more likely to develop breast cancer than tall women? 36) A) Experiment without blinding

B) Experiment with double blinding C) Observational study D) Experiment with single blinding E) Case-control study

The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau. Annual Growth Rate (Percentage)

Use the graph to answer the question. 37) Describe the trend in world population during the period 1990-2000 A) It increases at a steady rate B) It decreases at a steady rate

C) It decreases at a faster and faster rate

37)

D) It increases at a slower and slower rate

Answer the question. 38) Which of the following quantities of interest would be the most difficult to define? A) The levels of lead in various brands of paint

38)

B) The paint with the best looking finish C) The least expensive brand of paint D) How water resistant a brand of paint is Answer as requested. 39) Which of the following pairs of variables is likely to have a negative correlation? A) The unemployment rate and the number of homeless people

39)

B) The price of jet fuel and the price of airline tickets. C) Height and weight. D) Interest rates and the number of real estate transactions 40) Which of the following is likely a cause-and-effect relationship? A) When the temperature drops, consumption of heating oil rises. B) When I drive to work, the sun rises. C) When I see stars, I also see the moon. D) When the rooster crows, the morning glories open.

40)

Answer the question. 41) Which of the following describes the bias that can occur when members of a study's sample are volunteers? A) Sample bias B) Participation bias

C) Single-blind bias

41)

D) Selection bias

Answer as requested. 42) Which of the following best describes our level of confidence in causality when we have discovered a correlation but cannot yet determine whether the correlation implies causality? A) Probable cause B) Absolute certainty

C) Possible cause

42)

D) Cause beyond reasonable doubt

In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 43) What percentage of the population reads a newspaper on a regular basis? 43) A) Observational study

B) Experiment with single blinding C) Case-control study D) Experiment without blinding E) Experiment with double blinding Answer the question. 44) In a study to determine the average weight of a house cat, which of the following is the most representative sample? A) Some of the cats in each of several neighborhoods

44)

B) All of the cats in your neighborhood C) All of the cats that a pet groomer sees in one week D) All of the cats that a veterinarian sees in one week In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 45) Does smoking elevate blood pressure? 45) A) Observational study

B) Experiment without blinding C) Case-control study D) Experiment with double blinding E) Experiment with single blinding

The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau. Annual Growth Rate (Percentage)

Use the graph to answer the question. 46) Describe the trend in world population during the period 1960-1962 A) It remains constant B) It increases at a constant rate

C) It increases at a faster and faster rate

46)

D) It decreases at a steady rate

47) In which year(s), if any, during the period 1960-2010 is world population constant? A) 1962-1964 B) 1962-1964, 1969-1971, 1975-1980 C) None D) 1969-1971 Choose the best wording for the question in the study. 48) If you wanted to determine if your customers are satisfied with the selection in your store, which of the following survey questions would give you the most accurate results? A) Are you satisfied with the selection at this store?

B) Is there anything you would have purchased if our stock was not without it? C) Is our selection as good as the selection of our competitor? D) Do you agree that our selection is better than our competitor?

47)

48)

Log World Population

Year Use the graph to answer the question. 49) During the period 4000 BC to 1000 BC, approximately what was the doubling time for world population?

A) Approximately 1000 years C) Approximately 5000 years

49)

B) Approximately 3000 years D) Approximately 23,000 years

Answer the question. 50) Which of the following quantities of interest would be most difficult to determine? A) The percentage of second graders who read above grade level

50)

B) The percentage of children who brush their teeth at least twice a day C) The number of children living below the poverty line D) The number of children not counted in the last census In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 51) Does an hour of meditation per day lower blood pressure? 51) A) Experiment without blinding

B) Case-control study C) Experiment with double blinding D) Experiment with single blinding E) Observational study

Choose the best wording for the question in the study. 52) A recent newspaper article stated that Snazzy's is the most popular restaurant in the city. The city council decided to sponsor its own survey to determine the accuracy of the article. Which of the following survey questions will give the most accurate results? A) Do you agree that Snazzy's is the most popular restaurant in the city?

52)

B) Which restaurant do you think is the most popular in the city? C) Which restaurant in the city do you think is the most crowded? D) Which restaurant in the city do you visit most often? Answer the question. 53) A poll is taken of likely voters the day before the mayoral election in the town of Ingleside. The poll reveals that 54% of voters plan to vote for Anne Sanchez. The margin of error is 3.9 percentage points. Which of the following statements best describes Anne Sanchez's chance of winning? A) It is about 50-50 B) She has a 54% chance of winning

C) She is certain to win

53)

D) She is very likely to win

In order to answer the given question, which of the following types of study would be the most appropriate: an experiment without blinding, an experiment with single blinding, an experiment with double blinding, an observational study, or a case-control study? 54) In which of these four soil types will the plants grow fastest? 54) A) Observational study

B) Experiment without blinding C) Experiment with single blinding D) Case-control study E) Experiment with double blinding Answer as requested. 55) A researcher finds a positive correlation between the amount of wine people drink and the number of friends they have. Which of the following statements must be true? More than one statement may be true. A: People who drink more tend, on average, to have more friends. B: If a person starts drinking more wine, they are likely to find themselves with more friends. C: If a person stops drinking wine, they are likely to find themselves with fewer friends. D: If Anna has more friends then Pierre, she must drink more wine than Pierre. A) A and D B) B and C C) A D) A and B

55)

Log World Population

Year Use the graph to answer the question. 56) How does world population in the year 2000 AD compare with world population in the year 4000 BC?

56)

A) The 2000 AD population is roughly three billion larger than the 4000 BC population. B) The 2000 AD population is roughly one thousand times as large as the 4000 BC population. C) The 2000 AD population is roughly thirty times as large as the 4000 BC population. D) The 2000 AD population is roughly 44% larger than the 4000 BC population. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Describe how you would apply the five basic steps of a statistical study to the given issue. 57) As an executive of a large software company, you want to know whether there has been an increase in levels of stress amongst your employees.

57)

Provide an appropriate response. 58) Shortly before an election, a market research firm took a poll to find out whether people were planning to vote for or against a particular ballot measure. The results are shown below.

58)

Position Frequency Against 3087 In favor 3691 Undecided 910 The ballot measure will pass if a simple majority (more than 50%) vote in favor of the measure. You wish to construct a graph to represent the data. It should be easy to see from your graph whether more than 50% of the people are planning to vote in favor of the measure. Which graph would be more useful, a bar graph or a pie chart? Explain your thinking.

Use the graph to answer the question. 59) This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period.

59)

Compare the trend in the number of male athletes during the four-year period and the trend in the number of female athletes during the four-year period .

Describe how you would apply the five basic steps of a statistical study to the given issue. 60) You want to know the percentage of adults in the U.S. who have ever sought treatment from a practitioner of complementary medicine.

60)

Make a bar graph to represent the data. 61) The table lists the winners of the Wimbledon women's singles title for the years 1976-1995. Construct a vertical bar graph for the given relative frequencies. Winner

Frequency

C. Evert V. Wade M. Navratilova C. Martinez S. Graf E. Goolagong

61)

Relative frequency

2 1 9 1 6 1

0.10 0.05 0.45 0.05 0.30 0.05

Use the indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 62) The weekly incomes (in dollars) of 20 college students are shown below. 62) 120 178 90 74

180 215 144 136

240 268 336 85

330 0 116 165

165 305 0 62

Use 50-point bins (0-49, 50-99, etc)

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 63) An educational researcher wishes to compare the effectiveness of two different math textbooks. She has the tenth graders at one school use the first book for one year and the tenth graders at another school use the second textbook for one year. At the end of the year, she gives the same math test to both classes and compares the results. Answer the question. 64) The mayor of one city has been conducting an anti-smoking campaign in high schools. Each year local government researchers estimate the number of teenagers in the city who smoke. The number of smokers has declined steadily in each of the past five years. The mayor's office constructs a bar graph showing the number of teenage smokers in each of the past five years. If the mayor wished to exaggerate the success of his anti-smoking campaign, would it be to his advantage to truncate the bar graph? Explain your thinking. Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 65) An acupuncturist notes that after a month of acupuncture 80% of her patients who had been suffering from depression are feeling better. The acupuncturist determines the level of depression by interviewing the patients at the beginning of the month and at the end of the month. She concludes that acupuncture has an 80% success rate in relieving depression. Describe how you would apply the five basic steps of a statistical study to the given issue. 66) You want to know the average amount paid in rent by tenants of the city of Hazelwood.

63)

64)

65)

66)

Construct the specified histogram. 67) In a survey, 20 voters were asked their age. The results are summarized in the frequency table below. Construct a histogram . Age 20-29 30-39 40-49 50-59 60-69

67)

Number of voters 5 5 6 0 4

Solve the problem. 68) A researcher finds a positive correlation between the amount of coffee people drink and anxiety level. Can you conclude that drinking coffee causes anxiety? Propose other explanations for the correlation. Suggest some ways that the researcher could go about establishing causality. Refer to the six guidelines for establishing causality.

69) A researcher finds a negative correlation between blood pressure and the number of

68)

69)

vacations that people take. Can you conclude that taking vacations lowers blood pressure? Propose other explanations for the correlation. Suggest some ways that the researcher could go about establishing causality. Refer to the six guidelines for establishing causality.

Answer the question. 70) Andrew creates a bar graph to show the increase in his company's sales. He wants to show the milestones - years in which sales reached 10 million, 20 million, 30 million, 40 million, and 50 million dollars respectively. The data are shown in the table below: Year Sales (millions of dollars) 1975 10 1985 20 1993 30 1999 40 2003 50

In the graph, Andrew draws 5 equally spaced bars of heights 1 in, 2 in, 3 in, 4 in, and 5 in respectively. The height of each bar corresponds to the amount of sales. He labels each bar with the corresponding year (1975, 1985, 1993, 1999, 2003 respectively). Why is the graph misleading?

70)

Provide an appropriate response. 71) Suppose that you want to construct a pie chart to represent the following data.

71)

Blood Type Frequency O 90 A 84 B 18 AB 8 Explain how you would calculate the angle for the pie-shaped piece corresponding to the blood type O.

Describe how you would apply the five basic steps of a statistical study to the given issue. 72) You want to know the percentage of college seniors who regret their choice of major. Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 73) A researcher randomly selects 300 adults from the city of Kentwood by using a random number generator and a list of residents of the town. She calls the people in the sample and asks the following question: "Do you agree that more of the city's budget should be spent on social services for the poor? " She announces that 54% of the people in Kentwood feel that more of the city's budget should be spent on social services for the poor.

74) A researcher from an environmental group wishes to gauge political sentiment regarding

72)

73)

74)

a proposed environmental law. He obtains a list of 1000 email addresses from an internet provider, uses a random number table to select a random sample of 100 of these addresses, emails the people in the sample asking them "How do you feel about the proposed environmental law which will improve the quality of our air?" He requests that people respond to his question by email. After the study he announces that 72% of Americans are in favor of the new environmental law.

Solve the problem. 75) A researcher finds a positive correlation between the number of vaccinations and the incidence of autism. Can you conclude that vaccinations can cause autism? Suggest some ways that the researcher could go about establishing causality. Refer to the six guidelines for establishing causality. Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 76) A researcher is interested in why Americans have such a high divorce rate. She randomly selects 100 American married couples and 100 Japanese married couples. She invites each couple to come into her office and interviews each couple, asking them about their satisfaction with their marriage. The researcher also notes that a high percentage of the American women had full time jobs outside the home, whereas a high percentage of the Japanese women did not have full time jobs. The researcher concluded that marriages in which the woman has a full time job have a lower rate of success.

75)

76)

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 78) The host of a conservative talk show asked his listeners to respond to the following question: "Do you think that environmental laws which restrict growth should be weakened?" Twenty people responded, and the next day the talk show host announced that the results of his survey suggested that 76% of Americans feel that environmental laws should be weakened.

78)

Use the indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 79) On a math test, the scores of 24 students were as follows: 79) 99 78 77 66 77 77 99 87 77 68 89 78 78 89 77 78 89 77 78 87 78 89 87 66 Use ten-point bins (60-69, 70-79, etc)

80) The ages of 25 patients who suffered strokes are as follows. 69 50 77 47 61

72 57 58 53 66

46 61 74 60 55

81 48 73 58 79

45 56 80 46 84

Use 5-point bins ( 45-49, 50-54, etc)

80)

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 81) A documentary which appeared on a TV station owned by a large biotech company announced that 77% of Americans are in favor of genetically modified foods. The researcher for the documentary had conducted a telephone poll of 200 people selected randomly from the phone book. Each person in the sample had been asked "Are you in favor of increasing the production of genetically modified foods in order to increase the world food supply?"

82) A TV show announced that their survey had revealed that 87% of Americans would

81)

82)

rather be free than rich.

Describe how you would apply the five basic steps of a statistical study to the given issue. 83) As a marketing executive for a computer company you wish to determine the average length of time that owners of personal computers in the U.S. keep a computer before buying a newer model. Answer the question. 84) A television manufacturer sold three times as many televisions in 1995 as it did in 1985. To illustrate this fact, the manufacturer draws a pictogram as shown below. The television on the right is three times as tall and three times as wide as the television on the left.

Why is this pictogram misleading? What visual impression is portrayed by the pictogram?

83)

84)

Make a bar graph to represent the data. 85) The following table shows the number of male infants born at Hospital X on New Year's Day (Jan. 1). Create a horizontal bar graph.

85)

No. of Male Year Infants Born on Jan 1 1950 12 1951 28 1952 20 1953 32 1954 20 1955 20

Construct the specified histogram. 86) 30 police detectives were asked how many days they had taken off in the previous year. The results are summarized in the frequency table below .

86)

Days off Frequency 0- 1 10 2 -3 1 4-5 7 6-7 7 8-9 1 10 -11 4 Construct a histogram.

Describe how you would apply the five basic steps of a statistical study to the given issue. 87) You want to know the average volume of juice in your company's 500 mL bottles of orange juice.

87)

Use the graph to answer the question. 88) The following time-series diagram tracks the performance of two stocks during the month of October.

88)

Describe the overall trend in the value of each stock during the month of October. By what percentage did the value of each stock increase or decrease during the month of October?

89) The bar graph below shows the relative frequencies of the different blood types. Write a

89)

sentence describing what is revealed by the graph.

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 90) The principal of Laney High School interviews all the seniors at his school and asks them whether they have ever used drugs. The principal of Little Heath High School interviews all the seniors at her school and asks them whether they have ever used drugs. The results suggest that Laney has a lower rate of drug use. A researcher concludes that the counseling program available at Laney High School is effective in lowering drug use.

90)

Make a bar graph to represent the data. 91) The following table shows the number of inches of rainfall measured at City X during the following days. Create a horizontal bar graph.

Day April 7 April 22 May 7 May 22 June 7 June 22

91)

No. of Inches of Rainfall 0.63 0.97 1.63 1.27 1.01 0.93

Use the graph to answer the question.

92)

Mike decides to buy shares of companies A, B, and C, which were initially selling for the same price. The changes in each stock's value are shown in the graph above. Could Mike ever have made a profit off stock A if he had sold at the right time? If so, when should he have sold to make the maximum profit? Answer the same questions for stocks B and C.

Provide an appropriate response. 93) Construct a frequency table and the corresponding histogram in which the following conditions are satisfied: - The frequency for the second class is twice the frequency of the first class - In the histogram, the area of the bar corresponding to the second class is four times the area of the bar corresponding to the first class

93)

Make a bar graph to represent the data. 94) Construct a vertical bar graph for the relative frequencies given. Blood type O A B AB

Frequency

Relative frequency

22 19 6 3

0.44 0.38 0.12 0.06

Construct the specified histogram. 95) 24 high school students were asked how many hours they had spent preparing for a test. The times (in hours) are as follows: 6, 5, 6, 4, 6, 6, 9, 7, 6, 3, 8, 5, 5, 8, 6, 5, 8, 6, 5, 7, 5, 8, 7, 4 Use 2-point bins (3 to 4, 5 to 6, etc) to construct the relative frequency histogram.

94)

95)

Answer the question. 96) The bar graph below shows the number of car accidents occurring in one city in each of the years 1993 through 1998. The number of accidents dropped in 1995 after a new speed limit was imposed. Why is the graph misleading? How would you redesign the graph so that it is less misleading? What impression is conveyed by the graph?

97) The graph below shows estimated world population for the period 4000 BC - 2000 AD. Note that the logarithm of the world population and not actual population is plotted on the vertical axis. This means, for example, that when the graph reaches 7 on the vertical scale, world population is 107 and when the graph reaches 9 on the vertical scale, world population is 109 .

Log World Population

-4000

-2000

2000

Why must the graph be interpreted with care? If the graph is not interpreted with care what misleading impression might one have of world population during the period 4000 BC - 2000 AD? Why do you think that the graph was presented in this form?

96)

97)

98) The bar graph below shows the average cost of renting a studio in a certain city in each of

98)

the years 1994 through 1998.

By what percentage does the average rental price increase from 1994 to 1995? Obtain a truncated version of the graph by sliding a piece of paper over the bottom portion of the graph so that the scale on the vertical axis starts at 300. In the truncated graph, by what percentage does the price appear to increase from 1994 to 1995? Why is the truncated graph misleading?

Provide an appropriate response. 99) Explain in your own words the difference between a bar graph and a histogram. Give an example of data for which you might use a histogram and an example of data for which you might use a bar graph.

99)

Female 237 225 282 270 216 192 189 236

Provide an appropriate response. 101) Suppose that you construct a frequency histogram and a relative frequency histogram corresponding to a particular frequency table. In what ways will the two histograms be similar? In what ways will they differ?

101)

Use the indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 102) Kevin asked some of his friends how many hours they had studied for the test. The times 102) are shown below: 5 5

5 5 3 7 5 5

5 5 7 5

9 5

8 5 4 7 5 8 5 7 8 3

Use 2-point bins (3-4, 5-6, etc)

Provide an appropriate response. 103) Consider the frequency table below which has single values as classes: Value 10 11 12 13 14 15 16 17 18 19 20 21

103)

Frequency 1 3 7 18 10 4 2 7 16 10 6 2

Construct a new frequency table for this data with 4 classes. Now construct another frequency table for this data with 6 classes. Suppose that you construct a histogram corresponding to the original data and histograms corresponding to each of the new frequency tables. Describe the shapes of the three histograms. Does the histogram with six classes capture the distribution of the data? Does the histogram with four classes capture the distribution of the data?

104) Shortly before a mayoral election, a market research firm took a poll to find out which candidate people were planning to vote for. The results are shown below. Candidate Frequency Li Fong 2120 Bob Green 2329 Sue Moore 1042 Jose Alvarez 399 You wish to construct a graph to represent the data. It should be easy to see from your graph which candidate is in the lead. Which graph would be more useful, a bar graph or a pie chart? Explain your thinking.

104)

Make a bar graph to represent the data. 105) The following table shows the number of female infants born at Hospital X on New Year's Day (Jan. 1). Create a vertical bar graph.

105)

No. of Female Year Infants Born Jan 1 1960 35 1961 20 1962 30 1963 50 1964 45 1965 40

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 106) A pharmaceutical company wants to test its new medication to lower blood pressure. It randomly selects 1000 people with high blood pressure and randomly assigns each person to one of two groups. The first group receives the medication for a month and also suggestions as to how to improve their diet. The control group receives a placebo medication and no dietary suggestions. At the end of the month each person's blood pressure is again taken. The average change in blood pressure is compared for the two groups. Solve the problem. 107) A researcher suspects that pesticides in foods cause cancer. Suggest some ways that she could go about establishing causality. Refer to the six guidelines for establishing causality. For each guideline suggest some research that should be pursued. Discuss any challenges that the researcher would face in establishing causality.

106)

107)

Answer the question. 108) The graph below shows the approximate annual percentage growth rate in world population for the years 1960 through 2010. Data is estimated by the UN Census Bureau.

108)

Annual Growth Rate (Percentage)

Why must the graph be interpreted with care? If the graph is not interpreted with care what misleading impression might one have of world population during the period 1960-2010? In which year during the period 1960-2010 is estimated world population the greatest? During which years did world population increase at the fastest rate? Summarize the overall trends in world population during the period 1960-2010.

Create a graphical display for the data given. You may choose any graphic type that you feel is appropriate. Write a few sentences explaining why you chose this type of display and a few sentences describing any interesting patterns in the data. 109) The table below gives information about U.S. families with children under the age of 18. 109) The table shows the percentage of these families that are two-parent families, the percentage that are maintained by a single mother, and the percentage that are maintained by a single father. U.S. Families with Children Under 18 Year Two-parent Single mother Single father 1981 77.6% 20.0% 2.4% 1984 74.2% 22.9% 2.8% 1987 73.0% 23.7% 3.2% 1990 71.9% 24.2% 3.9% 1993 69.8% 25.9% 4.3% 1996 68.4% 26.6% 5.0% 1999 68.2% 26.3% 5.5% 2002 68.3% 25.9% 5.8%

Provide an appropriate response. 110) Suppose that a histogram is constructed for the frequency table shown below:

110)

Age Frequency 30-39 11 40-49 23 50-59 17 60-69 12 70-89 6 The class 60-69 has twice the frequency of the class 70-89. In the histogram, will the area of the bar for the class 60-69 be twice the area of the bar for the class 70-89? In other words, will areas be proportional to frequencies in this histogram? Explain your thinking. Are there any conditions under which areas are proportional to frequencies in histograms?

111) Suppose that you want to construct a graph to represent the following data.

111)

Blood Type Frequency O 90 A 84 B 18 AB 8 If you are primarily interested in the number of people in each category as a percentage of the total number of people, would a bar chart or a pie chart be more useful? Explain your thinking.

Use the graph to answer the question.

112)

Mike decides to buy shares of companies X and Y, which were initially selling for the same price. The changes in the value of each stock over a 90-day period are shown in the graph above. Describe the trend in the value of each stock over the 90-day period.

113) The time series line chart below shows the price of a volatile stock from January to

113)

December of the same year. Describe the overall trend in the price during that period.

1950 1960 1970 1980 1990 2000

U.S. Brazil India 152.3 53.4 369.9 180.7 71.7 445.9 205.1 95.7 555.0 227.7 123.0 687.0 250.1 151.1 841.7 282.3 175.6 1002.7

Answer the question. 115) A parcel delivery service lowered its prices and finds that it has delivered twice as many parcels this year as it did last year. To illustrate this fact, the manager draws a pictogram as shown below. Each cube depicts a parcel. The side length of the "parcel" on the right is twice the side length of the "parcel" on the left.

Why is this pictogram misleading? What visual impression is portrayed by the pictogram?

115)

Create a graphical display for the data given. You may choose any graphic type that you feel is appropriate. Write a few sentences explaining why you chose this type of display and a few sentences describing any interesting patterns in the data. 116) The table below shows statistics for AIDS. The first column shows the estimated number 116) of people living with HIV/AIDS worldwide in various years. The second column shows the estimated number of new HIV infections worldwide in various years. Number Living Year with HIV/AIDS New HIV Infections (Millions) (Millions) 1997 30.6 5.8 1998 33.4 5.8 1999 33.6 5.6 2000 36.1 5.3 2001 40.0 5.0 2002 42.0 5.0

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 117) A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers. A) Stratified B) Simple random

C) Convenience

117)

D) Systematic

A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 118) When gasoline prices fall, the number of cars on the freeways increases. 118) A) Negative correlation; direct cause

B) Positive correlation; common underlying cause C) Negative correlation; common underlying cause D) Positive correlation; direct cause Construct a line chart for the data. 119) The ages of employees of a company are summarized in the frequency table. Age Frequency 18-24 11 25-31 38 32-38 35 39-45 27 46-52 22 53-59 14 60-66 5

119)

Age (years)

D) None of the above

Age (years)

Answer the question. 120) What name is given to a statistical graph that is embellished with additional art work? A) Stack plot B) Multiple bar graph

C) Contour map

D) Pictograph

120)

Use the graph to answer the question.

121)

In what quarter was the revenue the least for 2,000? A) second quarter B) first quarter

C) third quarter

D) fourth quarter

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 122) A tax auditor selects every 1000th income tax return that is received. A) Convenience B) Systematic

C) Simple random

122)

D) Stratified

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 123) "38% of adults in the United States regularly visit a doctor". This conclusion was reached by a college student after she had questioned 520 randomly selected members of her college. What is wrong with her survey? A) Setting may not encourage honest responses

123)

B) Selection bias C) Confounding variables D) Wording of question E) Participation bias Identify the variable as either qualitative or quantitative. 124) The heights of individuals in meters A) Quantitative

124) B) Qualitative

Construct a pie chart representing the given data set.

125) Main form of exercise for employees of one company: None: Walking: Running: Golf: Weight Training: Other:

125)

27% 16% 7% 12% 23% 15%

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation.

126)

A) Weak negative correlation B) Weak positive correlation C) Strong positive correlation D) Strong negative correlation E) No correlation Use the graph to answer the question.

127)

In what quarter was the revenue the greatest for 1,999? A) third quarter B) second quarter C) fourth quarter

D) first quarter

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 128) "38% of adults in the United States regularly visit a doctor". This conclusion was reached by a 128) college student after she had questioned 520 randomly selected members of her college. A) Participation bias B) No bias

C) Selection bias

D) Participation bias and selection bias

Identify the variable as either qualitative or quantitative. 129) The political affiliations of residents of a city A) Quantitative

129) B) Qualitative

Construct a line chart for the data. 130) The table shows the end-of-the-month checking account balance of a statistics teacher for the months January through December of the same year as determined by the closing balance on the last banking day of the month. The balance is rounded to the nearest dollar. Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov Dec

1112

1356

1627

1936

1743

1481

1490

1340

1139

910

700

Construct a time series line chart for the data.

500

130)

D) None of the above Identify the variable as either qualitative or quantitative. 131) The population of a town A) Qualitative

131) B) Quantitative

Use the graph to answer the question.

132)

What was the revenue for the second quarter of 1,999? A) $4 million B) $20 million C) $5 million

D) $25 million

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 133) A health researcher randomly selected 500 high school students from the city of Oak Grove. In a private interview the researcher asked the students whether they had ever used drugs. She concluded that only 8% of the high school students of Oak Grove have ever used drugs. A) The wording of the question

B) Selection bias C) Participation bias D) The source of the study E) The setting may discourage honest responses

133)

Use the graph to answer the question. 134) The following chart shows the percentage of cigarette smokers in Gotham City.

134)

In which year does the percentage of men who smoke exceed the percentage of women who smoke by roughly 9 percentage points. A) 1995 B) 1975

C) 1985

D) None of the above

Make a scatter diagram for the data. 135) The following table gives the total sales (revenue) and profits for 8 retailers. Total Sales Profits Company (Millions of $) (Millions of $) Adams 9.5 0.5 Browns 22.0 1.4 Clay 35.0 1.8 Donners 64.0 3.0 Esters 27.5 0.9 Framer 45.0 2.6 Gillies 15.0 0.8 Hays 57.0 2.2

135)

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 136) A film critic is interested in knowing which is the most popular film of the year amongst Americans. To answer this question, he conducts a telephone poll in the New York metropolitan area and asks each person to name their favorite film of the year. A) Confounding variables

136)

B) Setting may not encourage honest responses C) Selection bias D) Participation bias E) Wording of the question A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 137) People who eat a lot of junk food are heavier, on the whole, than those who do not. 137) A) Negative correlation; direct cause

B) Positive correlation; coincidence C) Positive correlation; direct cause D) Positive correlation; common underlying cause

Solve the problem. 138) For the study described below, identify the sample statistic.

138)

1500 American women working for large companies were polled to determine the percentage that felt that women were under represented in management positions in their company. A) The 1500 women polled

B) The percentage of American women working for large companies who feel that women are

under represented in management positions in their company. C) The percentage of women in the sample who feel that women are under represented in management positions in their company. D) The number of women polled.

139) For the study described below, identify the population parameter.

139)

A researcher is interested in the level of stress among emergency-room nurses in the U.S. 275 emergency-room nurses were interviewed to determine their level of stress. Each nurse was assigned a stress rating based on his or her answers to a number of questions. The average stress rating for the 275 nurses was determined. A) The average stress rating for all emergency-room nurses in the U.S.

B) The average stress rating for all emergency-room nurses in the world C) All emergency-room nurses in the U.S. D) The average stress rating for the 275 emergency-room nurses interviewed Identify the variable as either qualitative or quantitative. 140) Waiting time at a bus stop (in minutes) A) Quantitative

140) B) Qualitative

Solve the problem. 141) For the study described below, identify the sample. A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. 27 of the 300 were extremely dissatisfied with the amount of time they had had to wait in line in recent months. A) All customers of the bank

B) The customers who were waiting in line at the bank the day of the poll C) The 300 customers polled D) The 27 people who were dissatisfied.

141)

The stack plot below shows the value of each of Danny's investments. The stack plot contains three regions. The uppermost unshaded region represents the value of Danny's investment in individual stocks. The center shaded region represents the value of Danny's investment in mutual funds and the bottom region in black represents the value of Danny's investment in a CD. The thickness of a region at a particular time tells you its value at that time.

Use the graph to answer the question. 142) In year 0, approximately what percentage of Danny's total investment was in the CD? A) 30% B) 20% C) 15% D) 25%

142)

Use the graph to answer the question.

143)

Identify the utility that makes up about 25% of the total bill in May. A) Gas

B) Water C) Electric D) None of the utilities makes up 25% of the total bill in May

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 144) A researcher randomly selected 500 college students and asked "How many IQ points would you sacrifice to become better looking?". The following conclusion was published in the student newspaper "Students would sacrifice 18 IQ points to be better looking." A) Participation bias

144)

B) Variables are hard to define/measure C) Selection bias D) The source E) Confounding variables Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 145) You are interested in the percentage of people in your city who favor tax cuts. You interview 145) every twentieth person as they leave the church in your neighborhood. A) Selection bias B) No bias

C) Participation bias and selection bias

D) Participation bias

Solve the problem. 146) For the study described below, identify the sample statistic.

146)

A manufacturer of light bulbs wants to determine the average lifetime of its 75-watt light bulbs. Among 120 randomly selected 75-watt light bulbs, the average lifetime was 1007 hours. A) The average lifetime of all 75-watt light bulbs manufactured by the company

B) The 120 randomly selected 75-watt light bulbs C) 120, the number of light bulbs in the sample D) The average lifetime of the 120 randomly selected 75-watt light bulbs Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 147) A market researcher randomly selects 500 drivers under 30 years of age and 500 drivers over 30 years of age. A) Simple random B) Convenience

C) Stratified

D) Systematic

147)

Use the graph to answer the question.

148)

Identify the utility that accounts for over half the total bill in two months. A) Water

B) Gas C) Electric D) No single utility accounts for more than half the total bill in two months. State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation.

149)

A) Strong positive correlation B) Weak negative correlation C) Weak positive correlation D) No correlation E) Strong negative correlation Construct a pie chart representing the given data set.

150)

150) Favorite Food Chinese Indian Mexican Thai

Number of Responses 69 45 72 54

22.5%

28.8%

30%

18.7%

21%

31%

32%

20%

23%

30%

29%

19%

54%

72%

69%

45%

A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameter of interest and answer the question. 151) Ten years ago, according to government records, 17% of the population of Elmwood had no health 151) insurance. This year a poll revealed that 19.4% were without insurance. The margin of error was 2.2 percentage points. Find a confidence interval for the true percentage without insurance this year. Can we conclude that the percentage without insurance has increased from ten years ago? A) 15% to 19.4%; no B) 18.3% to 20.5%; yes

C) 17.2% to 21.6%; yes

D) 19.4% to 21.6%; yes

Use the graph to answer the question. 152) In which year was the value of Danny's investment in individual stocks the highest? A) year 5 B) year 8 C) year 0 D) year 4

153) In which year was the value of Danny's investment in individual stocks the least? A) year 0 B) year 7 C) year 1 D) year 8 49

152)

153)

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation.

154)

A) No correlation B) Weak negative correlation C) Weak positive correlation D) Strong positive correlation E) Strong negative correlation A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 155) In Angela's class, the taller students got lower scores on the test. 155) A) Negative correlation; common underlying cause

B) Negative correlation; coincidence C) Positive correlation; common underlying cause D) Positive correlation; coincidence

Use the graph to answer the question. 156) This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period.

156)

Compare the trend in the number of male athletes during the four-year period and the trend in the number of female athletes during the four-year period . A) The number of male athletes and the number of female athletes increased steadily over the four-year period. B) The number of female athletes increased steadily over the four-year period. The number of male athletes increased to a peak in 1988 and then decreased again in 1989. C) The number of male athletes increased steadily over the four-year period. The number of female athletes increased in 1987 then decreased again in 1988 and 1989. D) The number of male athletes increased steadily over the four-year period. The number of female athletes increased to a peak in 1988 and then decreased again in 1989.

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 157) You would like to know if the customers of your video store are satisfied. You hand a customer satisfaction questionnaire to every customer who comes into the store and ask them to fill it out and place it in a box after they check out. The questionnaire asks customers to rate their satisfaction on a scale of 1-10 with regard to the video selection and customer service. A) Confounding variables

157)

B) Participation Bias C) Setting may not encourage honest responses D) Wording of the questions E) Selection Bias Construct a line chart for the data. 158) The table shows the price of a volatile stock from the months January through December of the same year as determined by the closing price on the last trading day of the month. The price is rounded to the nearest dollar. Jan Feb

Mar

Apr

May

Jun Jul Aug

Sep Oct Nov Dec

111

184

Construct a time series line chart for the data.

111

158)

D) None of the above 52

Use the graph to answer the question. 159) In year 8, approximately what percentage of Danny's total investment was in mutual funds? A) 60% B) 70% C) 50% D) 80%

Solve the problem. 160) For the study described below, identify the population parameter.

159)

160)

1500 American women working for large companies were polled to determine the percentage that felt that women were under represented in management positions in their company. A) The percentage of all American women who feel that women are under represented in management positions in large companies. B) The percentage of women in the sample who feel that women are under represented in management positions in their company. C) The percentage of American women working for large companies who feel that women are under represented in management positions in their company. D) All American women working for large companies

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 161) The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. A) Convenience B) Systematic

C) Simple random

D) Stratified

Make a scatter diagram for the data.

161)

162) The table shows the unemployment rate and the median price of renting an apartment in nine cities.

Unemployment Median Rent for Rate (Percent) Apartment (dollars) 2.1 950 4.6 760 6.4 1100 7.1 650 3.2 1070 7.2 620 5.0 840 2.4 1050 3.8 650

Plot unemployment rate on the horizontal axis and median rental price on the vertical axis.

162)

Construct a pie chart representing the given data set.

163)

163) Favorite Beverage Number of responses Cola 340 Juice 210 Milk 230 Tea 310 Water 150

A) 150%

340%

310%

230%

210%

B) 12%

27%

25%

19%

17%

C) 5%

32%

28%

19%

16%

D) 8%

24%

28%

19%

21%

Answer the question. 164) In a graph that displays the annual percent increase in the price of grain, what does it mean if the graphs falls over a certain period? A) The real cost of grain has gone down

B) The price of grain is decreasing C) The rate at which the price is rising is decreasing D) Inflation has gone down

164)

A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameter of interest and answer the question. 165) A poll conducted the day before the student-body presidential election at a midwestern 165) university showed that 53.0 percent favored Mario, the rest favoring Yin Ling. The margin of error was 4.8 percentage points. Should Yin Ling have conceded the election? A) 50.6% to 55.4%; yes B) 53.0% to 57.8%; yes

C) 48.2% to 53.0%; no

D) 48.2% to 57.8%; no

Answer the question. 166) What name is given to a statistical graph that plots three or more related quantities simultaneously? A) Pictograph B) Contour map

C) Three dimensional graph

166)

D) Multiple bar graph

Solve the problem. 167) For the study described below, identify the population.

167)

B) All 75-watt light bulbs manufactured by the company C) The average lifetime of all 75-watt light bulbs manufactured by the company D) The 120 randomly selected 75-watt light bulbs Construct a pie chart representing the given data set. 168) Main form of exercise for employees of one company: None: 28% Walking: 19% Running: 6% Golf: 11% Weight Training: 25% Other: 11%

168)

Use the graph to answer the question. 169) In which year was the total value of Danny's investments the greatest? A) year 8 B) year 5 C) year 4

169) D) year 0

Construct a pie chart representing the given data set. 170) Intended major of high school students: Science: 32% Social Science: 8% Humanities: 20% Business: 16% Other: 24%

170)

Identify the variable as either qualitative or quantitative. 171) The professions of adults A) Qualitative

171) B) Quantitative

Use the graph to answer the question.

172)

Identify the utility that reaches its greatest percentage of the total bill in April.

A) Gas B) Electric C) Water D) None of the utilities reaches its greatest percentage in April. Identify the variable as either qualitative or quantitative. 173) The area of apartments in a city A) Qualitative

173) B) Quantitative

Make a scatter diagram for the data. 174) The table shows the life expectancy at birth for females and per capita GDP for nine countries. (Data for 1995) Life Expectancy Country at birth (female) Per Capita GDP (dollars) Afghanistan 45 200 Chile 78 7000 Ghana 58 1500 Guatemala 68 3000 Kenya 54 1200 Spain 81 12,700 Thailand 72 5500 New Zealand 80 15,700 United States 80 24,700 Plot per capita GDP on the horizontal axis and life expectancy on the vertical axis.

174)

B) Per Capita GDP

Life Expectancy

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 175) The unemployment rate and the number of homeless people. 175) A) No correlation

B) Strong negative correlation C) Weak negative correlation D) Strong positive correlation E) Weak positive correlation 176) Height and body temperature of adults. A) Strong positive correlation B) No correlation C) Weak positive correlation D) Strong negative correlation E) Weak negative correlation

176)

Answer the question. 177) What name is given to a statistical graph where a quantity is represented by a curve and has the same value everywhere along the curve? A) Contour map B) Multiple bar graph

C) Pictograph

177)

D) Stack plot

A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 178) As the temperature has been rising over the past three months, the Dow Jones Industrial Average 178) has also been rising. A) Negative correlation; coincidence

B) Positive correlation; common underlying cause C) Positive correlation; direct cause D) Positive correlation; coincidence Construct a pie chart representing the given data set.

179)

179) Computers Number of per household households 0 54 1 96 2 57 3 27

27%

54%

57%

96%

14%

20%

21%

45%

10%

25%

26%

39%

12%

23%

24%

41%

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 180) 49 students are selected at random from the Sophomore class, 39 from the Junior class, and 48 from the Senior classes. A) Simple random B) Stratified

C) Convenience

180)

D) Systematic

Answer the question. 181) Which type of graphs can be difficult to interpret because of visual distortion on a flat page? A) Contour map B) Three dimensional graph

C) Stack plot

181)

D) Multiple bar graph

Solve the problem. 182) For the study described below, identify the population parameter.

182)

A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. 27 of the 300 people were extremely dissatisfied with the amount of time they had had to wait in line in recent months. A) All customers of the bank

B) The average wait time for all the bank's customers. C) The average wait time for the 300 customers polled. D) The percentage of dissatisfied customers. A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameter of interest and answer the question. 183) The CEO of a company claims that 90% of its employees have very high job satisfaction. A poll of 183) the company's employees revealed that 86 percent had very high job satisfaction with a margin of error of 4.2 percentage points. Can we conclude that the CEO was lying? A) 83.9% to 88.1%; yes B) 81.8% to 90.2%; no

C) 81.8% to 86%; yes

D) 86% to 90.2%; no

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 184) Time spent walking and distance walked 184) A) No correlation

B) Strong negative correlation C) Strong positive correlation D) Weak positive correlation E) Weak negative correlation Construct a pie chart representing the given data set. 185) Main form of exercise for employees of one company: None: 30% Walking: 18% Running: 4% Golf: 11% Weight Training: 26% Other: 11%

185)

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 186) An educational researcher wishes to compare the effectiveness of two different math textbooks. She has the tenth graders at one school use the first book for one year and the tenth graders at another school use the second textbook for one year. At the end of the year, she gives the same math test to both classes and compares the results. A) The setting

186)

B) Confounding variables C) Participation bias D) The source E) Selection bias State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 187) The age of a computer and its value. 187) A) Weak positive correlation

B) Strong positive correlation C) No correlation D) Weak negative correlation E) Strong negative correlation A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 188) As Thomas's income rose over the last 20 years so has his stress level. 188) A) Positive correlation; direct cause

B) Negative correlation; common underlying cause C) Positive correlation; common underlying cause D) Positive correlation; coincidence

Use the graph to answer the question. 189) In year 8, what was the approximate value of Danny's investment in mutual funds? A) $2500 B) $6000 C) $4000 D) $1900

Solve the problem. 190) For the study described below, identify the sample.

189)

190)

B) The questionnaire given to the 275 emergency-room nurses interviewed C) The average stress rating for the 275 emergency-room nurses interviewed D) The 275 emergency-room nurses interviewed A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 191) Over the last 10 years in this town, as the amount of open space has decreased, consumer 191) spending has increased. A) Positive correlation; direct cause

B) Positive correlation; common underlying cause C) Negative correlation; common underlying cause D) Negative correlation; direct cause

Identify the variable as either qualitative or quantitative. 192) The movie critics' ratings of the new movie on a scale of 0-10 where 10 = the best movie ever seen and 0 = the worst movie ever seen A) Qualitative B) Quantitative

192)

Use the graph to answer the question. 193) In which year was the total value of Danny's investments the least? A) year 8 B) year 3 C) year 1

193) D) year 0

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 194) A market researcher selects 500 people from each of 10 cities. A) Systematic B) Convenience

C) Stratified

194)

D) Simple random

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 195) Test score and height for adults 195) A) Weak negative correlation

B) Strong positive correlation C) No correlation D) Weak positive correlation E) Strong negative correlation

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 196) To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day. A) Simple random B) Systematic

C) Stratified

196)

D) Convenience

Construct a line chart for the data.

197)

197) Student Test Scores Score Frequency 10-14 2 15-19 5 20-24 13 25-29 17 30-34 6

D) None of the above

A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 198) People with higher incomes tend to live longer than those with lower incomes. 198) A) Positive correlation; common underlying cause

B) Positive correlation; coincidence C) Negative correlation; common underlying cause D) Positive correlation; direct cause State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 199) Actual temperature on a given day and the temperature that had been forecast for that day 10 199) days previously. A) Weak negative correlation

B) Strong negative correlation C) Strong positive correlation D) Weak positive correlation E) No correlation A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 200) Towns with a lot of churches had a lot of homicides last year. Towns with fewer churches had 200) fewer homicides. A) Positive correlation; common underlying cause

B) Positive correlation; direct cause C) Positive correlation; coincidence D) Negative correlation; common underlying cause Construct a line chart for the data.

201)

201) Weight of Cat (lb) Frequency 5-7 2 8-10 9 11-13 18 14-16 13 17-19 4 20-22 1

D) None of the above

202) A medical researcher recorded the ages of patients who had strokes caused by stress. The ages of 34 patients are summarized in the table below: Age (years) Frequency 23-27 3 28-32 3 33-37 6 38-42 4 43-47 5 48-52 3 53-57 5 58-62 5

Age (years)

Age (years) D) None of the above

Age (years)

202)

A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameter of interest and answer the question. 203) Following the Republican National Convention, a poll of voters in a Central Illinois community 203) showed that 55.7% would choose the Republican ticket to win over the Democrat ticket no matter whom the Democrats chose for vice-president. The margin of error was 4.8 percentage points. Should the Democrats expect to lose Central Illinois? A) 50.9% to 60.5%; yes B) 46.1% to 55.7%; no

C) 55.7% to 60.5%; yes

D) 53.3% to 58.1%; yes

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 204) As voters left various polls across the city, every tenth voter at each polling place was asked who 204) they had chosen to be the next mayor. A) Participation Bias and Selection Bias B) Participation Bias

C) Selection Bias

D) No Bias

Answer the question. 205) The strengths of the last 5 major earthquakes to hit California have differed by factors of 10. If you were to display data describing the strengths of these earthquakes what could you use to make the graph more readable? A) A color coded map B) An exponential scale

C) A stack plot

205)

D) A three dimensional graph

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 206) A sample consists of every 20th student who leaves the library. A) Convenience B) Simple random

C) Stratified

206)

D) Systematic

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 207) A researcher was interested in the exercise habits of the residents of the village of Pine Heights. She interviewed every 10th person who left the post office until she had interviewed 100 people. Each of the people interviewed was asked to rate their exercise level according to the following scheme "(1) very little, (2) some, (3) moderate, (4) a lot, (5) extensive". The researcher reported that, on average, the residents of Pine Heights exercise moderately. A) Measurement of the variable is not well defined

B) The source of the study C) Participation bias D) Selection bias E) Confounding variables

207)

208) A medical researcher randomly selects 500 Japanese people and 500 Americans. She questions the

208)

1000 people. She finds that the Americans work longer hours on average and also that the Americans have a higher rate of heart disease. She concludes that working longer hours is associated with a higher incidence of heart disease. A) The source

B) Confounding variables C) Participation bias D) Selection bias E) Variables are hard to define/measure State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 209) Age and remaining life expectancy. 209) A) Weak positive correlation

B) Strong positive correlation C) No correlation D) Strong negative correlation E) Weak negative correlation 210) Number of appliances sold and revenue of appliance store A) Strong negative correlation B) Weak positive correlation C) No correlation D) Strong positive correlation E) Weak negative correlation

210)

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation.

211)

A) Strong positive correlation B) Weak positive correlation C) Strong negative correlation D) No correlation E) Weak negative correlation

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 212) A researcher published this survey result: "74% of people would be willing to spend 10 percent 212) more for energy from a non-polluting source". The survey question was announced on a national radio show and 1200 listeners responded by calling in. A) Selection bias only B) No bias

C) Participation bias and selection bias

D) Participation bias only

A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 213) People who drive faster, cover the distance in a shorter time. 213) A) Positive correlation; common underlying cause

B) Negative correlation; common underlying cause C) Negative correlation; direct cause D) Positive correlation; direct cause State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation.

214)

A) Weak negative correlation B) No correlation C) Strong positive correlation D) Weak positive correlation E) Strong negative correlation Construct a pie chart representing the given data set.

215)

215) Favorite Pizza Topping Black olives Mushrooms Onions Pepperoni

Number of Responses 36 30 14 78

A) 19%

57%

17% 7%

B) 23%

49%

19% 9%

C) 23%

47%

21% 9%

D) 36%

78%

30% 14%

Identify the variable as either qualitative or quantitative. 216) The marital status of individuals A) Quantitative

216) B) Qualitative

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 217) A high school principal wanted to know how the teachers at her school felt about early dismissal for Homecoming. She put the names of the 114 faculty in a hat and randomly selected 30 of the names. She gave questionnaires to those 30 people asking whether they agreed or disagreed with the following statement: "Valuable learning time should not be sacrificed for extracurricular social activities." The questionnaires were filled out anonymously. Her conclusion was that 80% of the faculty were opposed to early dismissal for Homecoming. A) Confounding variables

217)

B) Participation bias C) The setting may discourage honest responses D) The wording of the question E) Selection bias Answer the question. 218) What name is given to a statistical graph where each category has its own wedge and the wedges are displayed on top of one another? A) Contour map B) Stack plot

C) Multiple bar graph

218)

D) Pictograph

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 219) A pharmaceutical company conducted a study to test the effectiveness of its new anti-depression medication. 500 adults suffering from depression were selected at random and were randomly assigned to either a treatment group or a placebo group. The experiment was double blind. The results were analyzed by the company. A) Confounding variables

B) Selection bias C) The source of the study D) The setting may not encourage honest responses E) Variables are difficult to define/measure

219)

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 220) A researcher interviews 19 work colleagues who work in his building. A) Simple random B) Stratified

C) Convenience

220)

D) Systematic

Solve the problem. 221) For the study described below, identify the sample statistic.

221)

A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. A) The average wait time for all of the bank's customers

B) The percentage of dissatisfied customers among all of the bank's customers. C) The average wait time for the 300 customers polled D) The 300 people polled Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 222) You are interested in the degree of satisfaction amongst customers at your video store. For one 222) week, you hand a customer satisfaction questionnaire to every customer who comes into the store and ask them to fill it out and place it in a box after they check out. A) No Bias B) Participation Bias

C) Participation Bias and Selection Bias

D) Selection Bias

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 223) Hours of exercise per week and blood pressure. 223) A) Strong negative correlation

B) Strong positive correlation C) Weak positive correlation D) Weak negative correlation E) No correlation

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation.

224)

A) Strong negative correlation B) Strong positive correlation C) Weak positive correlation D) No correlation E) Weak negative correlation State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 225) Number of siblings and number of pairs of shoes owned by children 225) A) Weak positive correlation

B) Weak negative correlation C) Strong negative correlation D) Strong positive correlation E) No correlation Identify the variable as either qualitative or quantitative. 226) The colors of the houses in a city A) Quantitative

226) B) Qualitative

Solve the problem. 227) For the study described below, identify the population. 1500 American women working for large companies were polled to determine the percentage that felt that women were under represented in management positions in their company. A) All American women

B) The 1500 women polled C) The percentage of American women working for large companies who feel that women are under represented in management positions in their company.

D) All American women working for large companies

227)

A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. 228) People who take more vacations score higher on standardized tests. 228) A) Negative correlation; common underlying cause

B) Positive correlation; common underlying cause C) Positive correlation; coincidence D) Positive correlation; direct cause A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameter of interest and answer the question. 229) In a survey conducted in a certain city it was found that 5.5% of men and 6.7% of women were 229) unemployed. The margin of error for each report was 0.8 percentage points. Use each sample statistic to find a confidence interval. Can we conclude that the unemployment rate is higher amongst women than amongst men? A) men: 4.7% to 5.5% B) men: 5.5% to 6.3% women: 6.7% to 7.5% women: 5.9% to 6.7% yes no C) men: 5.1% to 5.9% D) men: 4.7% to 6.3% women: 6.3% to 7.1% women: 5.9% to 7.5% yes no

Identify the variable as either qualitative or quantitative. 230) The speed of a car in miles per hour A) Qualitative

230) B) Quantitative

Answer Key Testname: CHAPTER 5

1) A 2) A 3) D 4) A 5) A 6) D 7) C 8) A 9) A 10) A 11) C 12) D 13) C 14) C 15) B 16) D 17) D 18) A 19) C 20) C 21) B 22) B 23) C 24) B 25) D 26) D 27) A 28) C 29) C 30) C 31) B 32) D 33) D 34) B 35) D 36) C 37) D 38) B 39) D 40) A 41) B 42) C 81

Answer Key Testname: CHAPTER 5

43) A 44) A 45) C 46) C 47) C 48) A 49) A 50) D 51) A 52) D 53) D 54) B 55) C 56) B 57) Step 1: Population is all employees of the software company; goal is to determine level of stress among employees.

Step 2: Choose a representative sample Step 3: Determine level of stress for those in the sample. Step 4: Infer level of stress for all employees of the company. Step 5: Assess results and formulate conclusion 58) Answers will vary. Possible answer: A pie chart would be more useful. A pie chart is useful for comparing the size of each category with the whole (i.e. - the proportion of the whole population falling in each category). A bar graph is more useful for comparing the sizes of different categories with each other. 59) The number of male athletes increased steadily over the four-year period. The number of female athletes increased to a peak in 1988 and then decreased again in 1989. 60) Step 1: Population is all adults in the U.S. ; goal is to determine the percentage of adults in the U.S. who have ever sought treatment from a practitioner of complementary medicine. Step 2: Choose a representative sample Step 3: Determine percentage of people within the sample who have ever sought treatment from a practitioner of complementary medicine. Step 4: Infer percentage of all adults in the U.S. who have ever sought treatment from a practitioner of complementary medicine. Step 5: Assess results and formulate conclusion

61)

Answer Key Testname: CHAPTER 5

Bin Freq. Relative Freq. Cumulative Freq. 0-49 2 0.1 2 50-99 4 0.2 6 100-149 4 0.2 10 62) 150-199 4 0.2 14 200-249 2 0.1 16 250-299 1 0.05 17 300-349 3 0.15 20 Total 20 1.00 20

63) There are confounding variables. In order to evaluate which of the two books is better it is important that the two

groups be alike, in every respect other than the textbook used. In this case there are other differences between the two groups - they have different teachers, also one school may have students who work harder or have a greater aptitude for math. One of the classes may already have a higher level of math at the beginning of the study. If there is a large difference between the test scores for the two classes it will be impossible to know whether this is because of the textbook or because of the other confounding variables. 64) Answers will vary. Possible answer: Yes, when a bar graph is truncated, differences between the bars appear exaggerated. 65) The study was observational. It should have been a controlled experiment with a placebo group and a treatment group. Also because the acupuncturist could easily influence results by how she questions, the experiment should have been double-blind, the interviewer should not have known whether the patient was in the treatment group or the placebo group. Also the sample is probably too small.

66) Step 1: Population is all tenants in the city of Hazelwood; goal is to determine the average amount paid in rent by tenants of the city of Hazelwood. Step 2: Choose a representative sample Step 3: Determine the average amount paid in rent by the people in the sample. Step 4: Infer average amount paid in rent by all tenants of Hazelwood. Step 5: Assess results and formulate conclusion

67)

Answer Key Testname: CHAPTER 5

68) The correlation could be due to a common underlying cause such as the level of stress in a person's life. Those with stressful, demanding jobs for example are likely to have more anxiety and are also likely to drink more coffee.

The following are ways of establishing causality. 1. Look for a correlation between coffee drinking and anxiety among various groups - women, men, people of different incomes, ages, races, cultures, lifestyles, professions. 2. Find two groups which are alike in every respect except the amount of coffee they drink. Do those who drink more coffee have higher levels of anxiety? Such groups may be difficult to find. 3. Look for evidence that the more coffee people drink, the higher their anxiety level. 4. Look for evidence that after other potential causes of anxiety have been accounted for, that the remaining cases occur among those who drink a lot of coffee. 5. Conduct an experiment. This may be necessary because of the difficulties mentioned in 2. But consideration should also be given to whether an experiment would be ethical. 6. The researcher should try to determine the physical mechanism by which coffee causes anxiety. 69) The correlation could be due to a common underlying cause such as income. People with higher incomes tend to take more vacations and also to have access to better health care and to a healthier diet. 1. Look for a correlation between vacations and blood pressure among various groups - women, men, people of different incomes, ages, races, cultures, lifestyles. 2. Find two groups which are alike in every respect except the number of vacations they take. Do those who take more vacations have lower blood pressure? Such groups may be difficult to find - people who take more vacations also tend to have access to better health care and to a healthier diet. 3. Look for evidence that the greater the number of vacations, the lower the blood pressure. 4. Look for evidence that after other potential ways of lowering blood pressure have been accounted for, that the remaining cases occur among those who take many vacations. 5. Conduct an experiment. This may be necessary because of the difficulties mentioned in 2. 6. The researcher should try to determine the physical mechanism by which vacations could lower blood pressure. 70) The graph is misleading because it gives the impression that sales have been rising linearly. The bars are equally spaced even though the time intervals on the horizontal axis are not uniform in size. So for example, it took 10 years for sales to increase from 10 to 20 million but only 4 years for sales to increase from 40 to 50 million. 71) Answers will vary. Possible answer: First calculate the relative frequency for the blood type O. Relative frequency = 90/200 = 0.45. The angle is 45% of 360° or 162°. 72) Step 1: Population is all college seniors; goal is to determine the percentage of college seniors who regret their choice of major. Step 2: Choose a representative sample Step 3: Determine percentage of seniors within the sample who regret their choice of major Step 4: Infer percentage of all college seniors who regret their choice of major Step 5: Assess results and formulate conclusion 73) Limited choice is given in the question. There is not enough information to answer the question - what other choices are there? If more is spent on social services, will cuts be made elsewhere? It is impossible to decide on one piece of the budget without seeing the whole picture and knowing all the alternatives. 74) There is selection bias as the sample was obtained from among people who own a computer. This group may not be representative of Americans as a whole. Also there is participation bias as the group consists of those who chose voluntarily to respond. People who respond voluntarily are likely to have stronger opinions than the average person. The wording of the question is not neutral, will probably influence people to say that they favor the proposed law. The researcher works for an environmental group and is probably strongly in favor of the new law. For this reason the researcher may not be unbiased.

Answer Key Testname: CHAPTER 5

75) The researcher should not conclude that vaccinations cause autism without further research. Possible types of

research are as follows: 1. Look for a correlation between vaccinations and autism among various groups - male, female, people of different incomes, ages, races, cultures, lifestyles. 2. Find two groups which are alike in every respect except the number of vaccinations . Do those who have had more vaccinations have a higher incidence of autism? 3. Look for evidence that the greater the number of vaccinations, the higher the incidence of autism. 4. Look for evidence that after other potential causes of autism have been accounted for, that the remaining cases occur among those who receive many vaccinations. 5. Conduct an experiment. Consideration should be given to whether this would be ethical. 6. The researcher should try to determine the physical mechanism by which vaccinations could cause autism. 76) The setting will not encourage honest answers, people may not feel free to talk honestly about their marriage in front of their spouse. There are confounding variables - there are numerous differences between the two groups. If it is found that one group has a higher percentage of happy marriages, it will be impossible to know what this can be attributed to. 77) Answers will vary. One possible answer:

Two separate bar graphs work to show the individual distributions more clearly.

78) The flaws are as follows:

1. The wording of the question is not neutral because of the phrase "which restrict growth." 2. There is participation bias as the sample is self-selected, those with particularly strong views are more likely to respond. 3. There is selection bias as the listeners of a particular conservative talk show are not representative of Americans as a whole. 4. The sample is too small.

Answer Key Testname: CHAPTER 5

79) Bin Frequency Relative Freq. Cumulative Freq. 60-69 3 0.125 3 70-79 12 0.5 15 80-89 7 0.292 22 90-99 2 0.083 24 Total 24 1.000 24

80)

Bin Freq. Relative Freq. Cumulative Freq. 45-49 5 0.20 5 50-54 2 0.08 7 55-59 5 0.20 12 60-64 3 0.12 15 65-69 2 0.08 17 70-74 3 0.12 20 75-79 2 0.08 22 80-84 3 0.12 25 Total 25 1.00 25

81) The source is biased. Since the TV station is owned by biotech company, the producers of the documentary may be biased toward making favorable statements about genetically modified food. The wording of the question is not neutral and will influence the answers. There is selection bias as the poll is restricted to those who own a phone 82) The variables are poorly defined and hard to measure. What does it mean to be free? How rich is rich? No information is given about how the sample was obtained. Was the sample representative of most Americans? 83) Step 1: Population is all owners of personal computers in the U.S; goal is to determine average length of time that owners of personal computers keep a computer before buying a newer model. Step 2: Choose a representative sample Step 3: Determine average length of time that people within the sample keep a personal computer before buying a newer model. Step 4: Infer average length of time for all owners of personal computers in the U.S. Step 5: Assess results and formulate conclusion 84) Answers will vary. Possible answer: The area of the television on the right is nine times (not three times) the area of the television on the left. The pictogram gives the visual impression that sales in 1995 were nine times the sales in 1985.

Answer Key Testname: CHAPTER 5

85) Answers may vary. A possible answer follows.

1955 1954 1953 1952 1951 1950 0

16 24

86)

87) Step 1: Population is all 500 mL bottles of orange juice made by your company; goal is to determine average volume of juice in those bottles. Step 2: Choose a representative sample Step 3: Determine average volume of juice for bottles in the sample. Step 4: Infer average volume of juice for all 500 mL bottles of orange juice made by your company. Step 5: Assess results and formulate conclusion

Answer Key Testname: CHAPTER 5

88) The value of stock 1 fluctuated during days 1-8 then fell sharply from days 8-14. From days 14 to 20 its value

fluctuated with little overall change. From day 20 to 23 its value increased. For the remainder of the month its value fluctuated with little overall change. Overall the value of stock 1 fell by 33% during the month of October. The value of stock 2 fell sharply during days 1-3 then increased sharply during days 3-13. Between days 13 and 16 its value fell. Between days 16 and 21 its value fluctuated with little overall change. Between days 21 and 29 its value increased overall with some fluctuations. On day 30 its value fell. Overall, the value of stock 2 increased by 100% during the month of October.

89) The majority of people have either blood type A or O. Blood types B and AB are much less common. Type O is a little more common than type A and type B is a little more common than type AB.

90) The setting will not encourage honest answers

There are confounding variables - there may be other differences between the two schools other than the counseling program 91) Answers may vary. The following is a possible answer.

June 22 June 7 May 22 May 7 April 22 April 7 0.6

0.8

1.2

1.4

1.6

1.8

92) Stock A: yes; best time to sell would have been at day 52.

Stock B: yes; best time to sell would have been around day 50 Stock C: no 93) Answers will vary. The class width of the second class should be twice the class width of the first class.

Answer Key Testname: CHAPTER 5

94)

95)

96) Answers will vary. Possible answer: The graph is misleading because it is truncated. The scale on the vertical axis

should start at zero so that the bars will be in the correct proportions. The truncated graph conveys the impression that the number of accidents fell by about 33% in 1995 when in fact the number of accidents fell by about 17%. 97) The graph must be interpreted with care because each tick mark on the vertical axis represents a tenfold increase in population. If the graph is not interpreted with care, one might have the impression that world population increased at a linear rate between 4000 BC and 1000 AD. The graph is presented in this form because the data ranges over a large range of values. Population has grown so rapidly in recent years that an ordinary scale makes it impossible to see any detail in the early years shown on the graph.

98) Answers will vary. Possible answer: The average price increases by 25% from 1994 to 1995. Using the truncated

graph, the price appears to double from 1994 to 1995 (i.e. it appears to increase by 100%). Using the truncated graph, the differences between the bars appear bigger (relatively) than they really are. 99) Answers will vary. Possible answer: A histogram is used for quantitative data, has a continuous numerical scale on the horizontal axis, and there are no gaps between the bars. A bar graph is used to represent qualitative data. It does not have a continuous numerical scale on the horizontal axis, but names of the different categories. There are gaps between the bars. Examples of data will vary.

Answer Key Testname: CHAPTER 5

100) Answers will vary. One possible answer:

The line graphs show the trend over time. There has been a dramatic decline in male diagnoses, while female cases have remained relatively steady over time. 101) The two histograms will have the same shape. They will also have the same scale on the horizontal axis. They will differ only in the scales on the vertical axis: the frequency histogram will show frequencies on the vertical axis while the relative frequency histogram will show relative frequencies.

102) Bin Freq. Relative Freq. Cumulative Freq. 3-4 3 0.125 3 5-6 13 0.542 16 7-8 7 0.292 23 9-10 1 0.042 24 Total 24 1.001 24 103) The data is bimodal because it has two peaks one near 13 and one near 18. The two frequency tables are as follows:

Class 10-12 13-15 16-18 19-21

Frequency 11 32 25 18

Class 10-11 12-13 14-15 16-17 18-19 20-21

Frequency 4 25 14 9 26 8

The bimodal distribution of the data will be clearly seen in the histogram of the original data and in the histogram with six classes. In the histogram with four classes the shape of the data is lost. 104) Answers will vary. Possible answer: A bar graph would be more useful. A bar graph is useful for comparing the sizes of different categories with each other, since it is easy to compare the heights of different bars.

Answer Key Testname: CHAPTER 5

105) Answers may vary. A possible answer follows.

50 40 30 20 10

1960

1961

1962

1963

1964

1965

106) The source - the pharmaceutical company is not unbiased and should not be testing its own medication.

There is a confounding variable, the group taking the medication is also being given dietary suggestions. It will be impossible to know whether any difference in blood pressure between the two groups is due to the medication or to differences in diet between the two groups. 107) 1. Look for a correlation between pesticides and cancer rates among various groups - women, men, people of different ages, races, cultures, lifestyles. 2. Find two groups which are alike in every respect except the level of pesticides in their diet. The researcher should compare the incidence of cancer for the two groups. Is the incidence of cancer higher for those with higher levels of pesticides in their diet? Such groups may be difficult to find - people who voluntarily choose to eat organic food may also make other healthy life style choices. 3. Look for evidence that the higher the level of pesticides in a person's diet, the greater the risk of cancer. 4. Look for evidence that after other potential causes of cancer have been accounted for, that the remaining cases occur among those exposed to pesticides in their diet. 5. In this case an experiment would be unethical since the researcher suspects that pesticides cause cancer. 6. The researcher should try to determine the physical mechanism by which pesticides could cause cancer. 108) The graph must be interpreted with care because it portrays annual percentage increase in population, not actual population. If the graph is not interpreted with care, one might have the impression that world population increased until 1962 and then decreased from 1963 until 2010 (with minor fluctuations). Estimated world population is greatest in 2010. World population increased at the fastest rate between 1962 and 1964. Overall the trend is as follows: Between 1960 and 1962 world population increased at a faster and faster rate.Between 1962 and 1964 world population increased at a constant rate. From 1964 to 2010, world population continues to increase but at a slower and slower rate (although there are minor fluctuations in this overall pattern).

Answer Key Testname: CHAPTER 5

109) Answers will vary. One possible answer:

The graph displays the three categories in proportion. There was a steady decrease in Two-Parent families from 1981 to 2002. 110) The areas of the bars for the two classes will actually be the same. This is because the bar for the class 60-69, while it is twice as tall as the bar for the class 70-89, is also only half the width because the class widths are not the same. Heights, not areas are proportional to frequencies. For classes of equal width, areas will also be proportional to frequencies. 111) Answers will vary. Possible answer: A pie chart would be more useful. A pie chart clearly shows the proportion of the whole "pie" represented by each piece of pie. A bar chart is more useful for comparing the sizes of different categories with each other. 112) The value of stock Y increased sharply initially until day 35 then decreases steadily until day 90. The value of stock X increased very slowly until day 70, then increased more and more rapidly until day 90. 113) The price rose sharply from January to February, remained fairly constant from February to March, rose sharply from March to May, fell sharply from May to July, remained fairly constant from July to August, then rose steadily from August to December. 114) Answers will vary. One possible answer:

The multiple bar graph distinguishes the three categories. India's population has been growing at a much higher rate than the U.S. or Brazil 115) Answers will vary. Possible answer: The volume of the cube on the right is eight times (not twice) the volume of the cube on the left. The pictogram gives the visual impression that eight times as many parcels were delivered this year as last year.

Answer Key Testname: CHAPTER 5

116) Answers will vary. One possible answer:

The multiple bar graph shows an increase in people living with HIV/AIDS, but a decrease in new cases of HIV.

117) B 118) A 119) C 120) D 121) A 122) B 123) B 124) A 125) B 126) B 127) C 128) C 129) B 130) C 131) B 132) D 133) E 134) B 135) A 136) C 137) C 138) C 139) A 140) A 141) C 142) B 143) A 144) B 93

Answer Key Testname: CHAPTER 5

145) A 146) D 147) C 148) C 149) D 150) C 151) C 152) C 153) D 154) E 155) B 156) D 157) B 158) B 159) A 160) C 161) C 162) B 163) B 164) C 165) D 166) C 167) B 168) B 169) B 170) C 171) A 172) C 173) B 174) D 175) E 176) B 177) A 178) D 179) D 180) B 181) B 182) B 183) B 184) C 185) C 186) B 94

Answer Key Testname: CHAPTER 5

187) E 188) C 189) C 190) D 191) C 192) A 193) C 194) C 195) C 196) D 197) B 198) A 199) D 200) A 201) B 202) A 203) A 204) D 205) B 206) D 207) A 208) B 209) D 210) D 211) A 212) C 213) C 214) C 215) B 216) B 217) D 218) B 219) C 220) C 221) C 222) B 223) D 224) E 225) B 226) B 227) D 228) B 95

Answer Key Testname: CHAPTER 5

229) D 230) B

Exam

Chapter 6

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A data set consists of 9 values which are not all the same. Which of the following is possible? A) The mean is equal to the largest value. B) The mode is equal to the largest value.

C) The median is equal to the largest value.

D) None of the above is possible.

2) Which of the following statements is true? A) The mean is always one of the data points in a set of data. B) The median is always one of the data points in a set of data C) The mode is always one of the data points in a set of data. D) None of the above is true

3) A hypothesis test is conducted with the following hypotheses:

Answer the question. 4) Tell which of the following distributions would have the least variation. A) 100-meter times for adults

Null hypothesis: population mean = 100 Alternative hypothesis: population mean > 100 A sample is selected and the sample mean turns out to be 118 If the result is significant at the 0.01 level, which of the following is true? A) If the null hypothesis were true, the chance that the sample mean would have been as big as 118 or bigger is greater than 0.01. B) If the null hypothesis were true, the chance that the sample mean would have been as small as 118 or smaller is less than 0.01. C) If the null hypothesis were true, the chance that the sample mean would have been as big as 118 or bigger is less than 0.01. D) If the alternative hypothesis were true, the chance that the sample mean would have been as big as 118 or bigger is less than 0.01.

B) 100-meter times for male Olympic sprinters C) 100-meter times for male college seniors D) 100-meter times for college seniors Provide an appropriate response. 5) Scores on a test are normally distributed. Which of the following statements is (are) plausible? A: Margo's score was in the 90th percentile and she got a C B: Helena's score was in the 40th percentile and she got an A C: Monica's score was in the 5th percentile and she failed D: Gale's score was in the 70th percentile and she got a D A) A and B B) C and D C) C only D) D only E) B and C

6) If a hypothesis test is conducted at a significance level of 0.05, which of the following statements is

true?

A) The probability that the null hypothesis will not be rejected when it is false is 0.05. B) The probability that the null hypothesis will be rejected when it is false is 0.05. C) The probability that the result will be significant is 0.05. D) The probability that the null hypothesis will be rejected when it is true is 0.05. Answer the question. 7) Tell which of the following distributions would have the most variation. A) Scores on a test in which all students got a perfect score

B) Scores on a test in which half the students got a C and half failed C) Scores on a test in which half the students got an A and half failed D) Scores on a test in which half the students got an A and half got a B Provide an appropriate response. 8) Which of the following is not possible? A) A distribution has a single peak and the mean and median are different

B) A distribution is not symmetric and the median is equal to the mean C) A distribution is right-skewed and the mean is greater than the median D) A distribution is left-skewed and the mean is equal to the median 9) A variable is normally distributed with a mean of 100. Which of the following is the largest? A) The percentage of observations between 80 and 90 B) The percentage of observations between 95 and 105 C) The percentage of observations between 100 and 110 D) The percentage of observations between 90 and 100

10) Which quantity describes how widely data values are spread about the center of a distribution? A) Variation B) Number of peaks C) Mean D) Skewness

10)

11) Of the mean, median, and mode, which take(s) into account the numerical size of all the data

11)

values? A) The mean and median

B) The median and mode D) The mean only

C) All of them

12) For women at Durham College, times to run the 400 meters are normally distributed. Which of the following are the most plausible values for the mean and standard deviation? A) Mean = 77 sec, standard deviation = 20 sec

B) Mean = 77 sec, standard deviation = 2.1 sec C) Mean = 77 sec, standard deviation = 9.1 sec D) Mean = 77 sec, standard deviation = 16 sec

12)

Select the requested distribution. 13) Which of the distributions is multimodal?

13)

Provide an appropriate response. 14) Scores on a test are normally distributed. Which of the following statements is (are) plausible? A: Daniel had a standard score of 1.9 and got an A B: Jon had a standard score of 0.7 and got a D C: Eric had a standard score of -1.6 and got a B D: Raul had a standard score of 0 and got a C A) C and D B) A only C) B and C D) A and B E) A and D

15) A data set consists of 9 values which are all different. Which of the following is possible? A) The mode is equal to the second smallest value. B) The mean is equal to the second smallest value. C) The median is equal to the second smallest value. D) None of the above is possible.

14)

15)

16) Which of the following statements is not true for a left-skewed distribution? A) The median is smaller than the mode B) The mode is at the peak C) The mean is greater than the median D) The mode is greater than the mean

16)

17) Heights of gymnasts at a certain college are normally distributed. Which of the following are the

17)

most plausible values for the mean and standard deviation? A) Mean = 60 in., standard deviation = 0.5 in.

B) Mean = 61 in., standard deviation = 6.2 in. C) Mean = 61 in., standard deviation = 2.1 in. D) Mean = 60 in., standard deviation = -1 in. 18) Which of the following is not possible? A) A distribution is symmetric and single peaked and the mode is greater than the mean. B) A distribution is symmetric and single peaked and the mean, median, and mode are all

18)

equal.

C) Two data sets have equal means and modes but still have very different distributions. D) A distribution is symmetric and the mode is different from the mean. Answer the question. 19) Tell which of the following distributions would have the least variation. A) Weights of all pet dogs

19)

B) Weights of all pet cats C) Weights of all pets D) Weights of all children who have a pet cat Select the requested distribution. 20) Which of the distributions is symmetric?

20)

21) Which of the distributions is multimodal and approximately symmetric? A)

21)

Provide an appropriate response. 22) Traditionally in hypothesis testing the null hypothesis represents the "status quo" which will be overturned only if there is evidence against it. Which of the statements below might represent a null hypothesis? A) The mean temperature this decade is higher than the mean temperature over the past century. B) The treatment has no effect.

22)

C) The defendant is guilty. D) The teaching method raises SAT scores. Answer the question. 23) Tell which of the following distributions would have the most variation. A) The number of hours of light per day over a one-year period in Mexico City

23)

B) The number of hours of light per day over a one-year period at the equator C) The number of hours of light per day over a one-year period at the North Pole D) The number of hours of light per day over a one-year period in New York Provide an appropriate response. 24) Weights of adults in a certain age group are normally distributed. Which of the following are plausible values for the mean and standard deviation? A) Mean = 158 lb, standard deviation = 5 lb

B) Mean = 155 lb, standard deviation = -20 lb C) Mean = 155 lb, standard deviation = 12 lb D) Mean = 160 lb, standard deviation = 25 lb

24)

25) Of the mean, median, and mode, which is (are) affected by outliers? A) The mean only B) The mean and mode C) The median and mode D) The mean and median Select the requested distribution. 26) Which of the distributions is skewed to the right?

25)

26)

Answer the question. 27) Tell which of the following distributions would have the most variation. A) Temperature over a one-month period in San Diego.

27)

B) Temperature over a one-year period in Boston. C) Temperature over a one-year period in San Diego. D) Temperature over a one-month period in Boston. Provide an appropriate response. 28) Toni is conducting a hypothesis test concerning a population proportion. The hypotheses are as follows. Null hypothesis: population proportion = 0.2 Alternative hypothesis.: population proportion > 0.2 She selects a sample and finds that the sample proportion is 0.21. She then does some calculations and is able to make the following statement: If the population proportion were 0.2, the chance that the sample proportion would have come out as big as 0.21 or bigger is 0.4. Which of the following is a reasonable conclusion? A) Accept the null hypothesis. The sample provides evidence to support the null hypothesis.

28)

B) Accept the null hypothesis. The sample provides no evidence against the alternative hypothesis.

C) Do not reject the null hypothesis. The sample provides no evidence against the null

hypothesis. D) Accept the alternative hypothesis. The sample provides evidence to support the alternative hypothesis.

29) A criminal trial can be compared to a hypothesis test. The hypotheses are as follows:

29)

Null hypothesis: The defendant is innocent Alternative hypothesis: The defendant is guilty Suppose that in one trial, if convicted, the defendant will receive the death penalty. Do you think that a significance level of 0.05 or 0.01 is more appropriate in this case. Why? A) 0.05. It is important not to reject the null hypothesis if it is true.

B) 0.01. It is important not to reject the null hypothesis if it is true. C) 0.01. It is important to reject the null hypothesis if it is false. D) 0.05. It is important to reject the null hypothesis if it is false. Answer the question. 30) Tell which of the following distributions would have the most variation. A) Salaries of CEOs of U.S. corporations B) Salaries of waitresses

C) Salaries of bank clerks

D) Salaries of high-school teachers

30)

Select the requested distribution. 31) Which of the distributions has the greatest variation?

31)

Answer the question. 32) Tell which of the following distributions would have the least variation. A) Number of children for women in Haiti

32)

B) Number of children for women in India C) Number of children for women in Portland, Oregon D) Number of children for women in Kenya 33) Tell which of the following distributions would have the least variation. A) Weights of adult men B) Weights of 20-year old women C) Weights of all adults D) Weights of 20-year olds Provide an appropriate response. 34) Rank the mean, median, and mode in order of ascending size for a right-skewed distribution. A) Mode, Mean, Median B) Mode, Median, Mean

C) Mean, Median, Mode

D) Median, Mode, Mean

33)

34)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

35) We want to compare two different groups of students, students taking Composition 1 in a

35)

36) A company advertises an average of 42,000 miles for one of its new tires. In the

36)

traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation?

manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small standard deviation? Justify your answer.

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given context to formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the null hypothesis. 37) A public bus company official claims that the mean waiting time for bus number 14 37) during peak hours is only 10 minutes. Karen finds this hard to believe as she seems to be invariably late for work. For 42 randomly selected days, her mean waiting time for bus 14 during peak hours was 11.3 minutes. Assuming that the population mean waiting time is 10 minutes , the probability of selecting a random sample with a mean waiting time of 11.3 minutes or more is 0.0026.

Provide an appropriate response. 38) Discuss the differences between the distributions represented by the two boxplots below. Explain your reasoning.

38)

39) Can the sample variance ever be a negative number? If so, for what types of data? If not,

39)

40) An environmental group is investigating global warming and is conducting a hypothesis

40)

why not? Can the sample variance ever be zero? If so, for what types of data? If not, why not? Explain your reasoning.

test. The hypotheses are as follows: Null hypothesis: The mean temperature has not changed in recent years Alternative hypothesis: The mean temperature has increased in recent years Do you think that the environmental group would prefer a significance level of 0.05 or 0.01. Why? Do you think that car manufacturers would prefer a significance level of 0.05 or 0.01? Why?

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 41) Suppose that a state introduces a state income tax which will be at a flat rate of 3%. The 41) state legislature wishes to estimate how much money they will receive in taxes, and to do this they need to know the average income of residents of the state. Which information would be most useful, the mean income, the median income, or the mode of the incomes? Why?

42) Dave is a college student contemplating a possible career option. One factor that will

42)

influence his decision is the amount of money he is likely to make. He decides to look up the average starting salary of graduates in that profession. Which information would be most useful to him, the mean starting salary, the median starting salary, or the mode of the starting salaries. Why?

Provide an appropriate response. 43) Boxplots are graphs that are useful for revealing central tendency, the spread of the data, the distribution of the data and the presence of outliers. Draw an example of a box plot and comment on each of these characteristics as shown by your boxplot.

43)

44) You are the coach of a basketball team. Player A's mean score per game over the last

44)

45) The range and standard deviation of the data set below are 35 and 12.47 respectively.

45)

season has been 24 with a standard deviation of 2. Player B's mean score per game over the last season has been 23 with a standard deviation of 6. Contrast the performance of the two players. Which player would be your choice to play in a game in which you all you need is a medium performance to win? Which player would be your choice to play in a game in which your team needs an exceptional performance in order to win?

5, 24, 25, 26, 40 If the 26 is replaced with 39, how will this affect the range? How will this affect the standard deviation. Use your answers to explain why the standard deviation is preferable to the range as a measure of variation.

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given context to formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the null hypothesis. 46) In the city of Heathville, the proportion of births that are by Caesarean section is 0.23 46) (23%). A small private hospital claims that at their hospital, the proportion of Caesarean births is lower. In a random sample of 120 births at the private hospital, the proportion of Caesarean births was 0.18. Assuming that the true proportion of Caesarean births at the private hospital is 0.23, the probability of selecting a sample in which the proportion of Caesareans is 0.18 or less is roughly 0.09.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 47) The table below provides a frequency distribution for the winner of the Davis Cup during 47) the period 1977-1994. Winner of Davis Cup United States Germany Czechoslovakia Australia France Sweden

Frequency 6 3 1 3 1 4

Which measure of center, the mean, the median, or the mode is most appropriate here? Why?

48) Before a mayoral election, a pollster tries to predict which candidate will win the most

48)

votes. Which average does the pollster need to know?

Provide an appropriate response. 49) Four different distributions are represented by the four boxplots below.

49)

Which distribution has the smallest median? Which has the greatest variation? Which is skewed to the left?

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 50) A state governor is planning a tax cut. A researcher calculates the average amount that 50) will be saved by residents of the state. Which average would best convey the amount that will be saved by most residents of the state?

Provide an appropriate response. 51) You are late for work. You have two options for getting to work. You may take the bus which takes on average 40 minutes with a standard deviation of 12 minutes. Or you can cycle which takes on average 50 minutes with a standard deviation of 2 minutes. Compare these two distributions. You leave your house at 8.20 am and are supposed to start work at 9.00 am. Which option would you choose if you will be fired if you are even a few minutes late? Which option would you choose if you know that up to 15 minutes late is OK but after that there is trouble? Explain your thinking.

51)

52) Describe any similarities or differences in the two distributions represented by the

52)

53) Jenny is conducting a hypothesis test concerning a population mean. The hypotheses are

53)

boxplots below. Assume the two boxplots have the same scale.

as follows. Null hypothesis: population mean = 50 Alternative hypothesis: population mean > 50 She selects a sample and finds that the sample mean is 54.2. She then does some calculations and is able to make the following statement: If the population mean were 50, the chance that the sample mean would have come out as big as 54.2 or bigger is 0.3. Do you think that she should reject the null hypothesis? Why or why not?

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given context to formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the null hypothesis. 54) The mayor of a city claims that racial profiling is not a problem in his city. A civil rights 54) group disagrees. The proportion of Caucasians who have been stopped while driving, without good reason, at least once in the past year is 0.19 (19%). In a random sample of 340 African Americans , the proportion who have been stopped is 0.37 (37%). Assuming that the proportion of all African Americans in the city that have been stopped is 0.19, the probability of selecting a sample in which the proportion who have been stopped is 0.37 or more is less than 0.001.

55) The mean resting heart rate for students at Northridge College is 72 beats per minute. An exercise physiologist believes that for athletes, the mean resting heart rate will be lower. She finds that for a random sample of 55 athletes at the college, the mean resting heart rate is 71 beats per minute. Assuming that the mean resting heart rate for all athletes at the college is 72 beats per minute, the probability of selecting a random sample with a mean of 71 or less beats per minute is 0.14.

55)

Provide an appropriate response. 56) You wish to test the hypotheses shown below. Null hypothesis: mean = 40 Alternative hypothesis: mean > 40 Would you be inclined to reject the null hypothesis if the sample mean turned out to be much smaller than 40? Explain your thinking.

57) Draw one boxplot to illustrate bell-shaped data, another for uniform data, and a third for

56)

57)

skewed data. Which of these shapes matches the boxplot for the first 100 digits of ? (Below is the frequency table for the first 100 digits of .) x f

0 1 2 3 4 5 6 7 8 9 8 8 12 11 10 8 9 8 12 14

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 58) An engineer has designed an elevator and wishes to determine the maximum number of 58) people that will be allowed to ride in the elevator at a time. In order to do this, the engineer needs to know the average weight of the people likely to ride in the elevator. Which type of average would be the most useful?

Provide an appropriate response. 59) How does Q3 - Q2 compare to Q2 - Q1 for a distribution which is skewed to the right?

59)

for a distribution which is skewed to the left? for a uniform distribution? (The three quartiles of a data set from smallest to largest are denoted Q1 , Q2 , Q3 ).

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given context to formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the null hypothesis. 60) A company claims that the proportion of defectives among its new DVD players is only 60) 0.01 (1%). A consumer group believes that the proportion of defectives is higher than this. The consumer group picks a random sample of 200 of the DVD players and finds the proportion of defectives in the sample to be 0.022. Assuming that the proportion of defectives for all the company's DVD players is p = 0.01, the probability of selecting a sample in which the proportion of defectives is 0.022 or more is 0.044.

Provide an appropriate response. 61) In the Florida lottery, the numbers (between 1 and 49) are generated randomly with the expectation that each number has an equal chance of winning. Draw a boxplot which should illustrate the data set of all numbers picked for the lottery during the past year.

62) Marcella is nearing retirement age and has some money to invest. She is deciding

between Fund A which in the past has grown by a mean of 7% per year with a standard deviation of 2% and Fund B which has grown by a mean of 10% with a standard deviation of 6%. Which fund should she choose? Explain your thinking.

61)

62)

63) Do you think it is possible to find two data sets such that the first data set has a smaller

63)

range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given context to formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the null hypothesis. 64) A consumer group believes that the mean volume of juice in a company's 24 ounce juice 64) bottles is actually less than 24 ounces. In a random sample of 310 bottles, the mean volume of juice was 23.9 ounces. Assuming that the mean volume of juice for all the company's 24-ounce bottles is 24 ounces, the probability of selecting a random sample with a mean volume of 23.9 ounces or less is 0.00017.

65) A company claims that it pays women the same as men for comparable work. The union

65)

decides to investigate this claim. The mean monthly salary for men in entry level positions is $2250. Amongst a random sample of 60 female employees in similar positions , the mean monthly salary was $2210. Assuming that the mean salary for all female employees in entry level positions is $2250, the probability of selecting a sample in which the mean monthly salary is $2210 or less is 0.06.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 66) You are considering moving to a new city and would like to know the average price of a 66) new home in that city. Which type of average would be the most useful to you?

Provide an appropriate response. 67) A population consists of 100 professional gymnasts and 100 professional basketball players. For this group, the average height is 70 inches. However, most of the gymnasts are between 57 and 61 inches tall while most of the basketball players are between 78 and 82 inches tall. For this group, observations far from the mean are more common than observations close to the mean. Describe what a boxplot for the heights of this group would look like. Discuss, in particular, the lengths of the whiskers relative to the width of the box and explain your reasoning.

67)

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 68) A state governor is planning a tax cut. The governor is to announce the average amount 68) that people would save if the tax cut were to take effect. If the governor wants to exaggerate the benefit of the tax cut, which average would he quote?

69) A shoe manufacturer wants to know in which size they should make the most shoes.

69)

70) A parcel service wants to estimate how many vans it will need. It knows how many

70)

Which type of average would be the most useful?

parcels are delivered each day, but it also needs to know the average volume of the parcels. Which average would be the most useful?

Provide an appropriate response. 71) In essence, the standard deviation indicates how far, on average, the observations are from the mean. Do you think that for the data set below the standard deviation will give a good indication of the typical deviation from the mean?

71)

2, 3, 4, 4, 5, 5, 6, 6, 100 What drawback of the standard deviation is illustrated by this example?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 72) The heights of nine different mountains are shown in the table below. Find the mean height. Round your answer to the nearest foot. Mountain Height (feet) Mt Mckinley, Alaska 20,320 Aconcagua, Argentina 22,834 Kilimanjaro, Tanzania 19,340 Mont Blanc, France 15,771 Mt Everest, Nepal/Tibet 29,028 K2, Kashmir 28,250 Mt Cook, New Zealand 12,349 Mt Logan, Yukon 19,850 Citlaltepec, Mexico 18,700

A) 20,309 ft

B) 20,716 ft

C) 19,850 ft

D) 20,837 ft

72)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 73) An environmental group believes that the health of the residents of Castletown is adversely 73) affected by the oil refinery in their town. It believes that in Castletown, the proportion of children who suffer from asthma is higher than the nationwide proportion of 9.1%. The hypotheses are as follows: Null hypothesis: proportion of Castletown children with asthma = 9.1% Alternative hypothesis: proportion of Castletown children with asthma > 9.1% A) Rejecting the null hypothesis means there is evidence that the proportion of Castletown children with asthma is greater than 9.1% Accepting the null hypothesis means there is evidence to conclude that the proportion of Castletown children with asthma is equal to 9.1% B) Rejecting the null hypothesis means there is insufficient evidence that the proportion of Castletown children with asthma is equal to 9.1% Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of Castletown children with asthma is greater than 9.1% C) Rejecting the null hypothesis means there is evidence that the proportion of Castletown children with asthma is not equal to 9.1% Accepting the null hypothesis means there is evidence to conclude that the proportion of Castletown children with asthma is equal to 9.1% D) Rejecting the null hypothesis means there is evidence that the proportion of Castletown children with asthma is greater than 9.1% Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of Castletown children with asthma is greater than 9.1%

Use the 68-95-99.7 rule to solve the problem. 74) For women at Hartford College, times to run 400 meters are normally distributed with a mean of 85 seconds and a standard deviation of 7 seconds. What percentage of the times are more than 64 seconds? A) 0.3% B) 99.85% C) 99.7% D) 0.15% A hypothesis test is to be performed. State the null and alternative hypotheses. 75) An environmental group believes that the health of the residents of Castletown is adversely affected by the oil refinery in their town. It believes that in Castletown, the proportion of children who suffer from asthma is higher than the nationwide proportion of 9.1%. A) Null hypothesis: proportion of Castletown children with asthma = 9.1% Alternative hypothesis: proportion of Castletown children with asthma 9.1% B) Null hypothesis: proportion of Castletown children with asthma < 9.1% Alternative hypothesis: proportion of Castletown children with asthma > 9.1% C) Null hypothesis: proportion of Castletown children with asthma > 9.1% Alternative hypothesis: proportion of Castletown children with asthma = 9.1% D) Null hypothesis: proportion of Castletown children with asthma = 9.1% Alternative hypothesis: proportion of Castletown children with asthma > 9.1%

74)

75)

Provide an appropriate response. 76) What does it mean for an observed difference to be statistically significant at the 0.01 level? A) The probability of the observed difference occurring if the alternative hypothesis is true is 1 in 100 or more. B) The probability of the observed difference occurring if the alternative hypothesis is true is 1 in 100 or less. C) The probability of the observed difference occurring by chance is 1 in 100 or more.

76)

D) The probability of the observed difference occurring by chance is 1 in 100 or less. Find the median for the given sample data. 77) The weights (in ounces) of 21 cookies are shown. Find the median weight. 0.63 1.26 0.65 1.62 0.78 0.74 1.46 1.26 1.53 0.94 0.63 1.13 1.39 0.87 0.47 1.13 0.74 1.39 1.72 0.78 0.56 A) 0.91 ounces B) 0.94 ounces

C) 1.26 ounces

77)

D) 0.87 ounces

Find a 95% confidence interval for the true population proportion. 78) In a poll of 1,035 college students, 19% said that they had cheated at least once on an exam. A) 18.9% to 19.1% B) 17.4% to 20.6% C) 12.8% to 25.2% D) 15.9% to 22.1% A hypothesis test is to be performed. State the null and alternative hypotheses. 79) A consumer group believes that the proportion of defects among computers produced by one manufacturer is greater than the 2% claimed by the company. A) Null hypothesis: proportion of defectives > 2% Alternative hypothesis: proportion of defectives = 2% B) Null hypothesis: proportion of defectives < 2% Alternative hypothesis: proportion of defectives > 2% C) Null hypothesis: proportion of defectives = 2% Alternative hypothesis: proportion of defectives > 2% D) Null hypothesis: proportion of defectives = 2% Alternative hypothesis: proportion of defectives 2% Solve the problem. 80) In a certain country, weights of women are normally distributed with a mean of 138 lb and a standard deviation of 15 lb. What percentage of women in that country weigh more than 120 lb? A) 1.20% B) 53.98% C) 11.51% D) 88.49%

78)

79)

80)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 81) 20, 10, 6, 7, 11, 11, 19, 15, 8 81) A) 1.5 B) 5.1 C) 4.8 D) 5.4 Identify the distribution as symmetric, left-skewed, or right-skewed. 82) The amounts of tax paid by U.S. residents A) Right-skewed B) Symmetric

82) C) Left-skewed

Solve the problem. 83) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students, B's to the next 25%, and C's to the next 42%. What is the bottom cutoff for a C grade? Round your answer to the nearest whole number. A) 63 B) 68 C) 77 D) 65 Find the mode(s) for the given sample data. 84) The table shows the country represented by the winner of the 10,000 meter run in the Summer Olympic Games in various years. Year 1912 1920 1924 1928 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992

83)

84)

Country Finland Finland Finland Finland Poland Finland Czechoslovakia Czechoslovakia USSR USSR United States Kenya Finland Finland Ethiopia Italy Morocco Morocco

Find the mode of the country data. A) 1912 B) Morocco

C) Finland

D) 7

Find the median for the given sample data. 85) 8, 16, 19, 21, 30, 30, 49 Find the median for the data. A) 25.5 B) 19

C) 21

D) 30

Find the mode(s) for the given sample data. 86) -20, -34, -46, -34, -49, -34, -49 A) -34 B) -46

C) -49

D) -38

85)

86)

Identify the distribution as symmetric, left-skewed, or right-skewed. 87) Weights of new-born babies A) Left-skewed B) Symmetric

87) C) Right-skewed

A hypothesis test is to be performed. State the null and alternative hypotheses. 88) Carter Motor Company claims that its new sedan, the Libra, will average better than 27 miles per gallon, which is the gas mileage of its competitor. A) Null hypothesis: mean gas mileage = 27 mpg Alternative hypothesis: mean gas mileage > 27 mpg B) Null hypothesis: mean gas mileage < 27 mpg Alternative hypothesis: mean gas mileage > 27 mpg C) Null hypothesis: mean gas mileage = 27 mpg Alternative hypothesis: mean gas mileage 27 mpg D) Null hypothesis: mean gas mileage > 27 mpg Alternative hypothesis: mean gas mileage = 27 mpg Construct a boxplot as requested. 89) The highest temperatures ever recorded (in °F) in 32 different U.S. states are shown below. Construct a boxplot for the data set. 100 100 105 109 110 110 114 115 116 118 119 120

105 112 117 121

106 112 118 122

106 112 118 125

107 114 118 128

88)

89)

107 114 118 134

Solve the problem. 90) The numbers below represent the amount of precipitation, in inches, on January 1st in eleven different U.S. cities. Find the mean precipitation. Round your answer to the nearest ten-thousandth of an inch. 0.127 0.088 0.118 0.082 0.088 0.108 0.117 0.096 0.139 0.129 0.098 A) 0.1082 in. B) 0.108 in.

C) 0.0992 in.

D) 0.1190 in.

90)

Obtain the five-number summary for the given data. 91) The weights (in pounds) of 18 randomly selected adults are given below. 120 144 187 155 119 136 127 140 179 164 182 202 114 171 131 151 167 171 A) 114, 131, 153.0, 171, 202

91)

B) 114, 129.00, 151, 169.0, 202 D) 114, 129.00, 153.0, 169.0, 202

C) 114, 130.00, 153.0, 173.00, 202

Solve the problem. 92) The weights, in pounds, of twelve apples are given below. Find the mean weight. Round your answer to the nearest thousandth of a pound. 0.29 0.36 0.37 0.26 0.30 0.31 0.37 0.26 0.30 0.34 0.33 0.30 A) 0.305 lb B) 0.344 lb

C) 0.291 lb

Identify the distribution as symmetric, left-skewed, or right-skewed. 93) The diameters of the apples growing on a particular tree A) Right-skewed B) Symmetric

92)

D) 0.316 lb

93) C) Left-skewed

Solve the problem. 94) Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. To what percentile does a salary of $48,000 correspond? A) 91st B) 41st C) 43rd D) 93rd

94)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 95) 5, 5, 20, 15, 15, 18, 16, 16, 8 95) A) 5.6 B) 6.0 C) 1.6 D) 5.3 Use the 68-95-99.7 rule to solve the problem. 96) Assume that a distribution has a mean of 22 and a standard deviation of 5. What percentage of the values in the distribution do we expect to fall between 22 and 32? A) 47.5% B) 25% C) 95% D) 5% Obtain the five-number summary for the given data. 97) The normal annual precipitation (in inches) is given below for 21 different U.S. cities. 39.1 30.6 18.5 32.6 27.1 27.8 8.6 23.8 42.6 30.6 20.3 12.0 5.1 13.8 22.5 10.9 16.2 25.4 17.2 15.6 51.7 A) 5.1, 14.250, 21.40, 29.900, 51.7

B) 5.1, 14.70, 22.5, 30.60, 51.7 D) 5.1, 14.70, 21.40, 30.60, 51.7

C) 5.1, 14.250, 22.5, 29.900, 51.7

96)

97)

Solve the problem. 98) The monthly incomes of trainees at a local factory are normally distributed with a mean of $1600 and a standard deviation $150. What percentage of trainees earn less than $1390 a month? A) 91.92% B) 8.08% C) 1.40% D) 44.04%

99) Last year, nine employees of an electronics company retired. Their ages at retirement are listed

98)

99)

below. Find the mean retirement age. Round your answer to the nearest tenth. 50 64 66 50 64 58 62 53 54 A) 57.9

B) 58.0

C) 57.3

D) 56.6

Use the range rule of thumb to approximate the standard deviation. 100) The maximum value of a distribution is 41.2 and the minimum value is 2.8. Round results to the nearest tenth. A) 15.2 B) C) 14.6 D) 9.6

100)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 101) A consumer advocacy group believes that the mean volume of juice in a company's 16-ounce 101) juice bottles is actually less than 16 ounces. The hypotheses are as follows: Null hypothesis: mean volume = 16 ounces Alternative hypothesis: mean volume < 16 ounces A) Rejecting the null hypothesis means there is evidence that the mean volume is less than 16 ounces. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean volume is equal to 16 ounces. B) Rejecting the null hypothesis means there is evidence that the mean volume is less than 16 ounces. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean volume is less than 16 ounces. C) Rejecting the null hypothesis means there is evidence that the mean volume is not equal to 16 ounces. Accepting the null hypothesis means there is evidence to conclude that the mean volume is equal to 16 ounces. D) Rejecting the null hypothesis means there is evidence that the mean volume is less than 16 ounces. Accepting the null hypothesis means there is evidence to conclude that the mean volume is equal to 16 ounces.

Solve the problem. Round your answer to two decimal places. 102) Scores on a test are normally distributed with a mean of 103 and a standard deviation of 13. What is the exam score corresponding to a standard score of -0.38? A) 102.97 B) 107.94

C) 98.06

D) None of the above

102)

State how many peaks you would expect for the distribution described. 103) Heights of a group of college athletes consisting of the gymnastics team and the basketball team A) None B) One C) Two D) Three Find the margin of error for the survey results described. 104) In a poll of 395 adults, 57% said that they favored the proposed environmental laws. Give your answer as a decimal to three decimal places. A) 0.101 B) 0.050 C) 0.003 D) 0.025

103)

104)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 105) In a clinical study of an arthritis medication, 28% of those taking the placebo reported 105) improvement. The manufacturer of the medication claims that among those taking the medication, the proportion reporting improvement will be higher than this. The hypotheses are as follows: Null hypothesis: proportion reporting improvement = 28% Alternative hypothesis: proportion reporting improvement > 28% A) Rejecting the alternative hypothesis means there is evidence that the proportion reporting improvement is equal to 28% Accepting the null hypothesis means there is evidence to conclude that the proportion reporting improvement is equal to 28% B) Rejecting the null hypothesis means there is evidence that the proportion reporting improvement is not equal to 28% Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion reporting improvement is greater than 28% C) Rejecting the null hypothesis means there is evidence that the proportion reporting improvement is greater than 28% Accepting the null hypothesis means there is evidence to conclude that the proportion reporting improvement is equal to 28% D) Rejecting the null hypothesis means there is evidence that the proportion reporting improvement is greater than 28% Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion reporting improvement is greater than 28%

Use the range rule of thumb to approximate the standard deviation. 106) 15, 42, 53, 7, 9, 12, 14, 28, 47 A) 15.8 B) 11.5 C) 29.1

106) D) 16.6

Solve the problem. 107) The grocery expenses for six families were $74.29, $76.96, $61.21, $41.36, $60.13, and $56.56. Compute the mean grocery bill. Round your answer to the nearest cent. A) $92.63 B) $61.75 C) $74.10 D) $62.10

107)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 108) At Linden High School there are math tests at the end of each three-month session. On all of the 108) last 10 days when there was a math test at school, Brian got a cold and had to stay home. He didn't have colds at other times. A) Not statistically significant B) Statistically significant

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 109) 42 19 32 23 15 43 75 109) A) 8,857.3 B) 32 C) 20.5 D) 11,377 Find the range for the given data. 110) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below. 0.548 0.597 0.186 0.421 0.266 0.111 A) 0.548 m

B) 0.08 m

C) 0.111 m

D) 0.486 m

For the given data value, find the standard score and the percentile. 111) A data value 1.8 standard deviations below the mean. A) z = 1.8; percentile = 96.41 B) z = -1.8; percentile = 96.41

C) z = -0.18; percentile = 42.07

110)

111)

D) z = -1.8; percentile = 3.59

Obtain the five-number summary for the given data. 112) The test scores of 15 students are listed below.

112)

40 46 49 55 59 63 67 70 74 80 85 87 90 94 95 A) 40, 53.50, 70, 85.5, 95

B) 40, 55, 72.0, 87, 95 D) 40, 53.50, 72.0, 85.5, 95

C) 40, 55, 70, 87, 95

Use the 68-95-99.7 rule to solve the problem. 113) The annual precipitation for one city is normally distributed with a mean of 38.2 inches and a standard deviation of 4 inches. Fill in the blanks. In 99.7% of the years, the precipitation in this city is between ___ and ___ inches. A) 38.2, 50.2 B) 30.2, 38.2 C) 30.2, 46.2 D) 26.2, 50.2

113)

Use the range rule of thumb to approximate the standard deviation. 114) The race speeds for the top eight cars in a 200-mile race are listed below. Round results to the nearest tenth. 187.1 186.7 189.2 188.2 175.6 182.7 184.2 178.6 A) 3.4 B) 7.5 C) 1.1 D) 6.8 Find the margin of error for the survey results described. 115) During the questioning of 80 potential jury members, 39% said that they had already formed an opinion as to the guilt of the defendant. Give your answer as a percentage to one decimal place. A) 11.2% B) 1.3% C) 22.4% D) 5.6% Solve the problem. 116) The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score. Round your answer to the nearest tenth. 524 595 353 357 614 350 356 582 470 482 A) 468.3

B) 476.0

C) 477.9

37 57 71 82

41 59 74 83

44 63 74 86

46 65 75 89

48 66 77 92

53 68 78 95

55 69 79 99

115)

116)

D) 459.1

Construct a boxplot as requested. 117) The test scores of 32 students are listed below. Construct a boxplot for the data set. 32 57 70 81

114)

117)

For the given data value, find the standard score and the percentile. 118) A data value 2.3 standard deviations below the mean. A) z = -2.3; percentile = 1.07 B) z = -0.23; percentile = 40.13

C) z = -2.3; percentile = 98.93

118)

D) z = 2.3; percentile = 98.93

Construct a boxplot as requested. 119) Here are the ages of the male and female employees at First River Bank. Draw a box plot for each of the two data sets.

119)

Males Age Females Age Mike 18 Kellie 21 Steven 19 Lauren 21 Jeff 21 Pat 23 Kevin 21 Beth 26 Robert 24 Stacy 26 Jason 26 Tracie 28 Dean 27 Meredith 29 Roy 28 Tiffany 35 Ronald 29 Jackie 37

Provide an appropriate response. 120) Which of the following statements concerning areas under the standard normal curve is/are true? a. If a z-score is negative, the area to its right is greater than 0.5 b. If the area to the right of a z-score is less than 0.5, the z-score is negative. c. If a z-score is positive, the area to its left is less than 0.5 A) a, b B) b C) a, c D) b, c

E) a

120)

Find a 95% confidence interval for the true population proportion. 121) During the questioning of 90 potential jury members, 50% said that they had already formed an opinion as to the guilt of the defendant. A) 44.7% to 55.3% B) 49.9% to 50.1% C) 39.5% to 60.5% D) 48.9% to 51.1%

121)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 122) 201, 290, 152, 180, 122, 119, 131, 181, 204 122) A) 57.6 B) 53.9 C) 50.8 D) 21.9 Find the median for the given sample data. 123) A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.

123)

78, 38, 212, 106, 251, 242, 242 Find the median number of newspapers sold. A) 212 B) 106

C) 167

D) 242

Use the 68-95-99.7 rule to solve the problem. 124) The amount of Jen's monthly phone bill is normally distributed with a mean of $62 and a standard deviation of $12. Fill in the blanks. 68% of her phone bills are between $___ and $___. A) 62, 74 B) 38, 86

C) 50, 74

D) 38, 62

State whether you would expect the data set to be normally distributed. 125) The amount of property taxes paid by homeowners A) Normal B) Not normal Use the range rule of thumb to approximate the standard deviation. 126) The heights in feet of people who work in an office are as follows. Round results to the nearest tenth. 5.7 5.5 6.0 5.4 5.7 5.6 5.7 6.2 6.0 5.6 A) 0.5 B) 1.2 C) 0.1 D) 0.2

124)

125)

126)

A hypothesis test is to be performed. State the null and alternative hypotheses. 127) A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. A) Null hypothesis: mean fee = $1200 Alternative hypothesis: mean fee $1200 B) Null hypothesis: mean fee < $1200 Alternative hypothesis: mean fee > $1200 C) Null hypothesis: mean fee = $1200 Alternative hypothesis: mean fee > $1200 D) Null hypothesis: mean fee > $1200 Alternative hypothesis: mean fee = $1200 Obtain the five-number summary for the given data. 128) The National Education Association collects data on the number of years of teaching experience of high-school teachers. A sample taken this year of 19 high-school teachers yielded the following data on number of years of teaching experience. 33 13 1 20 31 9 3 12 2 23 25 1 33 26 6 18 24 22 31 A) 1, 6, 20, 26, 33

128)

B) 1, 5.25, 20, 25.25, 33 D) 1, 5.25, 19.0, 25.25, 33

C) 1, 6, 19.0, 26, 33

State how many peaks you would expect for the distribution described. 129) Speeds of everyone traveling on a country road, including cyclists and motorists A) Two B) One C) Three D) None Find the margin of error for the survey results described. 130) In a poll of 1,091 college students, 16% said that they had cheated at least once on an exam. Give your answer as a percentage to one decimal place. A) 0.1% B) 1.5% C) 3.0% D) 6.1% Find the range for the given data. 131) Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores. 25 40 19 49 56 A) 19

127)

B) 56

C) 15

State whether you would expect the data set to be normally distributed. 132) The diameters of the redwood trees in a forest. A) Normal B) Not normal

129)

130)

131)

D) 37

132)

State how many peaks you would expect for the distribution described. 133) Number showing when a single die is rolled 100 times A) None B) One C) Three

133) D) Two

Find the margin of error for the survey results described. 134) In a survey of 604 employees of a large company, 22% said that they had high job satisfaction. Give your answer as a decimal to three decimal places. A) 0.020 B) 0.002 C) 0.041 D) 0.081

134)

State whether the distribution appears to be (roughly) normal.

135)

A) Not normal

B) Normal

For the given data value, find the standard score and the percentile. 136) A data value 0.6 standard deviations above the mean. A) z = 0.6; percentile = 2.5 B) z = -0.6; percentile = 27.43

C) z = 0.6; percentile = 72.57

136)

D) z = 0.06; percentile = 51.99

State whether you would expect the data set to be normally distributed. 137) The amount of coffee which a filling machine puts into "4 ounce jars" A) Not normal B) Normal Find a 95% confidence interval for the true population proportion. 138) In a survey of 312 female employees of a large company, 24% said that they had experienced some form of sexual harassment while working for the company. A) 23.7% to 24.3% B) 23.9% to 24.1% C) 12.7% to 35.3% D) 18.3% to 29.7%

137)

138)

Construct a boxplot as requested. 139) The test scores of 40 students are listed below. Construct a boxplot for the data set. 25 59 72 81

35 62 73 82

43 63 74 83

44 65 76 85

47 66 77 89

48 68 77 92

54 69 78 93

55 69 79 94

56 71 80 97

139)

57 72 81 98

For the given data value, find the standard score and the percentile. 140) A data value 1.3 standard deviations above the mean. A) z = 0.13; percentile = 55.96 B) z = -1.3; percentile = 9.68

C) z = 1.3; percentile = 2.2

140)

D) z = 1.3; percentile = 90.32

Use the 68-95-99.7 rule to solve the problem. 141) The time it take Claudia to drive to work is normally distributed with a mean of 40 minutes and a standard deviation of 6 minutes. What percentage of the time will it take her less than 46 minutes to drive to work? A) 68% B) 32% C) 16% D) 84% Identify the distribution as symmetric, left-skewed, or right-skewed. 142) Shoe sizes of adult women A) Left-skewed B) Symmetric Find the standard score for the given data value. 143) A data value in the 88th percentile. A) z = 1.2 B) z = 81.59

141)

142) C) Right-skewed

143) C) z = -1.4

D) z = -2.4

A hypothesis test is to be performed. State the null and alternative hypotheses. 144) At one school, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. A) Null hypothesis: mean time < 21.6 hours Alternative hypothesis: mean time = 21.6 hours B) Null hypothesis: mean time = 21.6 hours Alternative hypothesis: mean time 21.6 hours C) Null hypothesis: mean time = 21.6 hours Alternative hypothesis: mean time < 21.6 hours D) Null hypothesis: mean time > 21.6 hours Alternative hypothesis: mean time < 21.6 hours Find the mode(s) for the given sample data. 145) The weights (in ounces) of 14 different apples are shown below. 6.3 4.9 5.3 5.9 6.0 6.3 4.9 4.0 6.5 5.9 6.3 4.0 5.9 5.0 A) 6.3, 5.9 B) 6.3

146) 83, 35, 32, 35, 29, 83 A) 83

144)

145)

C) None

D) 6.10

C) 35

D) 83, 35

C) z = -2.4

D) z = -1.4

146) B) 49.5

Find the standard score for the given data value. 147) A data value in the 8th percentile. A) z = 78.81 B) z = 0.85

147)

Solve the problem. 148) Frank's Furniture employees earned the following amounts last week:

148)

$312.19 $423.95 $394.65 $331.56 $445.00 $226.02 $453.04 $430.94 $467.58 What was the mean amount earned by an employee last week? Round your answer to the nearest cent. A) $387.21 B) $380.55 C) $435.62 D) $497.85

Find the median for the given sample data. 149) The salaries of ten randomly selected doctors are shown below.

149)

$104,000 $141,000 $190,000 $214,000 $220,000 $140,000 $126,000 $828,000 $208,000 $152,000 Find the median salary. A) $258,000

B) $232,000

C) $190,000

D) $171,000

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 150) The numbers listed below represent the amount of money that Tom has saved in each of the last 8 150) months. $218 $151 $446 $325 $161 $415 $379 $417 Compute the standard deviation. A) $890,542.0 B) $120.6 C) $289.0 D) $788,768.0 Find the mode(s) for the given sample data. 151) 20, 45, 46, 45, 49, 45, 49 A) 46 B) 49

151) C) 42.7

D) 45

Find a 95% confidence interval for the true population proportion. 152) In a random sample of 108 births at one hospital, 27% were by Caesarean section. A) 26.1% to 27.9% B) 17.4% to 36.6% C) 22.2% to 31.8% D) 26.9% to 27.1%

152)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 153) 34 of the 220 suicide cases occurred on a Monday. 153) A) Statistically significant B) Not statistically significant

A hypothesis test is to be performed. State the null and alternative hypotheses. 154) During one flu epidemic the proportion of adults nationwide who have come down with the flu is 8%. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu. A) Null hypothesis: proportion of those vaccinated catching the flu = 8% Alternative hypothesis: proportion of those vaccinated catching the flu 8% B) Null hypothesis: proportion of those vaccinated catching the flu = 8% Alternative hypothesis: proportion of those vaccinated catching the flu < 8% C) Null hypothesis: proportion of those vaccinated catching the flu < 8% Alternative hypothesis: proportion of those vaccinated catching the flu = 8% D) Null hypothesis: proportion of those vaccinated catching the flu > 8% Alternative hypothesis: proportion of those vaccinated catching the flu < 8% Provide an appropriate response. 155) The area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%? a. The percentage of scores between 120 and 130 b. The percentage of scores between 110 and 120 c. The percentage of scores between 80 and 90 d. The percentage of scores between 90 and 120

A) a, b

B) a

C) b

D) b, c

E) d

154)

155)

State whether you would expect the data set to be normally distributed. 156) Times for able bodied female college students to run 400 meters. A) Not normal B) Normal Find the margin of error for the survey results described. 157) In a poll of 1,599 adults, 38% said that they exercised regularly. Give your answer as a percentage to one decimal place. A) 2.5% B) 5.0% C) 1.3%

156)

157) D) 0.1%

Solve the problem. 158) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? A) 97.72% B) 47.72% C) 37.45% D) 2.28%

158)

State whether the distribution appears to be (roughly) normal.

159)

A) Not normal

B) Normal

Solve the problem. 160) Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. A score of 560 represents what percentile? Round the percentile to the nearest tenth. A) 70.1 B) 68.8 C) 66.7 D) 72.6

161) Scores on a test are approximately normally distributed with a mean of 70 and a standard

160)

161)

deviation of 9. The teacher wants to give A's to the top 10% of students, B's to the next 25%, C's to the next 40%, D's to the next 16%, and F's to the bottom 9%. What is the bottom cutoff for a D grade? Round your answer to the nearest whole number. A) 65 B) 62 C) 56 D) 58

Find the standard score for the given data value. 162) A data value in the 46th percentile. A) z = -1.7 B) z = -2.6

162) C) z = -0.1

D) z = 0.1

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 163) You draw a card at random from a deck of cards and replace it. You repeat this 100 times and get 163) an ace 40 times. A) Statistically significant B) Not statistically significant

Use the 68-95-99.7 rule to solve the problem. 164) At one college, GPA's are normally distributed with a mean of 2.6 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.1 and 3.1? A) 99.7% B) 95% C) 68% D) 84% Solve the problem. Round your answer to two decimal places. 165) Scores on a test are normally distributed with a mean of 94 and a standard deviation of 13. What is the standard score for an exam score of 101 ? A) -0.94 B) C) 0.94 D) Construct a boxplot as requested. 166) The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Construct a boxplot for the data set. 4.0 2.2 3.5 3.9

1.0 2.4 3.6 4.1

1.5 2.7 3.6 4.2

1.6 3.4 3.7 4.2

2.0 3.4 3.7 7.0

164)

165)

166)

State whether you would expect the data set to be normally distributed. 167) Scores on a test in which most students have near perfect scores and a few fail. A) Normal B) Not normal Use the 68-95-99.7 rule to solve the problem. 168) Assume that a distribution has a mean of 26 and a standard deviation of 7. What percentage of the values in the distribution do we expect to fall between 19 and 26? A) 68% B) 17% C) 25% D) 34% Identify the distribution as symmetric, left-skewed, or right-skewed. 169) Lengths of human pregnancies A) Right-skewed B) Left-skewed

167)

168)

169) C) Symmetric

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 170) In nine out of the last ten years, the stock market has gone up. 170) A) Not statistically significant B) Statistically significant

Use the 68-95-99.7 rule to solve the problem. 171) The amount of Jen's monthly phone bill is normally distributed with a mean of $68 and a standard deviation of $9. What percentage of her phone bills are between $41 and $95? A) 95% B) 99.9% C) 99.7% D) 68% Find a 95% confidence interval for the true population proportion. 172) In a survey of 320 adults, 61% said that they favored the proposed environmental laws. A) 60.7% to 61.3% B) 61% to 66.6% C) 55.4% to 66.6% D) 58.2% to 63.8%

171)

172)

Construct a boxplot as requested. 173) The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. Construct a boxplot for the data set.

173)

310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 174) You draw a card at random from a deck of cards and replace it. You repeat this 60 times and get a 174) heart 13 times. A) Not statistically significant B) Statistically significant

Find the range for the given data. 175) Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filter change at twelve competing service stations. 32.95 24.95 26.95 28.75 18.90 28.50 30.95 22.95 24.95 26.95 29.75 28.00 A) $14.05

B) $8.20

C) $12.05

D) $10.95

175)

Find the median for the given sample data. 176) The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period. 28 31 38 27 18

30 28 28 33 34 34 34 28 30 30 A) 30

31 30 32 23 30

B) 34

C) 29.85

D) 31

Find the range for the given data. 177) Each student in a sixth-grade class recorded the amount of time he or she had spent watching television during a one-week period. The times (in hours) are listed below. 23.8 29.4

176)

22.9 25.4 A) 8.3 hours

8.3 12.5

13.9 23.9 B) 0.9 hours

177)

16.4 26.4

C) 21.1 hours

D) 13.9 hours

Solve the problem. 178) The grades are given for a student for a particular semester. Use weighted means to find the grade point average. Assume the grade point values are A = 4, B = 3, C = 2, D = 1, and F = 0. Round your answer to the nearest tenth when necessary. Grade

Credit Hours

A D A D D

4 1 3 2 4

A) 14 C) 2.5

178)

B) 2.2 D) 2.8

Use the 68-95-99.7 rule to solve the problem. 179) For adults in the town of Bridgeport, systolic blood pressure is normally distributed with a mean of 132 mmHg and a standard deviation of 11 mmHg. What percentage of adults in the town have a systolic blood pressure less than 121 mmHg? A) 84% B) 16% C) 68% D) 32% Use the range rule of thumb to approximate the standard deviation. 180) 22, 29, 21, 24, 27, 28, 25, 36 A) 1.65 B) 2.8 C) 4.2

179)

180) D) 3.75

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 181) The manager of an electrical supply store measured the diameters of the rolls of wire in the 181) inventory. The diameters of the rolls (in m) are listed below. Compute the standard deviation. 0.481 0.489 0.465 0.244 0.122 0.553 0.526 A) 1.1849 m B) 0.1626 m C) 0.244 m D) 1.3436 m Identify the distribution as symmetric, left-skewed, or right-skewed. 182) Number of siblings of adults in the U.S. A) Symmetric B) Left-skewed Find the mode(s) for the given sample data. 183) 98, 25, 98, 13, 25, 29, 56, 98 A) 25 B) 55.3

182) C) Right-skewed

183) C) 98

D) 42.5

Find the range for the given data. 184) The amount that Jeremy has saved in each of the last six months is shown below. $115 $453 $150 $562 $436 $237 A) $453 B) $87

C) $115

D) $447

Solve the problem. 185) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students. What is the bottom cutoff for an A grade? Round your answer to the nearest whole number. A) 79 B) 90 C) 82 D) 80 State how many peaks you would expect for the distribution described. 186) Weights of the first graders at a school A) Two B) One C) None

184)

185)

186) D) Three

Find the median for the given sample data. 187) A new business had the following monthly net gains:

187)

$7,341 $2,871 $3,415 $8,195 $8,130 $2,891 $3,916 $6,281 $4,952 $4,961 Find the median net gain. A) $4,952.00

B) $5,295.30

C) $5,883.67

D) $4,956.50

State how many peaks you would expect for the distribution described. 188) Voice pitch for the people in the school auditorium consisting of 6 year olds giving a concert, their mothers, and their fathers A) Two B) Three C) None D) One

188)

Find the mode(s) for the given sample data. 189) The speeds (in mi/h) of the cars passing a certain checkpoint are measured by radar. The results are shown below. 44.6 40.4 44.6 42.7

41.3 42.0 41.3 42.5 42.5 44.2 42.7 42.0 A) 43.37

44.2 40.5 44.4 42.9

189)

40.4 44.2 41.3 44.6

B) 41.3

C) 44.6

D) 44.6, 44.2, 41.3

Find the margin of error for the survey results described. 190) In a survey of 130 adults, 33% said that they had tried acupuncture at some point in their lives. Give your answer as a decimal to three decimal places. A) 0.008 B) 0.044 C) 0.088 D) 0.175 State whether you would expect the data set to be normally distributed. 191) Amount of credit card debt of families in the U.S. A) Not normal B) Normal

190)

191)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 192) Last month the average waiting time at a bank was 8.4 minutes. The manager has installed a new 192) computer system and claims that people will no longer have to wait as long. The hypotheses are as follows: Null hypothesis: average waiting time = 8.4 minutes Alternative hypothesis: average waiting time < 8.4 minutes A) Rejecting the null hypothesis means there is insufficient evidence that the mean waiting time is equal to 8.4 minutes. Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to 8.4 minutes. B) Rejecting the null hypothesis means there is evidence that the mean waiting time is not equal to 8.4 minutes. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than 8.4 minutes. C) Rejecting the null hypothesis means there is evidence that the mean waiting time is less than 8.4 minutes. Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to 8.4 minutes. D) Rejecting the null hypothesis means there is evidence that the mean waiting time is less than 8.4 minutes. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than 8.4 minutes.

Use the range rule of thumb to approximate the standard deviation. 193) 496, 598, 503, 528, 565, 601, 576, 543 A) 170.2 B) 26.25 C) 60.6

193) D) 18.75

State whether you would expect the data set to be normally distributed. 194) Sales of birthday cards over a one-year period A) Normal B) Not normal

194)

Find the standard score for the given data value. 195) A data value in the 97th percentile. A) z = -2.3 B) z = 82.89

195) C) z = -1.3

D) z = 1.9

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 196) In eighteen of the last twenty years the annual precipitation in a certain region has been less than 196) in the previous year. A) Not statistically significant B) Statistically significant

Find a 95% confidence interval for the true population proportion. 197) In a survey of 225 adults, 20% said that they had tried acupuncture at some point in their lives. A) 19.6% to 20.4% B) 19.9% to 20.1% C) 16.7% to 23.3% D) 13.3% to 26.7%

197)

Find the median for the given sample data. 198) The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find the median of the data.

198)

3.5 3.9 3.7 2.7

1.6 2.4 1.0 3.6 2.2 1.5 0.4 3.7 A) 3.45 in.

3.7 4.2 4.2 2.0

4.1 3.4 3.4 3.6

B) 2.94 in.

C) 3.40 in.

D) 3.50 in.

A hypothesis test is to be performed. State the null and alternative hypotheses. 199) The governor of a state claims that since his tax cuts have taken effect, the unemployment rate has dropped. The unemployment rate in the state had been 6.3% prior to the tax cuts. A) Null hypothesis: unemployment rate = 6.3% Alternative hypothesis: unemployment rate 6.3% B) Null hypothesis: unemployment rate = 6.3% Alternative hypothesis: unemployment rate < 6.3% C) Null hypothesis: unemployment rate < 6.3% Alternative hypothesis: unemployment rate = 6.3% D) Null hypothesis: unemployment rate > 6.3% Alternative hypothesis: unemployment rate < 6.3%

199)

200) In a clinical study of an arthritis medication, 28% of those taking the placebo reported

200)

improvement. The manufacturer of the medication claims that among those taking the medication, the proportion reporting improvement will be higher than this. A) Null hypothesis: proportion reporting improvement < 28% Alternative hypothesis: proportion reporting improvement > 28% B) Null hypothesis: proportion reporting improvement = 28% Alternative hypothesis: proportion reporting improvement 28% C) Null hypothesis: proportion reporting improvement > 28% Alternative hypothesis: proportion reporting improvement = 28% D) Null hypothesis: proportion reporting improvement = 28% Alternative hypothesis: proportion reporting improvement > 28%

State how many peaks you would expect for the distribution described. 201) Sales of gloves in Boston over a one-year period A) Two B) Three C) None

201) D) One

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 202) 12.4, 20.0, 40.9, 29.2, 10.4, 18.7 202) A) 3,537.1 B) 2,886.4 C) 35.1 D) 11.41 A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 203) A health insurer has determined that the "reasonable and customary" fee for a certain medical 203) procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. The hypothesis tests are as follows: Null hypothesis: mean fee = $1200 Alternative hypothesis: mean fee > $1200 A) Rejecting the null hypothesis means there is evidence that the mean fee is greater than $1200. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean fee is greater than $1200. B) Rejecting the null hypothesis means there is evidence that the mean fee is greater than $1200. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean fee is equal to $1200. C) Rejecting the null hypothesis means there is evidence that the mean fee is not equal to $1200. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean fee is greater than $1200. D) Rejecting the null hypothesis means there is evidence that the mean fee is greater than $1200. Accepting the null hypothesis means there is evidence to conclude that the mean fee is equal to $1200.

Identify the distribution as symmetric, left-skewed, or right-skewed. 204) Amount of credit card debt of families in the U.S. A) Left-skewed B) Symmetric

204) C) Right-skewed

Solve the problem. 205) Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. What percentage of people in that profession earn less than $48,000? A) 6.68% B) 93.32% C) 55.96% D) 1.50% Identify the distribution as symmetric, left-skewed, or right-skewed. 206) Age at death for residents of the U.S. A) Symmetric B) Left-skewed

206) C) Right-skewed

Obtain the five-number summary for the given data. 207) The weekly salaries (in dollars) of sixteen government workers are listed below. 599 813 644 568 492 615 675 685 456 787 496 826 A) 456, 527, 615, 690, 826

205)

207)

690 728 527 560

B) 456, 543.5, 629.5, 709, 826 D) 456, 535.25, 629.5, 718.5, 826

C) 456, 535.25, 615, 718.5, 826

Use the 68-95-99.7 rule to solve the problem. 208) Scores on a test are normally distributed with a mean of 102 and a standard deviation of 20. What percentage of scores are greater than 162? A) 99.85% B) 0.15% C) 99.7% D) 0.3%

208)

State whether you would expect the data set to be normally distributed. 209) The number of siblings of the students at Bloomington High School A) Normal B) Not normal

209)

Use the range rule of thumb to approximate the standard deviation. 210) 3.5 1.6 2.4 3.7 4.1 3.9 1.0 3.6 4.2 3.4 3.7 2.2 A) 12.03 B) 1.09 C) 0.8

210) D) 1.4

Solve the problem. 211) The local Tupperware dealers earned these commissions last month: $1,982.80 $3,850.16 $1,270.62 $2,828.55 $1,569.06 $4,132.88 $4,611.23 $4,403.92 $2,490.20 $3,276.17 What was the mean commission earned? Round your answer to the nearest cent. A) $3,379.51 B) $3,801.95 C) $3,035.56 D) $3,041.56

211)

212) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a

212)

standard deviation of 1.2 oz. What percentage of bottles contain less than 32 oz of soda? A) 38.21% B) 0.25% C) 59.87% D) 40.13%

A hypothesis test is to be performed. State the null and alternative hypotheses. 213) Last month the mean waiting time at a bank was 8.4 minutes. The manager has installed a new computer system and claims that people will no longer have to wait as long. A) Null hypothesis: mean waiting time = 8.4 minutes Alternative hypothesis: mean waiting time 8.4 minutes B) Null hypothesis: mean waiting time = 8.4 minutes Alternative hypothesis: mean waiting time < 8.4 minutes C) Null hypothesis: mean waiting time > 8.4 minutes Alternative hypothesis: mean waiting time < 8.4 minutes D) Null hypothesis: mean waiting time < 8.4 minutes Alternative hypothesis: mean waiting time = 8.4 minutes Construct a boxplot as requested. 214) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set. 5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2 7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7

213)

214)

Identify the distribution as symmetric, left-skewed, or right-skewed. 215) Number of days worked last year by adult males in a U.S. city which has a low unemployment rate A) Symmetric B) Right-skewed C) Left-skewed

215)

Find a 95% confidence interval for the true population proportion. 216) In a survey of 803 employees of a large company, 28% said that they had high job satisfaction. A) 26.2% to 29.8% B) 24.5% to 31.5% C) 28% to 31.5% D) 27.9% to 28.1%

216)

For the given data value, find the standard score and the percentile. 217) A data value 2.5 standard deviations above the mean. A) z = 2.5; percentile = 99.38 B) z = 2.5; percentile = 1.95

217)

C) z = -2.5; percentile = 0.62

D) z = 0.25; percentile = 59.87

Find the mode(s) for the given sample data. 218) 7.32, 7.41, 7.56, 7.32, 7.88, 7.99, 7.62 A) 7.586 B) 7.41

218) C) 7.32

D) 7.56

Provide an appropriate response. 219) Which of the following statements concerning the standard normal curve is/are true (if any)?

219)

a. The area under the standard normal curve to the left of -3 is zero. b. The area under the standard normal curve between any two z-scores is greater than zero. c. The area under the standard normal curve between two z-scores will be negative if both z-scores are negative. d. The area under the standard normal curve to the left of any z-score is less than 1. A) a, c B) a, b C) a D) b, d

Find the median for the given sample data. 220) The distances traveled (in miles) to 7 different swim meets are given below:

220)

15, 18, 36, 55, 62, 70, 75 Find the median distance traveled. A) 62 miles B) 47 miles

C) 36 miles

D) 55 miles

Solve the problem. 221) Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. If you scored 560, what percentage of those taking the test scored below you? A) 51.99% B) 0.60% C) 27.43% D) 72.57%

221)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 222) 3, 5, 6, 6, 9, 1 222) A) 7.6 B) 2.5 C) 2.8 D) 5.4

For the given data value, find the standard score and the percentile. 223) A data value 0.9 standard deviations below the mean. A) z = -0.09; percentile = 46.02 B) z = 0.9; percentile = 81.59

C) z = -0.9; percentile = 81.59

223)

D) z = -0.9; percentile = 18.41

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 224) During one flu epidemic the proportion of adults nationwide who have come down with the flu is 224) 8%. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu. The hypotheses are as follows: Null hypothesis: proportion of those vaccinated catching the flu = 8% Alternative hypothesis: proportion of those vaccinated catching the flu < 8% A) Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to 8% Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%. B) Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8% Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than 8%. C) Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to 8% Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%. D) Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8% Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.

Use the range rule of thumb to approximate the standard deviation. 225) 2, 6, 15, 9, 11, 22, 1, 4, 8, 19 A) 5.25 B) 6.3 C) 2

225) D) 6.8

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 226) The numbers listed below represent the amount of precipitation (in inches) last year in six 226) different U.S. cities. 23.1 17.9 43.6 35.3 22.8 20.7 Compute the standard deviation s. A) 39.5 in. B) 9.99 in. C) 4,449.9 in. D) 4,949.4 in.

Find the mode(s) for the given sample data. 227) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mode(s). 51 61 63 53 50 67 66 58 52 A) 57.9

227)

B) No mode D) 58

C) 51, 61, 63, 53, 50, 67, 66, 58, 52 State whether the distribution appears to be (roughly) normal.

228)

A) Normal

B) Not normal

A hypothesis test is to be performed. State the null and alternative hypotheses. 229) A consumer advocacy group believes that the mean volume of juice in a company's 16-ounce juice bottles is actually less than 16 ounces. A) Null hypothesis: mean volume > 16 ounces Alternative hypothesis: mean volume < 16 ounces B) Null hypothesis: mean volume < 16 ounces Alternative hypothesis: mean volume = 16 ounces C) Null hypothesis: mean volume = 16 ounces Alternative hypothesis: mean volume < 16 ounces D) Null hypothesis: mean volume = 16 ounces Alternative hypothesis: mean volume 16 ounces

229)

State whether the distribution appears to be (roughly) normal.

230)

A) Not normal

B) Normal

Find the standard score for the given data value. 231) A data value in the 31st percentile. A) z = -0.5 B) z = 61.79

231) C) z = -1.9

D) z = 0.5

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 232) Of the people taking the medication, 38 out of 100 noticed improvement in their arthritis. Of the 232) people taking the placebo, 35 out of 100 noticed improvement in their arthritis. A) Not statistically significant B) Statistically significant

Find the standard score for the given data value. 233) A data value in the 58th percentile. A) z = 0.2 B) z = -1.6

233) C) z = -2.5

D) z = 72.57

Solve the problem. 234) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students and B's to the next 23%. What is the bottom cutoff for a B grade? Round your answer to the nearest whole number. A) 76 B) 71 C) 74 D) 66 Find the range for the given data. 235) Jeanne is currently taking college economics. On the past five quizzes, Jeanne got the following scores. 8 19 3 14 9 A) 3

B) 1

C) 19

234)

235)

D) 16

State whether the distribution appears to be (roughly) normal.

236)

A) Not normal

B) Normal

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 237) In 50 rolls of a die, you got 40 sixes. 237) A) Not statistically significant B) Statistically significant

Find a 95% confidence interval for the true population proportion. 238) In a poll of 1,431 adults, 39% said that they exercised regularly. A) 33.7% to 44.3% B) 38.9% to 39.1% C) 36.4% to 41.6%

238) D) 37.7% to 40.3%

Solve the problem. 239) Weights of adult females in a certain country are normally distributed with a mean of 140 lb and a standard deviation of 15 lb. A weight of 119 lb represents what percentile? Round the percentile to the nearest tenth. A) -1.4 B) 2.2 C) 8.1 D) 9.7 Construct a boxplot as requested. 240) Here are the heights of the male and female employees at First City Bank. Draw a double box plot for each of the two data sets. Males Height (inches) Females Height (inches) Ronald 62 Lauren 56 Robert 64 Tracie 59 Jeff 66 Kim 60 Kevin 66 Tiffany 62 Ralph 68 Stacy 66 Mike 70 Jackie 66 Dean 73 Kellie 68 Steven 75 Pat 71 Jason 78 Beth 73

239)

240)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 241) The numbers below represent the test scores of nine students. 241) 30, 74, 59, 25, 78, 84, 69, 74, 28 Find the standard deviation. A) 7.2 B) 22.3 C) 25.3 D) 23.7 State whether you would expect the data set to be normally distributed. 242) Resting heart rates for adults A) Normal B) Not normal

242)

Identify the distribution as symmetric, left-skewed, or right-skewed. 243) Exam scores for an exam in which most students did very well but a few students failed A) Left-skewed B) Symmetric C) Right-skewed

243)

Use the range rule of thumb to approximate the standard deviation. 244) A distribution of data has a maximum value of 95, a median value of 55.5, and a minimum of 16. Round results to the nearest tenth. A) 10.5 B) 19.8 C) 15.8 D) 39.5

244)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 245) Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per 245) gallon, which is the gas mileage of its competitor. The hypotheses are as follows: Null hypothesis: mean gas mileage = 23 mpg Alternative hypothesis: mean gas mileage > 23 mpg A) Rejecting the null hypothesis means there is evidence that the mean gas mileage is not equal to 23 mpg. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is greater than 23 mpg. B) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than 23 mpg. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is equal to 23 mpg. C) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than 23 mpg. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is greater than 23 mpg. D) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than 23 mpg. Accepting the null hypothesis means there is evidence to conclude that the mean gas mileage is equal to 23 mpg.

State how many peaks you would expect for the distribution described. 246) Sales of birthday cards over a one-year period A) Three B) One C) None

246) D) Two

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 247) The governor of a state claims that since his tax cuts have taken effect, the unemployment rate has 247) dropped. The unemployment rate in the state had been 6.3% prior to the tax cuts. The hypotheses are as follows: Null hypothesis: unemployment rate = 6.3% Alternative hypothesis: unemployment rate < 6.3% A) Rejecting the null hypothesis means there is evidence that the unemployment rate is less than 6.3%. Accepting the null hypothesis means there is evidence to conclude that the unemployment rate is equal to 6.3%. B) Rejecting the null hypothesis means there is evidence that the unemployment rate is not equal to 6.3%. Accepting the null hypothesis means there is evidence to conclude that the unemployment rate is equal to 6.3%. C) Rejecting the null hypothesis means there is evidence that the unemployment rate is less than 6.3%. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the unemployment rate is less than 6.3%. D) Rejecting the null hypothesis means there is insufficient evidence that the unemployment rate is equal to 6.3%. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the unemployment rate is equal to 6.3%.

Solve the problem. 248) Scores on a test are normally distributed with a mean of 73 and a standard deviation of 5. What is the percentile for an exam score of 72? Round the percentile to the nearest tenth. A) 42.1 B) -0.2 C) 2.9 D) 40.1

249) Bill kept track of the number of hours he spent exercising each week. The results for four months

248)

249)

are shown below. Find the mean number of hours Bill spent exercising per week. Round your answer to the nearest tenth of an hour. 6.8 7.3 8.2 8.2 8.5 6.8 7.6 8.2 7.9 6.8 8.2 8.3 7.8 7.3 7.3 7.3 8.5 7.6 A) 7.7 hours

B) 7.3 hours

C) 8.2 hours

D) 7.9 hours

250) Find the mean for the given sample data. Round your answer to the nearest tenth if necessary. 17, 16, 18, 17, 16 A) 16.8

B) 17

C) 21

State whether you would expect the data set to be normally distributed. 251) Age at death for residents of the U.S. A) Not normal B) Normal

250)

D) 16

251)

State how many peaks you would expect for the distribution described. 252) Numbers of people with birthdays in a particular month (January through December) A) None B) Three C) Two D) One

252)

Find the range for the given data. 253) The owner of a small manufacturing plant employs six people. The commute distances, in miles, for the six employees are listed below.

253)

2.4 5.8 1.4 4.2 6.2 3.7 A) 1.3 mi

B) 1.4 mi

C) 4.8 mi

D) 5.8 mi

Find the mode(s) for the given sample data. 254) The blood types for 30 people who agreed to participate in a medical study were as follows.

254)

O A A O A AB O B A O A O A B O O O AB A A A B O A A O O B O O Find the mode of the blood types. A) A B) O, A

C) O

D) 13

Use the range rule of thumb to approximate the standard deviation. 255) The following is a set of data showing the water temperature in a heated tub at different time intervals. Round results to the nearest tenth. 116.2 114.4 116.4 114.7 114.7 114.6 112.5 115.6 A) 0.8 B) -55.7 C) 1.0 D) 1.3 Provide an appropriate response. 256) Suppose that the proportion of left handers in a certain population is 0.1 (10%). If samples of size 100 are repeatedly drawn from this population and the proportion of left handers in each sample is recorded, what can you say about the distribution of the sample proportions? A) The sample proportions are approximately normally distributed with a mean of 0.1 and a standard deviation of approximately 1/10. B) The sample proportions are approximately uniformly distributed between the values of 0 and 0.2. C) The sample proportions are approximately normally distributed with a mean of 0.1 and a standard deviation of approximately 1/20. D) Each sample proportion will be equal to 0.1.

255)

256)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 257) There are two candidates for mayor, Maria Hernandez, and Eric Wong. Of 100 people polled, 53 257) say they will vote for Maria Hernandez. A) Not statistically significant B) Statistically significant

Find the standard score for the given data value. 258) A data value in the 16th percentile. A) z = -1.0 B) z = 55.96

258) C) z = 1.0

D) z = -2.1

Answer Key Testname: CHAPTER 6

1) B 2) C 3) C 4) B 5) C 6) D 7) C 8) D 9) B 10) A 11) D 12) C 13) B 14) E 15) B 16) C 17) C 18) A 19) B 20) C 21) C 22) B 23) C 24) D 25) A 26) A 27) B 28) C 29) B 30) A 31) A 32) C 33) B 34) B 35) Answers will vary. Possible answer: The standard deviation will give an indication of how widely the scores vary.

More precisely, it gives an indication of how much the scores deviate, on average, from the mean score of 85. 36) Answers will vary. Possible answer: A small standard deviation would be preferable as this would indicate that the lifetimes of the tires do not vary too widely around the mean. 37) Null hypothesis: mean waiting time = 10 minutes Alternative hypothesis: mean waiting time > 10 minutes The results is significant at the 0.01 level. There is strong evidence for rejecting the null hypothesis in favor of the alternative hypothesis that the mean waiting time is more than 10 minutes.

Answer Key Testname: CHAPTER 6

38) Answers will vary. Possible answer: The first boxplot represents a bell-shaped distribution since it is symmetrical

and has long whiskers relative to the width of the box (indicating that observations close to the mean are more common than those far from the mean). The second boxplot represents a left-skewed distribution, since the whisker to the left is relatively long. 39) Answers will vary. Possible answer: The variance can never be a negative number since it is a sum of squared terms each of which must be positive or zero. It can be zero only if all observations are identical, in which case all deviations from the mean will be zero. 40) The environmental group would prefer a significance level of 0.05 because it is important to reject the null hypothesis if it is false. With a significance level of 0.01, it is harder to reject the null hypothesis - stronger evidence against it is required before it will be rejected. The car manufacturers would prefer a significance level of 0.01 for this reason. Car manufacturers do not want to see the null hypothesis rejected as a finding that temperatures are increasing could lead to stricter regulations on emissions. 41) Answers will vary. Possible answer: The mean income would be most useful as it takes into account the numerical value of all incomes and thus best predicts how much tax will be paid. 42) The median salary would be most useful. Explanations will vary. Possible answer: The median gives the center of the data and is not affected by the few unusually high (or low) starting salaries. The median gives a better indication of the "typical" salary than either the mean or the mode. 43) Answers will vary. 44) Player A has been playing more consistently, with little variation from game to game. Player B has almost the same mean score per game as player A but a higher standard deviation. This means that there is more variation in his score per game, sometimes his score is very high, sometimes quite low If only a medium performance is needed, player A should be chosen as player A rarely has a poor game. If an exceptional performance is needed, player B should be chosen as he is more likely to have an exceptional game than player A 45) Answers will vary. Possible answer: The range will be unaffected, while the standard deviation will increase. The standard deviation is preferable as it takes into account the numerical value of all observations while the range depends only on the smallest and largest observations and disregards other observations. 46) Null hypothesis: proportion of births by Caesarean section = 0.23 Alternative hypothesis: proportion of births by Caesarean section < 0.23 Result is not significant at the 0.05 level. There are no grounds for rejecting the null hypothesis. There is insufficient evidence to conclude that the proportion of Caesarean births at the private hospital is less than 0.23. 47) The mode. The data (winning country) is qualitative. Since the data are not numerical values, it is not possible to find the median or mean, only the most frequently occurring value (i.e. the mode). 48) The mode. The pollster needs to know which candidate will receive the most votes - the most common "value" in the distribution, which is the mode. 49) Distribution C has the smallest median. Distribution D has the greatest variation. Distribution C is skewed to the left. 50) The median. Explanations will vary. Possible answer: The median gives the center of the data and is not affected by the few unusually high salaries. The median gives a better indication of the "typical" amount that will be saved than either the mean or the mode. 51) Taking the bus is faster on average but there is more variation in the times. Cycling takes longer on average but there is less variation in the times. Possibility one - you will be fired if you are even a few minutes late. You should take the bus. If you cycle you will definitely be a little late. If you take the bus you could be on time or could be very late but you at least have a chance of being on time. Possibility two: you will be OK if you are not more than 15 minutes late: You should cycle. If you cycle you will almost certainly be there by 9.15 am. If you take the bus there is a chance you will be more than fifteen minutes late.

Answer Key Testname: CHAPTER 6

52) Answers will vary. Possible answer: The distribution represented by the first boxplot is symmetric, while the

distribution represented by the second boxplot is skewed to the right. 53) Answers will vary. Possible answer. No, she should not reject the null hypothesis. If the null hypothesis were true, the sample mean could easily be as big as 54.2 by chance. So the sample provides no evidence against the null hypothesis 54) Null hypothesis: proportion of African Americans who have been stopped = 0.19 Alternative hypothesis: proportion of African Americans who have been stopped > 0.19 Result is significant at the 0.01 level, and provides strong evidence for rejecting the null hypothesis in favor of the alternative hypothesis that the proportion of African Americans who have been stopped is greater than 0.19. 55) Null hypothesis: mean resting heart rate for college athletes = 72 beats per minute Alternative hypothesis: mean resting heart rate for college athletes < 72 beats per minute The result is not significant at the 0.05 level and there are no grounds for rejecting the null hypothesis. There is insufficient evidence to conclude that the mean resting heart rate for college athletes is less than 72 beats per minute. 56) No. The alternative hypothesis is that the population mean is greater than 40. A sample mean much smaller than 40 does not provide evidence in favor of this alternative hypothesis. The null hypothesis should be rejected only if the sample mean turns out much larger than 40. 57) Check students' drawings. The boxplot for a skewed distribution has a long whisker on one side. The boxplots for uniform and bell-shaped distributions are symmetric but for a bell-shaped distribution, the whiskers are long relative to the width of the box. The distribution of the given frequency table is roughly uniform. 58) The mean. The mean takes into account the numerical value of all the weights and thus will allow the engineer to estimate the total weight of a given number of people. 59) For a distribution which is skewed to the right, Q3 - Q2 is greater than Q2 - Q1 . For a distribution which is skewed to the left, Q3 - Q2 is smaller than Q2 - Q1 . For a uniform distribution, Q3 - Q2 is equal to Q2 - Q1 .

60) Null hypothesis: proportion of defective DVD players = 0.01

Alternative hypothesis: proportion of defective DVD players > 0.01 Result is significant at the 0.05 level, and provides evidence for rejecting the null hypothesis in favor of the alternative hypothesis that the proportion of defectives is greater than 0.01. 61) Check students' drawings. Students should draw a boxplot for a uniform distribution (a symmetric boxplot with the length of each whisker roughly equal to half the width of the box). 62) Fund A would be less risky. Fund B has a higher mean return but also a higher standard deviation indicating that there is more variation in its returns. Since Marcella is nearing retirement age, this is probably a short-term investment. Marcella won't have time to ride out the fluctuations and will not have much flexibility about when to withdraw her money. Of course she may be lucky with Fund B but if she wants more security, she should choose Fund A. 63) It is possible to find two such data sets. Examples will vary. 64) Null hypothesis: mean volume of juice in 24-ounce bottles is 24 ounces Alternative hypothesis: mean volume of juice in 24-ounce bottles is less than 24 ounces The results is significant at the 0.01 level. There is strong evidence for rejecting the null hypothesis in favor of the alternative hypothesis that the mean volume is less than 24 ounces. 65) Null hypothesis: mean monthly salary for female entry level employees = $2250 Alternative hypothesis: mean monthly salary for female entry level employees < $2250 The result is not significant at the 0.05 level, there is insufficient evidence to conclude that the company pays female entry level employees less than male entry level employees. 66) The median. The median gives the center of the data and is not affected by the few unusually high home prices. The median gives a better indication of the "typical" home price than either the mean or the mode.

Answer Key Testname: CHAPTER 6

67) Answers will vary. Possible answer: For this data, the whiskers will be very short relative to the width of the box

since the first and third quartiles will be far apart. 68) The mean. The mean will affected by the few unusually high salaries and will be larger than the median. The mean will not be representative of the amount that most people will save. 69) The mode. The manufacturer needs to know the most common shoe size. 70) The mean. The mean takes into account the actual volume of all the parcels and thus will allow the parcel service to estimate the total volume of a given number of parcels. 71) Answers will vary. Possible answer: No, the standard deviation is 31.9. This is not a good indication of the typical deviation from the mean because the data set contains an extreme observation, namely 100. The standard deviation is very sensitive to extreme observations.

72) B 73) D 74) B 75) D 76) D 77) B 78) D 79) C 80) D 81) B 82) A 83) A 84) C 85) C 86) A 87) B 88) A 89) D 90) A 91) A 92) D 93) B 94) D 95) A 96) A 97) B 98) B 99) A 100) D 101) B 102) C 103) C 104) B 57

Answer Key Testname: CHAPTER 6

105) D 106) B 107) B 108) B 109) C 110) D 111) D 112) C 113) D 114) A 115) A 116) A 117) A 118) A 119) B 120) E 121) C 122) B 123) A 124) C 125) B 126) D 127) C 128) A 129) A 130) C 131) D 132) A 133) A 134) C 135) B 136) C 137) B 138) D 139) D 140) D 141) D 142) B 143) A 144) C 145) A 146) D 58

Answer Key Testname: CHAPTER 6

147) D 148) A 149) D 150) B 151) D 152) B 153) B 154) B 155) D 156) B 157) A 158) D 159) A 160) D 161) D 162) C 163) A 164) C 165) B 166) D 167) B 168) D 169) C 170) B 171) C 172) C 173) C 174) A 175) A 176) A 177) C 178) C 179) B 180) D 181) B 182) C 183) C 184) D 185) C 186) B 187) D 188) B 59

Answer Key Testname: CHAPTER 6

189) D 190) C 191) A 192) D 193) B 194) B 195) D 196) B 197) D 198) A 199) B 200) D 201) D 202) D 203) A 204) C 205) B 206) B 207) B 208) B 209) B 210) C 211) D 212) D 213) B 214) B 215) C 216) B 217) A 218) C 219) D 220) D 221) D 222) C 223) D 224) B 225) A 226) B 227) B 228) A 229) C 230) A 60

Answer Key Testname: CHAPTER 6

231) A 232) A 233) A 234) C 235) D 236) A 237) B 238) C 239) C 240) D 241) D 242) A 243) A 244) B 245) C 246) C 247) C 248) A 249) A 250) A 251) A 252) A 253) C 254) C 255) C 256) C 257) A 258) A

Exam

Chapter 7

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The permutation formula can be used to determine which of the following?

A: The number of possible license plates made with three letters and three digits given that repetition is allowed B: The number of ways of choosing 6 CDs from 20 to bring on vacation C: The number of ways of choosing a first place winner and a second place winner from 10 finalists A) B and C B) C only C) A and B D) A only E) A and C

2) Which of the following events has a probability of 0?

A: The sun will shine all day on January 1st in Portland, Oregon B: I will win the lottery if I buy one ticket C: Tomorrow will be Monday if today is Saturday A) C only

B) A only C) B and C D) All of them E) A and C 3) The combination formula can be used to determine which of the following?

A: The number of sequences of 3 letters using the letters A, B, C, and D if repetitions are not allowed B: The number of ways of choosing a president and a treasurer from 10 people C: The number of ways to choose 3 friends from 10 to invite to dinner A) B and C B) A and B C) C only D) A only E) B only

4) Event A is that it rains in Santa Cruz tomorrow. Event B is that rains in Paris, France tomorrow. Are events A and B: A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

A) A

B) D

C) C

D) B

5) Chantal noted that there are two equally likely outcomes when you flip a fair coin and heads is

one of those outcomes. She concluded that the probability of getting heads on a flip of a fair coin is 1/2 . Which method did Chantal use? A) Relative frequency method B) Empirical method

C) Subjective method

D) Theoretical method

6) The permutation formula can be used to determine which of the following?

A: The number of ways of completing a test consisting of 10 true/false questions B: The number of ways of arranging 8 people in a line C: The number of ways a panel of people could vote if each person votes yes or no A) C only B) A and B C) B and C D) A and C

E) B only

7) When a balanced die is rolled, the probability that a six will appear is 1 . Suppose that you have 6

just rolled the die five times without getting a six. What is the probability that you will get a six on the next roll of the die? A) 1 B) 1 6

C) Greater than 1 but less than 1

D) 0

8) Suppose that 4 items are to be selected from N items and that repetitions are not allowed. Which

of the following is true? A) There are 24 times as many combinations as permutations.

B) There are 4 times as many combinations as permutations. C) There are 4 times as many permutations as combinations. D) There are 24 times as many permutations as combinations. 9) In a large casino, the house wins on its blackjack games with a probability of 50.7%. Which of the

10) A fair coin is tossed 5 times. Which of the following statements is (are) true?

10)

following events is the most unlikely? A: You win at a single game. B: You come out ahead after playing forty times. C: You win at a single game given that you have just won ten games in a row. D: You win at a single game given that you have just lost ten games in a row. A) A B) C C) D D) B

A: The sequence HTHTH is more likely than the sequence HHHHH. B: The sequence HTHTH and the sequence HHHHH are equally likely. C: Getting 5 tails is less likely than getting 3 tails. D: Getting 5 tails and getting 3 tails are equally likely. A) A and C B) A and D C) B and D

D) B and C

11) A card is selected at random from a standard deck of 52 cards. Let

11)

A = event the card is a heart B = event the card is a red card Which of the following is (are) true? A: P(A or B) = P(A) B: P(A or B) = P(B) C: P(A and B) = P(B) D: P(A and B) = P(A) A) A and C B) A and D

C) B and D

D) B and C

12) When using the counting rules to count the number of possible outcomes, the combinations

12)

formula can be used in which of the following situations? A) When repetitions are not allowed and the order of arrangement is important

B) When repetitions are allowed and the order of arrangement is unimportant C) When repetitions are not allowed and the order of arrangement is unimportant D) When repetitions are allowed and the order of arrangement is important 13) Sean flipped a coin 100 times and got heads 42 times. He concludes that the probability of getting

13)

heads on a flip of his coin is 0.42. Which method did Sean use? A) Theoretical method B) Empirical method

C) Multiplication method

D) Subjective method

14) Event A is that Lisa votes for Candidate A in the gubernatorial election and event B is that she

14)

votes for candidate B. Are events A and B: A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

A) B

B) D

C) C

D) A

15) When using the counting rules to count the number of possible outcomes, the permutation

15)

formula can be used in which of the following situations? A) When repetitions are not allowed and the order of arrangement is unimportant

B) When repetitions are allowed and the order of arrangement is important C) When repetitions are not allowed and the order of arrangement is important D) When repetitions are allowed and the order of arrangement is unimportant 16) Which of the following are examples of independent events? A) Two people in the same family falling ill in the same week B) Two laughs by different people watching the same movie in a theater C) Two consecutive wins by a football team D) Two archeological discoveries at different locations, at the same time

16)

17) A game involves tossing a fair coin 200 times. For each tail that appears you lose $1. For each head

17)

that appears, you win $1. After 100 tosses, there have been 40 heads and 60 tails. At this point, with 100 tosses to go, what can you conclude? A: You are more likely to lose than to win. B: You are still equally likely to win or lose because in the long run there should be 50% heads. C: In the next 100 tosses you are likely to get more heads than tails. A) B only B) A and C C) A only D) B and C

18) When a balanced die is rolled, the probability that a four will appear is 1 .

18)

Which of the following statements is a reasonable conclusion? A: If I roll a balanced die 6 times I will get one four B: If I roll a balanced die 300 times I will get fifty fours C: If I roll a balanced die 1200 times, I will get approximately 200 fours A) All of them

B) C only C) B and C D) A and B E) B only 19) Which of the following events has a probability of 1?

19)

A: I will get a perfect score on my math test if I study B: I will die some day C: The world will go on turning if I fail my test A) All of them

B) A and B C) B only D) A and C E) B and C 20) Which pair(s) of events is (are) independent?

20)

A and B given the following: P(A) = 0.4, P(B) = 0.3, P(A and B) = 0.16 C and D given the following: P(C) = 0.4, P(D) = 0.3, P(C|D) = 0.4 A) Neither pair B) C and D C) Both pairs

D) A and B

21) For the students at one college the expected value for "number of siblings" is 1. Which of the

following statements is a reasonable conclusion? A) If a student selected at random has 2 siblings, the next student selected will have no siblings.

B) If 4 students are selected at random, the average number of siblings for the 4 students will be 1.

C) If 100 students are selected at random, the average number of siblings for the 100 students

will be close to 1. D) If a student is selected at random, the most likely number of siblings for the student is 1.

21)

22) Suppose that S and T are mutually exclusive events. Which of the following statements is true? A) S and T may or may not be independent. B) S and T must also be independent. C) S and T cannot possibly be independent.

22)

23) Melissa estimates that the probability that she will marry her boyfriend is 0.6. Which method for

23)

determining probabilities did she use? A) Relative frequency method

B) Subjective method D) Empirical method

C) Theoretical method

24) Given that P(E) = 1, what must be true about the event E? A) The event E is certain. B) The event E is possible but not likely. C) The event E is impossible. D) The event E is probable but not certain.

24)

25) Which of the following statements makes sense?

25)

A: When a balanced die is rolled, there are 6 possible outcomes, therefore the probability that I roll a six is 1/6 B: On my test there are four possible outcomes, I could get an A, a B, a C, or I could fail. Therefore the probability that I get an A is 1/4 C: When I flip two coins there are three possible outcomes: 0 tails, 1 tail, or 2 tails. Therefore the probability that I will get 1 tail is 1/3 A) C only

B) B and C C) A and C D) A only E) All of them 26) When tossing a fair coin, which of the following events is more unlikely? A: Getting 60% tails in 10 tosses B: Getting 60% tails in 100 tosses C: Getting 60% tails in 1000 tosses A) B

B) A D) All are equally likely

C) C

26)

27) Event A is that the weather forecast predicts sun for your hometown tomorrow.

27)

Event B is that it rains tomorrow in your home town. Are events A and B: A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

A) C

B) D

C) A

D) B

28) An insurance company sells an insurance policy for $1000. If there is no claim on a policy, the

28)

29) A knight may win a tournament. He may also fail to win the love of his lady. Are these events

29)

company makes a profit of $1000. If there is a claim on a policy, the company faces a large loss on that policy. The expected value to the company, per policy, is $250. Which of the following statements is (are) true? A: The most likely outcome on any single policy is a profit for the company of $250. B: If the company sells only a few policies, its profit is hard to predict. C: If the company sells a large number of policies, the average profit per policy will be close to $250. A) B and C B) A and C C) B only D) C only

overlapping? Why or why not? A) No, because all ladies love all winners

B) Yes, because some ladies love winners C) Yes, because not all ladies love all winners D) No, because not all ladies love all winners SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

30) A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run,

30)

the player can expect to win 0. Consider the following game. The game costs $1 to play and the payoffs are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following probabilities apply. What are your expected winnings? Does the game favor the player or the owner? Outcome Probability Red .02 Blue .04 Yellow .16 White .78

31) Suppose that the probability of winning at a single game of blackjack is 0.49. If you play ten times in a row, what is the probability you will win all 10 times? Would you be surprised? If 1000 people each play blackjack ten times in one evening, what is the probability that at least one person wins all ten times? Would you be surprised?

31)

32) A card is selected randomly from a standard deck of 52 cards. Let

32)

A = event that the card is an ace. Give examples of events B, C, and D such that A and B are independent, A and C are dependent and overlapping, and A and D are non-overlapping.

33) If you flip a fair coin 10 times would you be surprised if the coin comes up the same way

33)

34) For a particular game at a casino, the expected winning for the player is -$0.87. How

34)

35) Explain what is wrong with the statement below.

35)

36) Explain what is wrong with the statement below.

36)

37) Suppose a mathematician computed the expected winnings (to the player) of each of

37)

every time? What would be the probability of this? If 2000 people all flip a fair coin 10 times, on average how many people could be expected to get the same thing all 10 times?

would you interpret this statement?

It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of winning $100,000 is only 0.000000512.

It's quite a coincidence - the chance that I would have the birthday I do have is only 1/365.

seven different games in a casino. What would you expect to be true for all expected winnings?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. Round your answer to 6 decimal places when necessary. 38) A fair die is rolled. What is the probability of rolling a 3 or a 5? A) 1 B) 1 C) 1 D) 2 3 6 36

39) If two fair dice are rolled, what is the probability of not rolling a sum of 12? A) 1 6

B) 35 36

C) 1 36

39) D) 5 6

Use the at least once rule to find the indicated probability. 40) The probability of winning $20 in a particular lottery is 0.05. What is the probability that you will get at least one $20 winner if you buy 10 tickets? A) 0.599 B) 0.950 C) 0.032 D) 0.401

38)

40)

Find the expected value. 41) In a large casino, the house wins on one of its games with a probability of 50.7%. All bets in the game are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet. What is the expected value to the player of a single game? A) -$0.507 B) -$0.007 C) $0.014 D) -$0.014 Solve the problem. 42) A pizza restaurant advertises 56 different 5-topping pizzas. How many individual toppings does the restaurant use? Assume that no topping is used more than once on a pizza and that the order of the toppings on the pizza is unimportant. A) 7 B) 8 C) 14 D) 11 Find the indicated probability. 43) Three coins are tossed 80 times and the number of heads is recorded. The results are shown in the table below. Outcome Frequency

41)

42)

43)

0 heads 1 head 2 heads 3 heads 28 18 11 23

Compute the empirical probability that at most two heads occur. A) 29 B) 3 C) 29 90 4 2

D) 57 80

Solve the problem. 44) Mark can remember only the first 4 digits of his friend's phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers and if it takes him 20 seconds to try each one, how long would it take to try every possibility? A) 10 minutes B) 33.3 minutes C) 333.4 minutes D) 300 minutes Find the expected value. 45) You are given 12 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Round to the nearest cent. A) $0.75 B) -$0.63 C) $1.50 D) $0.63

46) A contractor is considering a sale that promises a profit of $29,000 with a probability of .7 or a loss

44)

45)

46)

(due to bad weather, strikes, and such) of $4,000 with a probability of .3. What is the expected profit? A) $19,100 B) $25,000 C) $20,300 D) $23,100

Solve the problem. 47) A singer-songwriter wishes to compose a melody. Each note in the melody must be one of the 23 notes in her vocal range. How many different sequences of 6 notes are possible? A) 6,436,343 B) 148,035,889 C) 138 D) 72,681,840

47)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 48) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. A) 11 B) 31 C) 334 D) 31 12 334 365 365 Evaluate the factorial expression. 49) 9! 7! 2!

A) 504

49) B) 36

C) 9

D) 1

Find the indicated probability. 50) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

48)

50)

Allergy Control drug Placebo (no treatment) Total 145 85 41 271 55 115 59 229 200 200 100 500

What is the probability that a randomly selected person was given a placebo or improved? Round your answer to the nearest thousandth when necessary. A) 0.772 B) 0.69 C) 0.17 D) 0.942

Find the indicated probability. Round your answer to 6 decimal places when necessary. 51) Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability that both marbles are white. A) 3 B) 9 C) 3 D) 3 28 56 8 32 Find the indicated probability. 52) The following table displays the number of siblings for students at one middle school. Find the probability that a randomly selected student in the school has 2 siblings. Round your answer to the nearest thousandth. Number of siblings Frequency 0 184 1 260 2 134 3 55 4 23 5 8 6 5 7 1

A) 0.212

B) 0.200

C) 0.276

D) 0.125

51)

52)

Solve the problem. Round your answer to 5 decimal places when necessary. 53) The table shows the leading causes of death for one country in a single recent year.

53)

Cause of Death Deaths Heart Disease 221,950 Cancer 154,400 AIDS 89,745 Stroke 58,865 Pulmonary Disease 54,233 Accidents 40,530 Diabetes 23,353 Pneumonia 21,616 Kidney Disease 11,387 Assume a population of 96.5 million. How much greater is the risk of death by cancer than the risk of death by accident? A) 0.00118 B) 38.09524 C) 3.42857 D) 3.80952

Provide an appropriate response. 54) Which of the following could not possibly be probabilities?

54)

A. -0.61 11 B. 7 C. 0 D. 0.51 A) A and C

B) A, B, and C C) B and C D) A and D E) A and B Find the indicated probability. Round your answer to 6 decimal places when necessary. 55) When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 11? A) 17 B) 7 C) 7 D) 1 36 36 6 66

55)

Make a probability distribution for the given set of events. 56) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

56)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Let X denote the smaller of the two numbers. If both dice come up the same number, then X equals that common value. Find the probability distribution of X. Leave your probabilities in fraction form.

B) x P(X = x) 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6

C) x P(X = x) 1 5/18 2 2/9 3 1/6 4 1/9 5 1/18 6 0

D) x P(X = x) 1 5/18 2 1/4 3 7/36 4 5/36 5 1/9 6 1/36

x P(X = x) 1 11/36 2 1/4 3 7/36 4 5/36 5 1/12 6 1/36

Decide whether events A and B are overlapping or non-overlapping. 57) You roll a red die and a blue die. Event A is that you get a sum of 10. Event B is that you get a six on the red die. A) Non-overlapping B) Overlapping Find the expected value. 58) You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. A) $0.39 B) $0 C) $0.09 D) $1.25 Find the indicated probability. Round your answer to 6 decimal places when necessary. 59) In one town, 77% of adults have health insurance. What is the probability that 9 adults selected at random from the town all have health insurance? A) 0.095152 B) 0.77 C) 6.93 D) 0.116883 Find the expected value. 60) In a large casino, the house wins on one of its games with a probability of 50,700%. All bets are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet. If patrons bet a total of $600,000 on this game in one evening, how much should the casino expect to earn? A) $304,200,000 B) $729,360,000 C) $607,800,000 D) $303,900,000

57)

58)

59)

60)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 61) An IRS auditor randomly selects 3 tax returns from 53 returns of which 8 contain errors. What is the probability that she selects none of those containing errors? A) 0.0024 B) 0.6121 C) 0.6057 D) 0.0034 Solve the problem. Round your answer to 5 decimal places when necessary. 62) The table shows the leading causes of death for one country in a single recent year.

61)

62)

Cause of Death Deaths Heart Disease 163,900 Cancer 119,200 AIDS 68,540 Stroke 41,720 Pulmonary Disease 41,869 Accidents 31,290 Diabetes 18,029 Pneumonia 16,688 Kidney Disease 8,791 Assume a population of 74.5 million. In a typical city of 500,000 , how many people would you expect to die by accident in a year? A) Approximately 2,100 people B) Approximately 1,565 people

C) Approximately 15,645 people

D) Approximately 210 people

Evaluate the factorial expression. 63) 4! 2!

A) 4 2

63) B) 12

C) 2!

D) 4

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 64) Sebastian lives in a rainy city. In his city, in 9 of the past 24 years there have been more than 100 64) days of rain. What is the probability that there will be more than 100 days of rain next year in his city? Give your answer as a fraction. A) 1 B) 3 C) 9 D) 5 2 8 100 8 Solve the problem. Round your answer to 2 decimal places when necessary. 65) In a recent year, there were 58 accidents in commercial aviation among major airlines over 16.0 million flight hours. Find the accident rate in units of accidents per 100,000 flight hours. A) 0.58 accidents per 100,000 flight hours B) 3.6 accidents per 100,000 flight hours

C) 5.8 accidents per 100,000 flight hours

D) 0.36 accidents per 100,000 flight hours

65)

Find the expected value. 66) Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your number comes up, you get $600.00. If your number doesn't come up, you lose your $1. Find the expected net winnings. A) -$0.42 B) -$0.50 C) -$0.40 D) -$1.00

67) In a game, you have a 1/34 probability of winning $121 and a 33/34 probability of losing $5. What is your expected winning? A) -$1.29

C) $3.56

B) -$4.85

66)

67)

D) $8.41

Solve the problem. 68) A shoe store carries one brand of shoe in 3 different styles, 5 sizes, and 5 colors. How many different shoes are available of this one brand? A) 13 B) 45 C) 75 D) 40

69) Ten thousand raffle tickets are sold. One first prize of $1,600, 3 second prizes of $900 each, and 8

68)

69)

third prizes of $400 each are to be awarded, with all winners selected randomly. If you are given one ticket, what are your expected winnings? A) 29 cents B) 107 cents C) 100 cents D) 75 cents

Decide whether events A and B are overlapping or non-overlapping. 70) Event A is that you study at least 5 hours for your math test. Event B is that you study at most 6 hours for your math test. A) Overlapping B) Non-overlapping

70)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 71) You count 61 heads when you toss a coin 100 times. If you don't know whether the coin is fair, 71) what is the probability that the next toss will be heads? A) 0.61 B) 0.061 C) 0.5 D) 1 Find the indicated probability. Round your answer to 6 decimal places when necessary. 72) A bag contains 5 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue? A) 5 B) 6 C) 3 D) 2 3 5 5

73) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the sum is a multiple of 3 or greater than 8. A) 1 B) 1 2 3

C) 17 36

D) 11 36

72)

73)

Solve the problem. Round your answer to 5 decimal places when necessary. 74) The table shows the leading causes of death for one country in a single recent year.

74)

Cause of Death Deaths Heart Disease 202,800 Cancer 126,750 AIDS 68,445 Stroke 47,320 Pulmonary Disease 47,489 Accidents 41,405 Diabetes 20,449 Pneumonia 18,928 Kidney Disease 9,971 Assume a population of 84.5 million. What is the empirical probability of death by AIDS during a single year? A) 0.68 B) 0.000081 C) 0.00081

D) 0.0081

75) The table shows the leading causes of death for one country in a single recent year. Cause of Death Deaths Heart Disease 204,750 Cancer 156,000 AIDS 83,850 Stroke 58,500 Pulmonary Disease 54,795 Accidents 47,775 Diabetes 23,595 Pneumonia 21,840 Kidney Disease 11,505 Assume a population of 97.5 million. What is the empirical probability of death by accident during a single year? A) 0.0049 B) 0.48 C) 0.00049

D) 0.000049

75)

Find the indicated probability. 76) The following table displays a distribution for a group of retired people by career and age at retirement.

182

155

163

303

169

697

76)

Suppose one of these people is selected at random. Compute the probability that the person selected was an attorney and that they retired between 61 and 65. Round your answer to the nearest thousandth. A) 0.261 B) 0.323 C) 0.141 D) 0.435

Determine whether the events A and B are independent. 77) A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random. Event A: A club is selected on the first draw Event B: An ace is selected on the second draw A) Yes B) No Evaluate the factorial expression. 78) 7! (7 - 4)!

A) 7

77)

78) B) 1

C) 210

D) 840

Find the indicated probability. Round your answer to 6 decimal places when necessary. 79) Find the probability of tossing 3 tails, then 4 heads, on the first 7 tosses of a fair coin. A) 3.5 B) 0.015625 C) 0.125 D) 0.007813

79)

Evaluate the factorial expression. 80) 10! 9!

A) 10

80) B) 10

C) 10!

D) 1

Find the indicated probability. Round your answer to 6 decimal places when necessary. 81) When a pair of dice is rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice is rolled 4 times, what is the probability of getting a sum of 5 every time? A) 4 B) 625 C) 1 D) 1 9 1,679,616 6561 1296

81)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 82) Every week, Joe plays chess with his father. Of the last 50 games, Joe has won 55% of the games. 82) What is the probability that Joe will win the next game? A) 0.55 B) 1 C) 0.055 D) 0.5 Determine whether the events A and B are independent. 83) 12 jurors are selected from a pool of 20 Event A: The first person selected has a birthday in May Event B: The second person selected has a birthday in May A) Yes B) No Find the indicated probability. 84) In a poll of registered voters shortly before a mayoral election, people were asked which candidate they were planning to vote for. The results are shown in the table.

83)

84)

Candidate Frequency Ford 662 Anderson 358 Garcia 527 Wong 533 Find the empirical probability that a randomly selected registered voter is planning to vote for Anderson. Round your answer to the nearest thousandth when necessary. A) 0.231 B) 0.003 C) 0.172 D) 358

Determine whether the events A and B are independent. 85) Two cards are selected at random from a standard deck of 52 cards without replacement. Event A: An ace is selected on the first draw Even B: An ace is selected on the second draw A) Yes B) No

85)

Solve the problem. 86) A local department store sells carpets in 4 sizes. Each carpet comes in 2 different qualities. One of the sizes comes in 7 colors. The other sizes come in 5 colors. How many choices of carpet are there? A) 56 B) 54 C) 44 D) 58

87) How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of digits is allowed. A) 2,000 B) 2,999 C) 1,512

C) 48

87)

D) 2,997

88) A sports shop sells tennis rackets in 4 different weights, 3 types of string, and 3 grip sizes. How many different rackets could they sell? A) 10 B) 36

86)

88)

D) 21

89) The table shows the prizes and probabilities of winning (on a single $1 ticket) for a particular state

89)

lottery.

Prize (dollars) Probability 24 million (jackpot) 1 in 76,275,360 150,000 1 in 2,179,296 5000 1 in 339,002 150 1 in 9686 100 1 in 7705 5 1 in 220 2 1 in 102 1 1 in 62 How much would you expect to win or lose if you bought one $1 ticket every day for a year? Round to the nearest dollar. A) Expected gain = $177 B) Expected loss = $204

C) Expected loss = $196

D) Expected loss = $188

Find the indicated probability. Round your answer to 6 decimal places when necessary. 90) Find the probability of rolling 6 successive 2s with 6 rolls of a fair die. A) 1 B) 0.000129 C) 0.015625 D) 0.000021 Solve the problem. 91) Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the fall play. What is the probability that no boys will be chosen? Order is not important. A) 5 B) 2 C) 1 D) 6 6 7 6 11

90)

91)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 92) On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct? A) 6 B) 1 C) 1 D) 0 6 Solve the problem. 93) How many different 4-topping pizzas can be made if there are 9 individual toppings to choose from? Assume that no topping is used more than once and that the order of the toppings on the pizza is unimportant. A) 6,561 B) 3,024 C) 126 D) 24 Find the indicated probability. Round your answer to 6 decimal places when necessary. 94) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. A) 25 B) 25 C) 1 D) 13 51 102 2652 51 Solve the problem. Round your answer to 2 decimal places when necessary. 95) A six mile strip of Sprinkle Road had 48 traffic fatalities last year. There were 2.4 million miles driven along this stretch. Determine the traffic fatality rate per 100,000 miles driven. A) 5,000.00 fatalities per 100,000 miles driven

92)

93)

94)

95)

B) 2.00 fatalities per 100,000 miles driven C) 24 fatalities per 100,000 miles driven D) 20.00 fatalities per 100,000 miles driven Solve the problem. Round your answer to 5 decimal places when necessary. 96) The table shows the leading causes of death for one country in a single recent year. Cause of Death Deaths Heart Disease 175,950 Cancer 130,050 AIDS 71,145 Stroke 44,370 Pulmonary Disease 42,993 Accidents 32,895 Diabetes 18,513 Pneumonia 17,136 Kidney Disease 9,027 Assume a population of 76.5 million. What is the empirical probability of death by stroke during a single year? A) 0.058 B) 0.00058 C) 0.000058

D) 0.0058

96)

Determine whether the events A and B are independent. 97) Event A: A couple's first child is a girl. Event B: The couple's second child is a girl A) Yes

97) B) No

Solve the problem. 98) At a lumber company, shelves are sold in 5 types of wood, 2 different widths and 6 different lengths. How many different types of shelves could be ordered? A) 60 B) 42 C) 50 D) 13 Find the indicated probability. Round your answer to 6 decimal places when necessary. 99) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.325. Find the probability that in a given year it will not snow on January 1st in that town. A) 0.481 B) 3.077 C) 1.325 D) 0.675

100) A sample of 4 different calculators is randomly selected from a group containing 44 that are

98)

99)

100)

defective and 23 that have no defects. What is the probability that all four of the calculators selected are defective? A) 0.1771 B) 15.3304 C) 0.0747 D) 0.1860

Solve the problem. 101) A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade? A) 715 B) 9295 C) 13 D) 728 Find the expected value. 102) A bus arrives at a bus stop at 10 am, 10 minutes past ten, and 11.00 am. You arrive at the bus stop at random times between 10.00 am and 11.00 am every day, so all arrival times are equally likely. Find your expected waiting time for the bus.

101)

102)

[Hint: Find the probability that you will arrive at the bus stop between 10.00 am and 10 minutes past ten and find your mean waiting time in that case. Then find the probability that you will arrive at the bus stop between 10 minutes past ten and 11.00 am and find your mean waiting time in that case.] A) 15 minutes B) 43.3 minutes C) 21.7 minutes D) 22.5 minutes

103) In a large casino, the house wins on one of its games with a probability of 50.5%. All bets are 1 : 1 .

103)

If you win, you gain the amount you bet; if you lose, you lose the amount you bet. If you play 200 games in an evening, betting $1 each time, how much should you expect to win or lose? A) Lose $2.00 B) Lose $1.00 C) Lose $101.00 D) Win $2.00

Find the indicated probability. Round your answer to 6 decimal places when necessary. 104) What is the probability that 4 randomly selected people all have different birthdays? A) 0.9836 B) 0.9729 C) 0.9891 D) 0.9918

104)

Find the indicated probability. 105) A die is rolled 50 times with the following results. Outcome Frequency

1 2 7 4

105)

3 4 5 6 9 0 20 10

Compute the empirical probability that the die comes up a 5. A) 2 B) 1 C) 3 5 6 10

D) 1 3

Solve the problem. 106) In a certain lottery, 5 different numbers between 1 and 9 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is unimportant. A) 59,049 B) 126 C) 15,120 D) 120 Solve the problem. Round your answer to 2 decimal places when necessary. 107) A country with a population of 102 million has 19,176 traffic fatalities. Find the fatality rate in deaths per 100,000 population. A) 188 deaths per 100,000 people B) 1.88 deaths per 100,000 people

C) 18.8 deaths per 100,000 people

107)

D) 1,918 deaths per 100,000 people

Find the indicated probability. Round your answer to 6 decimal places when necessary. 108) One card is selected from a deck of cards. Find the probability of selecting a black card or a queen. A) 15 B) 27 C) 1 D) 7 26 52 26 13

109) A family has five children. The probability of having a girl is 0.5. What is the probability of having 3 girls followed by 2 boys? A) 1 B) 1 16 120

C) 5

109)

Allergy Control drug Placebo (no treatment) Total 145 85 41 271 55 115 59 229 200 200 100 500

What is the probability that a randomly selected person was given the allergy drug and improved? Round your answer to the nearest thousandth when necessary. A) 0.652 B) 0.29 C) 0.942 D) 0.46

108)

D) 1

Find the indicated probability. 110) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

106)

110)

Use the at least once rule to find the indicated probability. 111) An unprepared student makes random guesses on all questions of her multiple choice test. If there are 13 questions and each question has 5 possible answers, what is the probability she will answer at least one question correctly? A) 0.055 B) 0.907 C) 0.945 D) 0.014 Solve the problem. Round your answer to 2 decimal places when necessary. 112) At an intersection in Normal, Illinois, there were 88 vehicle accidents with 168,295 vehicles passing through the intersection. Determine the accident rate per 1000 vehicles. A) 168.3 accidents per 1000 vehicles B) 0 accidents per 1000 vehicles

C) 1,912,443.18 accidents per 1000 vehicles

111)

112)

D) 0.52 accidents per 1000 vehicles

Find the indicated probability. 113) The following table displays a distribution for a group of retired people by career and age at retirement.

156

162

168

278

172

678

113)

Suppose one of these people is selected at random. Compute the probability that the person selected was a store clerk. Round your answer to the nearest thousandth. A) 0.027 B) 0.268 C) 0.300 D) 0.099

Determine whether the events A and B are independent. 114) Event A: It will rain today in Seattle, Washington Event B: It will rain tomorrow in Seattle, Washington A) No B) Yes

114)

Find the expected value. 115) Bob and Fred play the following game. Bob rolls a single die. If an even number results, Bob must pay Fred the number of dollars indicated by the number rolled. On the other hand, if an odd number is rolled, Fred must pay Bob the number of dollars indicated by the number rolled. Find Bob's expected winnings. A) -$0.50 B) -$0.25 C) $0 D) -$0.40 Solve the problem. 116) Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each, find the expected net winnings for a person who buys 1 ticket. A) -$0.81 B) -$0.85 C) -$0.83 D) -$1.00 Find the indicated probability. Round your answer to 6 decimal places when necessary. 117) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 6. A) 9 B) 1 C) 1 D) 12 10 10 13 13 Solve the problem. 118) A student is told to answer any 7 out of 10 questions on an exam. In how many different ways can he choose the 7 questions to answer? A) 120 B) 10,000,000 C) 21 D) 720 Find the expected value. 119) An insurance policy sells for $800. Based on past data, an average of 1 in 70 policyholders will file a $10,000 claim, an average of 1 in 140 policyholders will file a $20,000 claim, and an average of 1 in 400 policyholders will file a $50,000 claim. What is the expected value to the company per policy sold? A) $419 B) $410 C) $411 D) $389 Determine whether the events A and B are independent. 120) A person is selected at random from a group of college students. Event A: The person selected is a woman Event B: The person selected votes Republican A) Yes B) No Find the indicated probability. Round your answer to 6 decimal places when necessary. 121) Among the contestants in a competition are 42 women and 27 men. If 5 winners are randomly selected, what is the probability that they are all men? A) 0.10979 B) 0.0949 C) 0.00718 D) 0.08356

115)

116)

117)

118)

119)

120)

121)

Solve the problem. Round your answer to 5 decimal places when necessary. 122) The table shows the leading causes of death for one country in a single recent year.

122)

Cause of Death Deaths Heart Disease 193,200 Cancer 152,950 AIDS 77,280 Stroke 48,300 Pulmonary Disease 45,241 Accidents 34,615 Diabetes 19,481 Pneumonia 18,032 Kidney Disease 9,499 Assume a population of 80.5 million. What is the death rate due to heart disease in deaths per 100,000 of the population? A) 1.932 deaths per 100,000 B) 24 deaths per 100,000

C) 19.32 deaths per 100,000

D) 240 deaths per 100,000

Use the at least once rule to find the indicated probability. 123) In a blood testing procedure, blood samples from 5 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.08, what is the probability that the mixture will test positive? A) 0.00000328 B) 1.00 C) 0.341 D) 0.659 Evaluate the factorial expression. 124) 4! A) 24

123)

124) B) 48

C) 12

D) 6

125) 5!

125)

A) 1

B) 2!

C) 42

D) 1

Find the indicated probability. 126) The following table displays a distribution for a group of retired people by career and age at retirement.

173

182

157

311

188

715

126)

Suppose one of these people is selected at random. Find the probability that the person was a secretary or that they retired between ages 56 and 60. Round your answer to the nearest thousandth. A) 0.406 B) 0.063 C) 0.469 D) 0.253

Solve the problem. 127) The odds on (against) your bet are 8 to 5. If you bet $35 and win, how much will you gain? Use the definition of odds in betting. A) $22 B) $56 C) $35 D) $91 Find the indicated probability. Round your answer to 6 decimal places when necessary. 128) If a person is randomly selected, find the probability that his or her birthday is not on New Year's Day. Ignore leap years. A) 364 B) 11 C) 1 D) 30 365 12 365 31 Solve the problem. 129) In a certain lottery, 3 different numbers between 1 and 11 inclusive are drawn at random. These are the winning numbers. If you choose 3 different numbers at random between 1 and 11, what is the probability you will match the winning numbers? Assume that the order of the numbers is unimportant. A) 1 B) 1 C) 1 D) 1 165 6 990 1,331

127)

128)

129)

Use the at least once rule to find the indicated probability. 130) Find the probability of getting at least one tail when tossing 5 fair coins. A) 0.5 B) 0.031 C) 0.156

130) D) 0.969

Make a probability distribution for the given set of events. 131) The following table displays a frequency distribution of the number of siblings for students at one middle school. Make a probability distribution for number of siblings.

131)

Number of siblings 0 1 2 3 4 5 6 7 Frequency 193 248 139 60 23 8 5 3

B) Siblings Probability 0 0.125 1 0.125 2 0.125 3 0.125 4 0.125 5 0.125 6 0.125 7 0.125

Siblings Probability 1 0.510 2 0.286 3 0.123 4 0.047 5 0.016 6 0.010 7 0.006

D) Siblings Probability 0 0.299 1 0.351 2 0.216 3 0.077 4 0.034 5 0.012 6 0.007 7 0.004

Siblings Probability 0 0.284 1 0.365 2 0.205 3 0.088 4 0.034 5 0.012 6 0.007 7 0.004

Find the indicated probability. Round your answer to 6 decimal places when necessary. 132) The probability that Luis will pass his statistics test is 0.51. Find the probability that he will fail his statistics test. A) 0.26 B) 1.96 C) 1.04 D) 0.49 Solve the problem. 133) A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 8 questions on the survey? A) 64 B) 8 C) 5,040 D) 40,320

132)

133)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 134) Of the last 100 people who failed the lie detector test, 23 turned out to be telling the truth. What is 134) the probability that the next person who fails the test is actually telling the truth? A) 0.77 B) 0.5 C) 0 D) 0.23

Find the indicated probability. 135) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

135)

Allergy Control drug Placebo (no treatment) Total 145 85 41 271 55 115 59 229 200 200 100 500

What is the probability that a randomly selected person received no treatment or improved? Round your answer to the nearest thousandth when necessary. A) 0.082 B) 0.66 C) 0.89 D) 0.742

Solve the problem. Round your answer to 5 decimal places when necessary. 136) The table shows the leading causes of death for one country in a single recent year.

136)

Cause of Death Deaths Heart Disease 159,850 Cancer 104,250 AIDS 66,025 Stroke 42,395 Pulmonary Disease 39,059 Accidents 29,190 Diabetes 16,819 Pneumonia 15,568 Kidney Disease 8,201 Assume a population of 69.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke? A) 3.39344 B) 0.00169 C) 37.70492 D) 3.77049

Find the indicated probability. 137) A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. Sum 2 Frequency 1

3 9

4 1

5 6 12 9

7 5

8 0

9 1

137)

10 11 12 2 10 0

Compute the empirical probability of getting a sum greater than 9. A) 6 B) 13 C) 1 25 50 6

Solve the problem. 138) Find the odds for getting two heads when two fair coins are flipped. A) 4 to 1 B) 3 to 1 C) 1 to 3

D) 1

138) D) 1 to 4

139) Four married couples have reserved eight seats in a row at the theater. If they arrange themselves

139)

randomly, what is the probability that all the women will sit in adjacent seats and all the men will sit in adjacent seats? A) 1 B) 1 C) 1 D) 2 840 70 35 315

Find the indicated probability. 140) A die is rolled 100 times with the following results. Outcome Frequency

140)

1 2 3 4 5 6 16 11 16 19 13 25

Compute the empirical probability that the die comes up 2 or 3. A) 11 B) 1 C) 16 100 6 100

D) 27

100

Use the at least once rule to find the indicated probability. 141) Find the probability of at least one queen when you draw cards from a standard deck 17 times; assume you replace the card each time you draw , so there are always 52 cards to draw from. A) 0.992 B) 0.256 C) 0.021 D) 0.744 Solve the problem. 142) How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetition of digits is allowed? A) 120 B) 100,000 C) 3,125 D) 99,999

143) A committee of 17 members is voting on a proposal. Each member casts a yea or nay vote. On a

141)

142)

143)

random voting basis, what is the probability that the final vote count is unanimous? 1 1 A) 1 B) C) D) 1 272 131,072 131,052 65,536

Solve the problem. Round your answer to 2 decimal places when necessary. 144) A U.S. city with a population of 2.5 million reports 15,035 deaths. What is the death rate in deaths per 1000 people? A) 6.01 deaths per 1000 people B) 0.6 deaths per 1000 people

C) 16.63 deaths per 1000 people

144)

D) 60 deaths per 1000 people

Decide whether events A and B are overlapping or non-overlapping. 145) A card is drawn at random from a deck of cards. Event A is that the card selected is a queen and event B is that the card selected is a two. A) Overlapping B) Non-overlapping

146) You roll a red die and a blue die.

145)

146)

Event A is that you get a sum of 11. Event B is that you get a one on the blue die. A) Non-overlapping

B) Overlapping

Solve the problem. 147) Dave puts a collection of 15 books on a bookshelf in a random order. Among the books are 2 fiction and 13 nonfiction books. What is the probability that the 2 fiction books will be together on the left side of the shelf and the 13 nonfiction all together on the right side of the shelf? A) 0.01809 B) 0.01333 C) 0.01619 D) 0.00952 Find the indicated probability. Round your answer to 6 decimal places when necessary. 148) One card is selected from a deck of cards. Find the probability of selecting a club or a card less than 3 . (Note: The ace is considered a low card.) A) 4 B) 9 C) 23 D) 19 13 26 52 52 Solve the problem. Round your answer to 2 decimal places when necessary. 149) A U.S. city with a population of 2.4 million reports 36,179 births in one year. How many people are born per day in the city? A) 90 births per day B) 99 births per day

C) 696 births per day

Solve the problem. 151) There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible? A) 512 B) 336 C) 6 D) 56

152) Find the odds against correctly guessing the answer to a multiple choice question with 3 possible B) 2 : 3

C) 3 : 2

149)

150)

151)

152)

D) 3 : 1

Find the indicated probability. Round your answer to 6 decimal places when necessary. 153) Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e.either both black or both red)? A) 0.250 B) 0.490 C) 0.245 D) 0.500 Evaluate the factorial expression. 154) 6! 4! 2!

A) 30

148)

D) 6,575 births per day

Determine whether the events A and B are independent. 150) Eight friends are drawing straws. The one who picks the short straw must cook dinner for the others. Event A: The first person does not pick the short straw Event B: The second person picks the short straw A) No B) Yes

answers. A) 2 : 1

147)

153)

154) B) 1

C) 15

D) 6

Solve the problem. 155) A tourist in France wants to visit 11 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order? 1 A) 39,916,800 B) C) 1 D) 1 39,916,800 121 11 Decide whether events A and B are overlapping or non-overlapping. 156) A person is selected at random from a group of doctors. Event A is that the person selected is a woman. Event B is that the person selected is a surgeon. A) Non-overlapping B) Overlapping Find the expected value. 157) Four cards are numbered 1 through 4. Two of these cards are chosen at random without replacement and the numbers on them are multiplied. Find the expected value of this product. A) 6 B) 4 C) 25 D) 35 4 6 Solve the problem. Round your answer to 2 decimal places when necessary. 158) The overall U.S. death rate for 60-62 year-olds is approximately 13 deaths per 1000 people. If there are about 15,535 60-62 year olds in a U.S. city, how many 60-62 year olds can be expected to die in a year in that city? A) 2,020 deaths B) 84 deaths C) 202 deaths D) 20 deaths Solve the problem. 159) How many different 5-letter sequences can be made using the first 11 letters of the alphabet? Assume that repetition of letters is allowed. A) 55,440 B) 120 C) 161,051 D) 462

160) Suppose you are playing a game of chance. If you bet $4 on a certain event, you will collect $156

155)

156)

157)

158)

159)

160)

(including your $4 bet) if you win. Find the odds used for determining the payoff. A) 156 : 160 B) 1 : 38 C) 38 : 1 D) 39 : 1

Evaluate the factorial expression. 161) 13! A) 6.2270 × 109

161) B) 1.2454 × 1010

C) 4.7900 × 108

D) 3.1135 × 109

Solve the problem. Round your answer to 5 decimal places when necessary. 162) The table shows the leading causes of death for one country in a single recent year.

162)

Cause of Death Deaths Heart Disease 187,950 Cancer 152,150 AIDS 85,920 Stroke 51,910 Pulmonary Disease 50,299 Accidents 42,065 Diabetes 21,659 Pneumonia 20,048 Kidney Disease 10,561 Assume a population of 89.5 million. What is the death rate due to accident in deaths per 100,000 of the population A) 47 deaths per 100,000 B) 470 deaths per 100,000

C) 4.2065 deaths per 100,000

D) 0.42065 deaths per 100,000

Find the indicated probability. Round your answer to 6 decimal places when necessary. 163) Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10? A) 1 B) 3 C) 1 D) 5 12 18 18 Make a probability distribution for the given set of events. 164) When four fair coins are tossed, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Make a probability distribution for the number of tails when four fair coins are tossed.

B) Result Probability 0T 1/16 1T 1/8 2T 3/8 3T 1/8 4T 1/16

Result Probability 0T 1/16 1T 1/4 2T 3/8 3T 1/4 4T 1/16

D) Result Probability 0T 1/16 1T 3/16 2T 1/2 3T 3/16 4T 1/16

Result Probability 1T 1/4 2T 7/16 3T 1/4 4T 1/16

163)

164)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 165) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen. A) 4 B) 2 C) 13 D) 1 663 13 102 663 Find the expected value. 166) Experience shows that a ski lodge will be full (184 guests) if there is a heavy snow fall in December, while only partially full (76 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is .40? Assume that heavy snowfall and light snowfall are the only two possibilities. A) 110.4 B) 119.2 C) 140.8 D) 73.6

167) The following table gives the distribution of heights for female students at one U.S. college.

165)

166)

167)

Height category (inches) Percentage 57-59 8.0 60-62 20.7 63-65 35.9 66-68 19.4 69-71 11.0 72 and over 5.0

Find the expected value of height for women at this college. Use the midpoint of each category, (for example use 58 for the 57-59 category). Use 74 for the 72 and over category. A) 64.6 in. B) 65.0 in. C) 63.8 in. D) 64.2 in.

Solve the problem. 168) How many different five-card hands can be dealt from a deck that has only clubs (13 cards altogether)? A) 2,574 B) 1,287 C) 143 D) 3,861 Decide whether events A and B are overlapping or non-overlapping. 169) A student is selected at random. Event A is that the student speaks Spanish and event B is that the student speaks Chinese. A) Non-overlapping B) Overlapping Solve the problem. Round your answer to 2 decimal places when necessary. 170) In a recent year, there were 551 deaths in general aviation over 8.6 billion miles flown. Find the fatality rate in units of deaths per 1 billion miles flown. A) 64.07 deaths per billion miles flown B) 6.41 deaths per billion miles flown

C) 473.86 deaths per billion miles flown

D) 0.02 deaths per billion miles flown

168)

169)

170)

Determine whether the events A and B are independent. 171) 12 jurors are selected from a pool of 20 Event A: The first person selected is a woman Event B: The second person selected is a woman A) Yes

171) B) No

Find the indicated probability. 172) The table below describes the smoking habits of a group of asthma sufferers. Light Nonsmoker smoker Men 329 79 Women 346 76 Total 675 155

172)

Heavy smoker Total 74 482 87 509 161 991

If one of the 991 subjects is randomly selected, find the probability that the person chosen is a nonsmoker and a woman. Round your answer to the nearest thousandth when necessary. A) 0.513 B) 0.349 C) 0.514 D) 0.68

Find the expected value. 173) You are given 13 to 1 odds against drawing two hearts when two cards are selected at random from a standard deck of 52 cards (with replacement of the first card before the second card is drawn). This means that you win $13 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Round to the nearest cent. A) $2.50 B) $0.13 C) -$0.92 D) -$0.13 Find the indicated probability. Round your answer to 6 decimal places when necessary. 174) A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? A) 1 B) 1 C) 1 D) 3 7 3 13 16

175) In January in a certain city the unconditional probability of rain on any given day of the month is

173)

174)

175)

0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of rain on a day following a nonrainy day is 0.250. Find the probability of rain on three randomly selected consecutive days in January. A) 0.064 B) 0.090 C) 0.216 D) 0.144

Solve the problem. 176) How many ways can an IRS auditor select 3 of 12 tax returns for an audit? A) 1,320 B) 1,728 C) 220

176) D) 6

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 177) In a poll, respondents were asked whether they were planning to vote in the local election. 481 177) respondents indicated that they were planning to vote and 421 said that they were not. What is the probability that the next respondent questioned will indicate that they are planning to vote? A) 0.5 B) 0.47 C) 0.53 D) 1.14

Find the indicated probability. Round your answer to 6 decimal places when necessary. 178) Find the probability of selecting either a non-smoker or a woman when you select a person at random from a group composed of 40 female smokers, 50 male smokers, 30 female non-smokers, and 25 male non-smokers. A) 0.207 B) 0.862 C) 0.183 D) 0.655

179) If you are dealt two cards successively (with replacement of the first) from a standard 52-card

178)

179)

deck, find the probability of getting a heart on the first card and a diamond on the second. A) 1 B) 1 C) 1 D) 13 169 204 16 204

Decide whether events A and B are overlapping or non-overlapping. 180) You roll a red die and a blue die. Event A is that you get a sum of 9. Event B is that you get a sum of 3. A) Overlapping B) Non-overlapping

180)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 181) A bag contains 13 balls numbered 1 through 13. What is the probability that a randomly selected ball has an even number? A) 13 B) 1 C) 6 D) 2 6 2 13 13 Solve the problem. 182) Determine the probability that in a class of 35 students, at least two students have the same birthday. Assume that birth rates are constant throughout the year. (Hint: First determine the probability that no two students have the same birthday and then apply the complementation rule.) A) 0.894 B) 0.854 C) 0.814 D) 0.186 Find the indicated probability. Round your answer to 6 decimal places when necessary. 183) Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2? A) 13 B) 11 C) 1 D) 1 36 36 3 4

184) What is the probability that a family with three children does not have three children of the same gender? Assume boys and girls are equally likely. A) 7 B) 2 8 3

C) 1 4

185) If three fair coins are tossed, what is the probability of not tossing three heads? A) 7 8

B) 1 3

C) 2 3

181)

182)

183)

184)

D) 3 4

185) D) 1 8

Solve the problem. 186) Find the odds for getting two tails and a head when three fair coins are flipped. A) 1 to 7 B) 3 to 5 C) 3 to 8 D) 5 to 3

187) The library is to be given 5 books as a gift. The books will be selected from a list of 23 titles. If each

186)

187)

book selected must have a different title, how many possible selections are there? A) 4,037,880 B) 33,649 C) 279,841 D) 6,436,343

Find the indicated probability. Round your answer to 6 decimal places when necessary. 188) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 6. A) 1 B) 1 C) 11 D) 5 4 36 36 18 Find the indicated probability. 189) You toss four coins and record the number of tails. You repeat this many times. The results are shown below. Result 0 tails 1 tail 2 tails 3 tails 4 tails

188)

189)

Frequency 5 7 12 1 1

Find the empirical probability of getting 4 tails. Round your answer to the nearest thousandth. A) 0.036 B) 0.308 C) 0.040 D) 0.038

Decide whether events A and B are overlapping or non-overlapping. 190) You roll a red die and a blue die. Event A is that you get a sum of 9. Event B is that you get a double. A) Overlapping B) Non-overlapping Solve the problem. 191) A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown? A) 336 B) 512 C) 56 D) 24 Find the indicated probability. Round your answer to 6 decimal places when necessary. 192) The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.05. Find the probability that the region will be hit by a hurricane in 2 consecutive years. A) 0.10 B) 0 C) 0.05 D) 0.0025

190)

191)

192)

Find the indicated probability. 193) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

193)

Allergy Control drug Placebo (no treatment) Total 145 85 41 271 55 115 59 229 200 200 100 500

What is the probability that a randomly selected person was given a placebo and improved? Round your answer to the nearest thousandth when necessary. A) 0.772 B) 0.942 C) 0.69 D) 0.17

Use the at least once rule to find the indicated probability. 194) Find the probability of at least one club when you draw cards from a standard deck 5 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from. A) 0.330 B) 0.763 C) 0.079 D) 0.237 Find the indicated probability. Round your answer to 6 decimal places when necessary. 195) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. A) 31 B) 1 C) 1 D) 1 365 31 12 365 Provide an appropriate response. 196) Which (if any) of the following statements is/are true?

194)

195)

196)

A: If two events are dependent, then they must be mutually exclusive B: If two events are mutually exclusive, then they must be dependent A) Both statements are true. B) B only

C) Neither statement is true.

D) A only

Solve the problem. 197) How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O? A) 456,976 B) 35,152 C) 16,900 D) 33,800 Find the indicated probability. Round your answer to 6 decimal places when necessary. 198) What is the probability of not rolling a number larger than 4 with a fair die? A) 1 B) 5 C) 2 D) 1 2 6 3 3

197)

198)

Solve the problem. 199) There are 6 finalists in a singing competition. If a person guesses randomly the top three winners (in any order), what is the probability that they will guess correctly? A) 1 B) 1 C) 1 D) 1 216 20 18 120

200) In a certain town, 5% of people commute to work by bicycle. If a person is selected randomly from

199)

200)

the town, what are the odds against selecting someone who commutes by bicycle? A) 19 : 1 B) 19 : 20 C) 1 : 19 D) 1 : 20

Find the indicated probability. 201) The table shows the year and political party of a random sample of students from a certain college. Party Freshman Sophomore Independent 11 10 Democrat 24 21 Republican 10 11

Junior 18 10 24

201)

Senior 21 11 21

Find the empirical probability that a student at the college is an Independent. Round your answer to the nearest thousandth. A) 0.313 B) 0.109 C) 0.350 D) 0.344

Solve the problem. 202) A musician plans to perform 5 selections for a concert. If he can choose from 8 different selections, how many ways can he arrange his program? A) 6,720 B) 40 C) 56 D) 32,768

202)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 203) Of 1,801 people who came into a blood bank to give blood, 212 people had high blood pressure. 203) Estimate the probability that the next person who comes in to give blood will have high blood pressure. A) 0.12 B) 0.04 C) 0.17 D) 0.09 Solve the problem. 204) Find the odds against drawing a heart when a card is drawn at random from a normal deck of 52 playing cards. A) 4 to 1 B) 1 to 3 C) 3 to 1 D) 1 to 4 Solve the problem. Round your answer to 2 decimal places when necessary. 205) The population of a certain country is about 180 million. The overall death rate is 12.5 deaths per 1000. Approximately how many deaths are there in the country? A) 22,500 deaths B) 225,000 deaths

C) 22.5 million deaths

D) 2.25 million deaths

204)

205)

206) At an intersection in Normal, Illinois, there were 164 vehicle accidents with 255,694 vehicles

206)

passing through the intersection. Determine the accident rate per 10,000 vehicles. A) 1,559,109.76 accidents per 10,000 vehicles

B) 0 accidents per 10,000 vehicles C) 255.69 accidents per 10,000 vehicles D) 6.41 accidents per 10,000 vehicles Find the expected value. 207) Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 (and your wager) for rolling a 4 or a 3, nothing otherwise. What is your expected net winnings? A) $0.00 B) $3.00 C) -$1.00 D) $1.00

207)

208) A commercial building contractor is trying to decide which of two projects to commit her

208)

209) An insurance company will insure a $260,000 home for its total value for an annual premium of

209)

company to. Project A will yield a profit of $50,000 with a probability of 0.6, a profit of $82,000 with a probability of 0.3, and a profit of $10,000 with a probability of 0.1. Project B will yield a profit of $100,000 with a probability of 0.1, a profit of $66,000 with a probability of 0.7, and a loss of $20,000 with a probability of 0.2. Find the expected profit for each project. Based on expected values, which project should the contractor choose? A) Project A: $47,333 B) Project A: $55,600 Project B: $48,666 Project B: $60,200 Contractor should choose project A Contractor should choose project B C) Project A: $46,600 D) Project A:$55,600 Project B: $52,200 Project B: $52,200 Contractor should choose project B Contractor should choose project A

$510. If the company spends $30 per year to service such a policy, the probability of total loss for such a home in a given year is 0.001 and you assume either total loss or no loss will occur, what is the company's expected annual gain (or profit) on each such policy? A) -$260 B) $170 C) $250 D) $220

Solve the problem. 210) How many 6-letter passwords can be formed from the letters P, A, Y, M, E, N, T if no repetition of letters is allowed? A) 5,040 B) 42 C) 2,520 D) 7 Solve the problem. Round your answer to 2 decimal places when necessary. 211) The overall U.S. death rate for 60 year-olds is approximately 12 deaths per 1000 people. Suppose that a life insurance company insures 2,000 60-year-old people. The cost of the premium is $730 per year, and the death benefit is $50,000. What is the expected profit or loss for the insurance company? A) $242,480 profit B) $1,200,000 loss C) $360,000 profit D) $260,000 profit

210)

211)

Evaluate the factorial expression. 11! 212) 4!(11 - 4)!

A) 330

212) B) 3

C) 5,040

D) 1,980

Find the indicated probability. Round your answer to 6 decimal places when necessary. 213) In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of rain on a day following a nonrainy day is 0.250. Find the probability that January 1st and January 2nd are rainy and that January 3rd and 4th are not rainy given that December 31st was clear all day. A) 0.072 B) 0.045 C) 0.024 D) 0.038 Solve the problem. 214) A license plate is to consist of 2 letters followed by 5 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted. A) 19,656,140 B) 19,655,980 C) 67,600,000 D) 19,656,000 Find the indicated probability. Round your answer to 6 decimal places when necessary. 215) A die with 6 sides is rolled. What is the probability of rolling a number less than 5? A) 5 B) 4 C) 1 D) 2 6 6 3

216) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good

213)

214)

215)

216)

coils when two coils are randomly selected if the first selection is replaced before the second is made. A) 0.7744 B) 0.7733 C) 0.0144 D) 0.176

Decide whether events A and B are overlapping or non-overlapping. 217) Event A is that I get an A on my spanish test tomorrow. Event B is that I get a B on my spanish test tomorrow. A) Overlapping B) Non-overlapping Find the indicated probability. Round your answer to 6 decimal places when necessary. 218) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 4? A) 3 B) 2 C) 11 D) 1 3 12 12 Solve the problem. 219) How many different five-card hands can be dealt from a deck that has no face cards (40 cards altogether)? A) 319,865 B) 127,946 C) 658,008 D) 639,730

217)

218)

219)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 220) A class consists of 43 women and 67 men. If a student is randomly selected, what is the probability that the student is a woman? A) 1 B) 43 C) 67 D) 43 110 110 110 67 Decide whether events A and B are overlapping or non-overlapping. 221) A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card and event B is that the card obtained is a spade. A) Non-overlapping B) Overlapping Solve the problem. 222) Find the odds for drawing an ace when a card is drawn at random from a normal deck of 52 playing cards. A) 1 to 12 B) 12 to 1 C) 13 to 1 D) 1 to 13 Use the at least once rule to find the indicated probability. 223) In a batch of 8000 clock radios 4% are defective. A sample of 15 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected? A) 0.0667 B) 0.458 C) 0.0400 D) 0.542 Solve the problem. 224) A shirt company has 3 designs each of which can be made with short or long sleeves. There are 6 different colors available. How many different shirts are available from this company? A) 11 B) 18 C) 36 D) 9

220)

221)

222)

223)

224)

225) 8 basketball players are to be selected to play in a special game. The players will be selected from

225)

226) A baseball manager has 11 players of the same ability. How many 9 player starting lineups can he

226)

a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected? 1 1 A) B) 1 C) D) 8 2,220,075 40,320 213,127,200 27

create? A) 362,880

B) 55

C) 99

D) 19,958,400

Solve the problem. Round your answer to 2 decimal places when necessary. 227) In a given year, the population of a certain country is about 154 million. The overall birth rate is 15.9 births per 1000. The overall death rate is 10.7 deaths per 1000. If the population of the country increased by 1.04 million, what is the approximate net immigration to the country during this year? A) 2 million B) 23,920 C) 2,547 million D) 239,200

227)

Solve the problem. 228) A company wants to hire a software engineer, an administrative assistant, and a sales representative. There are 3 possible candidates for the position of software engineer, 5 for the position of administrative assistant, and 5 for the position of sales representative. How many ways are there to choose the three people who will be hired? A) 75 B) 13 C) 40 D) 45 Use the at least once rule to find the indicated probability. 229) A study conducted at a certain college shows that 56% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. A) 0.945 B) 0.560 C) 0.200 D) 0.984 Solve the problem. Round your answer to 5 decimal places when necessary. 230) The table shows the leading causes of death for one country in a single recent year.

228)

229)

230)

Cause of Death Deaths Heart Disease 147,600 Cancer 110,700 AIDS 55,965 Stroke 35,055 Pulmonary Disease 34,563 Accidents 27,060 Diabetes 14,883 Pneumonia 13,776 Kidney Disease 7,257 Assume a population of 61.5 million. In a typical city of 500,000, how many people would you expect to die of cancer in a year? A) Approximately 55,350 people B) Approximately 5,535 people

C) Approximately 900 people

D) Approximately 9,000 people

Find the indicated probability. 231) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

Allergy Control drug Placebo (no treatment) Total 145 85 41 271 55 115 59 229 200 200 100 500

What is the probability that a randomly selected person either was given the allergy drug or did not improve? Round your answer to the nearest thousandth when necessary. A) 0.748 B) 0.458 C) 0.11 D) 0.858

231)

Solve the problem. 232) There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? A) 10 B) 120 C) 125 D) 60

233) License plates are made using 2 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed? A) 11,881,376 B) 100,000

C) 67,600

233)

D) 676,000

Find the indicated probability. Round your answer to 6 decimal places when necessary. 234) Three fair coins are tossed. Find the probability of getting the same thing on all three coins. A) 1 B) 3 C) 1 D) 1 8 8 4 2 Solve the problem. 235) If 12 newborn babies are randomly selected, how many different gender sequences are possible? A) 144 B) 4,096 C) 479,001,600 D) 24 Solve the problem. Round your answer to 2 decimal places when necessary. 236) In a recent year, there were 40 accidents in commercial aviation among major airlines over 7.7 million departures. Find the accident rate in units of accidents per 100,000 departures. A) 5.2 accidents per 100,000 departures B) 1.9 accidents per 100,000 departures

C) 52 accidents per 100,000 departures

232)

234)

235)

236)

D) 0.52 accidents per 100,000 departures

Solve the problem. 237) A license plate is to consist of 3 letters followed by 5 digits. Determine the number of different license plates possible if the first letter must be an N , M , or P and repetition of letters and numbers is not permitted. A) 272,160,000 B) 54,432,000 C) 54,522,000 D) 9,072,000 Use the at least once rule to find the indicated probability. 238) Find the probability of at least one 3 in 4 rolls of a fair die. A) 0.518 B) 0.096 C) 0.482

238) D) 0.938

Solve the problem. Round your answer to 2 decimal places when necessary. 239) The population of a certain country is about 139 million. The overall birth rate is 14.7 births per 1000. Approximately how many births were there in the country? A) 20,400 births B) 204,000 births

C) 2.04 million births

237)

239)

D) 20.4 million births

Determine whether the events A and B are independent. 240) A balanced die is rolled twice. Event A: Six comes up on the first roll Event B: Six comes up on the second roll A) No

240) B) Yes

Solve the problem. 241) There are 8 women running in a race. How many different ways could first, second, and third place finishers occur? A) 24 B) 336 C) 56 D) 512 Find the indicated probability. Round your answer to 6 decimal places when necessary. 242) Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. A) 3 B) 1 C) 1 D) 1 3 64 36 Solve the problem. 243) In Morse code, each symbol is either a dot or a dash. How many sequences of 11 symbols are possible? A) 2,048 B) 39,916,800 C) 22 D) 121

241)

242)

243)

Make a probability distribution for the given set of events. 244) Suppose that you start with a normal deck of 52 cards and remove everything except the twos, threes, and fours. So you now have a deck of twelve cards consisting of four twos, four threes, and four fours. A card is drawn at random and replaced then another card is drawn at random and replaced. Make a probability distribution for the sum of the two numbers that are drawn.

Sum Probability 4 1/9 5 2/9 6 3/9 7 2/9 8 1/9

Sum Probability 4 1/3 6 1/3 8 1/3

Sum Probability 4 1/5 5 1/5 6 1/5 7 1/5 8 1/5

Sum Probability 4 1/9 5 1/9 6 1/9 7 1/9 8 1/9 9 1/9 10 1/9 11 1/9 12 1/9

Determine whether the events A and B are independent. 245) A balanced die is rolled twice. Event A: The sum of the two rolls is 8 Event B: The first roll comes up 3 A) No

244)

245) B) Yes

Find the indicated probability. Round your answer to 6 decimal places when necessary. 246) A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5? A) 16 B) 48 C) 2 D) 4 52 13 13

246)

Solve the problem. Round your answer to 2 decimal places when necessary. 247) A U.S. city with a population of 1.9 million reports 35,431 births. What is the birth rate in births per 1000 people? A) 53.63 births per 1000 people B) 186 births per 1000 people

C) 18.65 births per 1000 people

247)

D) 1.86 births per 1000 people

Find the indicated probability. Round your answer to 6 decimal places when necessary. 248) A fair die is rolled. What is the probability of rolling an odd number or a number less than 3? A) 1 B) 2 C) 1 D) 5 3 2 6 Solve the problem. 249) Find the odds for getting a sum of 12 when two fair dice are rolled. A) 35 to 1 B) 36 to 1 C) 1 to 36

249) D) 1 to 35

250) If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake? A) 1 to 20 B) 20 to 1 C) 18 to 1

248)

250)

D) 19 to 1

Solve the problem. Round your answer to 2 decimal places when necessary. 251) A certain U.S. city had 59 traffic fatalities last year. There were 3.4 million miles driven in the city.. Determine the traffic fatality rate per 1,000,000 miles driven. A) 1.74 fatalities per 1,000,000 miles driven

251)

B) 0.06 fatalities per 1,000,000 miles driven C) 17,352,941.18 fatalities per 1,000,000 miles driven D) 17.35 fatalities per 1,000,000 miles driven Make a probability distribution for the given set of events. 252) When two fair dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Find the probability distribution for the product of the two numbers that appear when two fair dice are rolled.

252)

A) Product Probability 1 1/36 2 1/18 3 1/18 4 1/12 5 1/18 6 1/9 8 1/18 9 1/36 10 1/18

Product Probability 12 1/9 15 1/18 16 1/36 18 1/18 20 1/18 24 1/18 25 1/36 30 1/18 36 1/36

Product Probability 1 1/18 2 1/18 3 1/18 4 1/18 5 1/18 6 1/18 8 1/18 9 1/18 10 1/18

Product Probability 12 1/18 15 1/18 16 1/18 18 1/18 20 1/18 24 1/18 25 1/18 30 1/18 36 1/18

Product Probability 2 1/36 3 1/18 4 1/12 5 1/9 6 5/36

Product Probability 7 1/6 8 5/36 9 1/9 10 1/12 11 1/18 12 1/36

Product Probability 2 1/18 3 1/18 4 1/12 5 1/18 6 1/9 8 1/18

Product Probability 10 1/12 12 1/9 15 1/12 18 1/12 20 1/12 24 1/12 30 1/18

Solve the problem. 253) The table shows the prizes and probabilities of winning (on a single $1 ticket) for a particular state lottery. Find the expected value of the winnings for a single lottery ticket.

253)

Prize (dollars) Probability 18 million (jackpot) 1 in 76,275,360 150,000 1 in 2,179,296 5000 1 in 339,002 150 1 in 9686 100 1 in 7705 5 1 in 220 2 1 in 102 1 1 in 62

A) -$0.55

B) -$0.64

C) -$0.59

D) $0.41

254) A restaurant offers pizzas with 2 types of crust, 6 different toppings, and in 6 different sizes. How many different pizzas could be ordered? A) 48 B) 14

C) 24

D) 72

255) Suppose there are 5 roads connecting town A to town B and 8 roads connecting town B to town C. In how many ways can a person travel from A to C via B? A) 40 ways B) 64 ways C) 13 ways

Solve the problem. 257) There are 6 women running in a race. If a person guesses randomly the first place, second place, and third place winners, what is the probability that they will guess all winners correctly? A) 1 B) 1 C) 1 D) 1 20 120 18 216 Find the indicated probability. Round your answer to 6 decimal places when necessary. 258) Of the 65 people who answered "yes" to a question, 8 were male. Of the 55 people who answered "no" to the question, 12 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male? A) 0.123 B) 0.708 C) 0.642 D) 0.167

255)

D) 25 ways

Use the at least once rule to find the indicated probability. 256) The probability that a certain region in Mexico will be hit by a hurricane in any given year is 0.04. What is the probability that the region will be hit by at least one hurricane in the next 15 years? A) 0.458 B) 0.960 C) 0.023 D) 0.542

Find the expected value. 259) Find the expected number of girls in a family of 4. A) 2.5 B) 2

254)

256)

257)

258)

259) C) 1.5

D) 1.75

Solve the problem. 260) How many different three-number "combinations" are possible on a combination lock having 22 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation locks.) A) 1.0534 × 106 three-number "combinations"

260)

B) 3.5112 × 105 three-number "combinations" C) 9,240 three-number "combinations" D) 1.7556 × 105 three-number "combinations" Solve the problem. Round your answer to 2 decimal places when necessary. 261) In a given year, the population of a certain country is about 191 million. The overall birth rate is 18.1 births per 1000. The overall death rate is 10.4 deaths per 1000. Based on births and deaths alone (not counting immigration), about how much does the population of the country increase during this year? A) 1.47 million people B) 0.15 million people

C) 14.71 million people

D) 3.46 million people

261)

Answer Key Testname: CHAPTER 7

1) B 2) A 3) C 4) A 5) D 6) E 7) B 8) D 9) D 10) D 11) C 12) C 13) B 14) B 15) C 16) D 17) C 18) B 19) E 20) B 21) C 22) C 23) B 24) A 25) D 26) C 27) D 28) A 29) C 30) The expected winnings are -$0.46. the game is not fair, and it favors the owner of the game. 31) 0.000798; yes

0.550; no 32) Examples will vary. Possible answer: Let B = event that the card is a heart C = event that the card is the ace of hearts D = event that the card is a king. 33) yes; 0.00195; approximately 4 people 34) Answers will vary. Possible answer: In the long run, the average amount lost by the player per game is 87 cents. 35) It is true that the chance of any one particular person winning is very small. But there are many people playing and it is not surprising that someone wins. For example if a million people play, the chance that at least one person wins is roughly 0.4.

Answer Key Testname: CHAPTER 7

36) It is true that the chance of having a birthday on any one particular day is quite small. However the chance of being born on some day is 1. P(born Jan 1 or born Jan 2nd or born Jan 3rd or........) = P(born Jan 1st) + P(born Jan 2nd) + P(born Jan 3rd) + ....... = 1 1 1 + + + ....... = 1. 365 365 365

One has to be born on one of the 365 days of the year, and whichever day it turned out to be, one could afterwards say "what a coincidence". 37) The expected winnings would be negative for the player, as casinos are designed to make money.

38) A 39) B 40) D 41) D 42) B 43) D 44) D 45) D 46) A 47) B 48) C 49) B 50) A 51) A 52) B 53) D 54) E 55) B 56) D 57) B 58) A 59) A 60) C 61) C 62) D 63) B 64) B 65) D 66) C 67) A 68) C 69) D 70) A 71) A 72) C 49

Answer Key Testname: CHAPTER 7

73) C 74) C 75) C 76) C 77) A 78) D 79) D 80) A 81) C 82) A 83) A 84) C 85) B 86) C 87) D 88) B 89) D 90) D 91) B 92) B 93) C 94) B 95) B 96) B 97) A 98) A 99) D 100) A 101) B 102) C 103) A 104) A 105) A 106) B 107) C 108) D 109) D 110) B 111) C 112) D 113) B 114) A 50

Answer Key Testname: CHAPTER 7

115) A 116) C 117) D 118) A 119) D 120) B 121) C 122) D 123) C 124) A 125) D 126) A 127) B 128) A 129) A 130) D 131) D 132) D 133) D 134) D 135) B 136) D 137) A 138) C 139) C 140) D 141) D 142) B 143) D 144) A 145) B 146) A 147) D 148) D 149) B 150) A 151) D 152) A 153) B 154) C 155) B 156) B 51

Answer Key Testname: CHAPTER 7

157) D 158) C 159) C 160) C 161) A 162) A 163) A 164) B 165) A 166) B 167) A 168) B 169) B 170) A 171) B 172) B 173) D 174) D 175) D 176) C 177) C 178) D 179) C 180) B 181) C 182) C 183) C 184) D 185) A 186) B 187) B 188) D 189) D 190) B 191) A 192) D 193) D 194) B 195) A 196) B 197) D 198) C 52

Answer Key Testname: CHAPTER 7

199) B 200) A 201) A 202) A 203) A 204) C 205) D 206) D 207) A 208) D 209) D 210) A 211) D 212) A 213) B 214) D 215) D 216) A 217) B 218) D 219) C 220) B 221) B 222) A 223) B 224) C 225) A 226) D 227) D 228) A 229) D 230) C 231) A 232) D 233) D 234) C 235) B 236) D 237) B 238) A 239) C 240) B 53

Answer Key Testname: CHAPTER 7

241) B 242) D 243) A 244) A 245) A 246) D 247) C 248) B 249) D 250) D 251) D 252) A 253) C 254) D 255) A 256) A 257) B 258) C 259) B 260) C 261) A

Exam

Chapter 8

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Which of the following sounds would you expect to have the highest decibel measurement? A) Ordinary conversation B) Background noise in an average home

C) Afternoon traffic in New York City

D) Rustling leaves

2) Earthquakes usually cause damage in all but which one of the following related ways? A) Collapsed building due to inferior construction B) Tsunamis C) Fires caused by heat from the earth's interior. D) Landslides

3) Which of the following are factors in the amount of damage caused by an earthquake? A) The economy of the region hit by the earthquake B) All of these C) The amount of energy released in surface waves as compared to interior waves D) The type of surface bedrock near the quake

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growing suburban town (based on a current population of 100,000). 4) Use the average growth rate between 1850 and 1950, which was about 0.5%. 4) A) 135 years; population in 50 years = 116,013

B) 142 years; population in 50 years = 134,590 C) 140 years; population in 50 years = 128,089 D) 150 years; population in 50 years = 121,901 Provide an appropriate response. 5) True or False? Within the next decade, world population will grow by more than twice the current population of the United States. A) True B) False

6) Use the growth rate of 1.8% to estimate the population of a growing country in 2,062. Start from

7) True or False? Earthquake strength is described in pH, the loudness of sounds is described in

the 2000 population of 58 million. Use the approximate doubling time formula. A) 107.2 million B) 99.2 million C) 89.6 million D) 175.1 million

magnitudes, and the acidity of household cleansers is described by decibels. A) False B) True

8) What are the conditions in which the approximate doubling time formula works well? A) small growth rates and breaks down for growth rates over 30% B) large growth rates and breaks down for growth rates below 30% C) large growth rates and breaks down for growth rates below 15% D) small growth rates and breaks down for growth rates over 15%

9) The doubling time of a population of flies is 2 hours. By what factor does the population increase

in 48 hours?

A) 48

B) 248

C) 224

10) True or False? 101.940 is between 10 and 100. A) False

D) 21/24 10)

B) True

11) Given log10 2 = 0.3010 and log10 3 = 0.4771, find log10 12 without using a calculator. A) 1.0791 B) 0.2872 C) 0.5677 D) 1.2552 Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 12) The value of your house is rising by $15,864 per year. If it is worth $210,686 today, what will it be worth in three years? A) Exponential; $261,951.47 B) Linear; $647,922.00

C) Exponential; $679,650.00

11)

12)

D) Linear; $258,278.00

Provide an appropriate response. 13) True or False? Pure water is neutral and has a pH of 0. A) True B) False

13)

14) Use the 1960s peak annual growth rate of 0.7% and population of 6 million to predict the current

14)

15) Consider a population that begins growing exponentially at a base rate of 8% per year and then

15)

16) A certain radioactive isotope decays at a rate of 0.175% per year. Determine the half-life of this

16)

growth rate with a logistic model. Assume a current country population of 18 million. Assume the carrying capacity is 26 million. A) 1.19% B) 0.42% C) 0.70% D) 0.28%

follows a logistic growth pattern. If the carrying capacity is 90 million, find the actual growth rate when the population is 87 million. A) 0.27% B) 0.30% C) 0.29% D) 0.24%

isotope, to the nearest year. A) 4 years B) 172 years

C) 396 years

D) 286 years

17) Inflation is causing prices to rise at a rate of 5% per year. Use the approximate double time formula to determine what the price will be in 7 years if the item costs $100 today. A) $105.08 B) $141.42 C) $282.84 D) $149.83

17)

Use the decibel scale to answer the question. 18) How many times as loud as the softest audible sound is the sound of strong risk of damage to human ear (120 decibels)? A) 1012 B) 1024 C) 103

18) D) 10120

Provide an appropriate response. 19) True or False? Money in a bank account earning compound interest at an annual percentage rate of 3% represents an example of linear growth. A) False B) True Use the earthquake magnitude scale to answer the question. 20) How much energy, in joules, is released by an earthquake of magnitude 6? A) 2.5 × 1016 joules B) 2.5 × 1010 joules

C) 2.4 × 1013 joules

19)

20)

D) 2.5 × 1013 joules

Provide an appropriate response. 21) A community of deer begins with an initial population of 1000 and grows 3.8% per year. Find the doubling time of the population. Round to the nearest year. A) 1 year B) 18 years C) 8 years D) 53 years

21)

22) True or False? Suppose you had a magic bank account in which your balance doubled each day.

22)

23) True or False? When the population is small relative to the carrying capacity, logistic growth is

23)

24) The following table gives the birth and death rates for four countries in three different years:

24)

If you started with just $1, you'd be a millionaire in less than a month. A) True B) False

exponential with a fractional growth rate close to the base growth rate r. A) True B) False

Birth rate (per 100) Death rate (per 100) Town year 1 year 2 year 3 year 1 year 2 year 3 Simpleton 1.9 1.5 0.9 1.2 1.2 0.8 Normalton 2.8 2.4 2.1 0.7 0.6 0.5 Ruralton 1.3 1.2 1.2 1.1 1.0 0.9 Littleton 1.4 1.6 1.5 0.9 0.8 0.7 Find Simpleton's net growth rate due to births and deaths in year 1. A) 0.9 per 100 B) 0.7 per 100 C) 0.4 per 100

D) 0.6 per 100

Use the decibel scale to answer the question. 25) How does the intensity of sound form a concert speaker at a distance of 1 meter compare to the intensity at a distance of 6 meters? A) Factor of 6 weaker at 6 m. B) Factor of 106 weaker at 6 m.

C) Factor of 36 weaker at 6 m.

D) Factor of 18 weaker at 6 m.

25)

Solve.

26) Using the chessboard parable, find the total weight (in pounds ) when all squares up to and

26)

including 20 are filled. Assume that each grain of wheat weighs 1/7000 pound. Round your answer to the nearest pound. A) 150 pounds B) 5 pounds C) 75 pounds D) 37 pounds

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 27) The population of Oak Forest is increasing at a rate of 4% per year. If the population is 83,237 today, what will it be in three years? A) Exponential; 86,611 people B) Exponential; 93,630 people

C) Linear; 108,237 people

27)

D) Linear; 259,699 people

Provide an appropriate response. 28) True or False? The carrying capacity of our planet depends on our consumption of energy. A) False B) True

28)

Use the pH scale to answer the question. 29) What is the hydrogen ion concentration of a solution with pH 3.5? A) 3.2 x 10-4 B) 3.2 x 10-6 C) 3.2 x 10-3

29) D) 3.2 x 10-5

Provide an appropriate response. 30) The Consumer Price Index is increasing at a rate of 7% per year. By what factor will prices increase in 5 years? Use the approximate doubling time formula (rule of 70). A) 1.41 B) 70 C) 1.01 D) 7.36

31) True or False? log102,000,000 is between 7 and 8. A) True

30)

31) B) False

32) A community of rats begins with an initial population of 100 and grows 6% per month. Find the doubling time of the population. Round to the nearest month. A) 10 months B) 23 months C) 12 months

D) 19 months

33) True or False? The earthquake magnitude scale relates the magnitude to the amount of electricity released. A) False

32)

33)

B) True

Use the decibel scale to answer the question. 34) What is the loudness, in decibels, of a sound 45 million times as loud as the softest audible sound? A) 92 dB B) 77 dB C) 61 dB D) 107 dB Provide an appropriate response. 35) True or False? log10 1 is between 0 and 1. 10

34)

35)

A) True

B) False

Use the pH scale to answer the question. 36) What is the pH of a solution with a hydrogen ion concentration of 0.1 mole per liter? Is this solution an acid or a base? A) pH = 8; base B) pH = 2; acid

C) pH = 7; neutral

D) pH = 1; acid

Provide an appropriate response. 37) True or False? The carrying capacity is the largest population the environment can support for extended periods of time. A) True B) False Use the decibel scale to answer the question. 38) How does the intensity of sound from a concert speaker at a distance of 20 meters compare to the intensity at a distance of 60 meters? A) Factor of 30 weaker at 60 m. B) Factor of 9 weaker at 60 m.

C) Factor of 3 weaker at 60 m.

37)

38)

D) Factor of 36 weaker at 60 m.

Provide an appropriate response. 39) Given that log103 = 0.477, find log1027 without using a calculator.

A) 27

36)

B) 0.109

C) 1.431

39) D) 9

Use the earthquake magnitude scale to answer the question. 40) Compare the energy of a magnitude 7 earthquake to that released by a 1-megaton nuclear bomb (5 x 1015 joules).

A) 0.7 times as much energy C) 4.2 times as much energy

40)

B) 6.3 times as much energy D) 3.6 times as much energy

Provide an appropriate response. 41) Suppose a population has a doubling time of 40 years. By what factor will it grow in 40 years? A) 1 B) 4 C) 3 D) 2

41)

42) True or False? Exponential growth leads to repeated doublings. With each doubling, the amount

42)

43) Use the growth rate of 0.7% to estimate the population of a growing country in 2,071. Start from

43)

44) Real populations sometimes increase beyond their environment's carrying capacity in a relatively

44)

of increase is approximately equal to the sum of all preceding doublings. A) False B) True

the 2000 population of 55 million. Use the approximate doubling time formula. A) 101.7 million B) 111.1 million C) 90.0 million D) 146.0 million

short period of time. What is the name of this phenomenon? A) Collapse B) Annual growth rate

C) Logistic growth

D) Overshoot

45) True or False? The world population growth rate is equal to the birth rate subtracted from the death rate. A) False

45)

B) True

Use the pH scale to answer the question. 46) If the pH of a solution increases by 4, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic? A) Increases by a factor of 10,000; more acidic

46)

B) Decreases by a factor of 10,000; more basic C) Increases by a factor of 40; more acidic D) Decreases by a factor of 40; more basic Provide an appropriate response. 47) The initial population of a town is 18,522 and it grows with a doubling time of 12 years. What will the population be in 3 years? A) 111,132 people B) 55,566 people C) 18,524 people D) 22,026 people

48) Poaching is causing a population of elephants to decline by 11% per year. Use the approximate

47)

48)

half-life formula to determine the fraction that remains in 55 years if there are 18,018 elephants today. A) 45 elephants B) 16,159 elephants

C) 77,864 elephants

D) 10,452 elephants

49) True or False? The loudness of a sound in decibels is defined by the formula

49)

intensity of the sound 10 log10 . intensity of loudest audible sound

A) False

B) True

50) In 2000, the population of Littletown was 18 thousand. Use the given doubling time to predict the population in 2010. Assume a doubling time of 46 years. A) 24.3 thousand B) 8,280 thousand C) 20.9 thousand

D) 1.2 thousand

51) The half-life of a radioactive substance is 63 years. If you start with some amount of this substance, what fraction will remain in 113 years? A) 3.47 B) 0.08

C) 0.02

50)

51)

D) 0.29

Solve.

52) Use the magic penny parable to determine how many days would elapse before you had a total of over 837,235. A) 30 days

B) 18 days

C) 26 days

D) 35 days

Provide an appropriate response. 53) Inflation is causing prices to rise at a rate of 8% per year. Use the exact double time formula to determine what the price will be in 9 years if the item costs $100 today. A) $199.90 B) $100.84 C) $100.08 D) $100.72

52)

53)

54) Use the 1960s peak annual growth rate of 3.2% and population of 3 million to predict the current

54)

55) Oil consumption is increasing at a rate of 2.3% per year. By what factor will oil consumption

55)

growth rate with a logistic model. Assume a current country population of 9 million. Assume the carrying capacity is 19 million. A) 3.20% B) 2.00% C) 3.00% D) 5.80%

increase in 3 years? Use the approximate doubling time formula (rule of 70). A) 2.37 B) 1.07 C) 1.01

D) 13.8

56) The current population of a threatened animal species is 1 million, but it is declining with a

56)

half-life of 23 years. How many animals will be left in 75 years? A) 522 animals B) 104,323 animals

C) 104 animals

D) 52,162 animals

57) _______ growth occurs when a quantity grows by the same relative amount in each unit of time. A) Exponential B) Static C) Linear D) None of the above 58) Given that log104 = 0.602, find log10 1 without using a calculator.

58)

A) -5.418

C) 0.218

B) -1.806

57)

D) -12.000

59) Urban encroachment is causing the area of a forest to decline at a rate of 6% per year. Use the

59)

60) Use the magic penny parable to determine how many days would elapse before you had a total of

60)

approximate half-life formula to determine the fraction that remains in 51 years. A) 0.942318 B) 0.603501 C) 2.185714 D) 0.048314

Solve. over $4,362,316. A) 38 days

B) 21 days

C) 33 days

D) 29 days

Provide an appropriate response. 61) True or False? If you increase the amount of water in the cup, you'll increase the pH of the water in the cup. A) False B) True Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 62) The price of a gallon of gasoline is increasing by 2¢ per week. If the price is $3.19 per gallon today, what will it be in ten weeks? A) Exponential; $3.25 B) Linear; $3.39

C) Linear; $3.37

D) Exponential; $3.89

61)

62)

Provide an appropriate response. 63) Urban encroachment is causing the area of a forest to decline at a rate of 8% per year. Use the approximate half-life formula to determine the half-life of the forest. A) 1.08 years B) 17.50 years C) 8.75 years D) 7.50 years Use the decibel scale to answer the question. 64) How much louder (more intense) is a 59-dB sound than a 40-dB sound? A) 63,095,734 times as loud B) 1.5 times as loud

C) 79 times as loud

63)

64)

D) 453 times as loud

Use the pH scale to answer the question. 65) If the pH of a solution decreases by 3.1, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic? A) Increases by a factor of 1,259; more acidic

65)

B) Decreases by a factor of 1,259; more basic C) Decreases by a factor of 31; more basic D) Increases by a factor of 31; more acidic Provide an appropriate response. 66) True or False? 10-0.456 is between 1 and 100.

66)

A) False

B) True

67) The Consumer Price Index is increasing at a rate of 7% per year. What is its doubling time? Use the approximate doubling time formula (rule of 70). A) 128 years B) 14 years

C) 10 years

D) 4.9 years

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 68) The price of computer memory is decreasing at a rate of 12% per year. If a memory chip costs $84 today, what will it cost in two years? A) Linear; $63.84 B) Exponential; $65.05

C) Exponential; $74.22

67)

68)

D) Linear; $104.16

Solve.

69) Use the bacteria parable to determine how many bacteria are in the bottle at 11:20. A) 40 bacteria B) 220 bacteria C) 22 bacteria D) 219 bacteria Use the decibel scale to answer the question. 70) How does the intensity of sound form a concert speaker at a distance of 1 meter compare to the intensity at a distance of 100 meters?

A) Factor of 100 weaker at 100 m. C) Factor of 10100 weaker at 100 m.

B) Factor of 10,000 weaker at 100 m. D) Factor of 300 weaker at 100 m.

69)

70)

Provide an appropriate response. 71) If a population has exceeded the carrying capacity of its environment, it may suffer a rapid and severe decrease in the population. What is the name of this type of population decrease? A) Logistic growth B) Overshoot

C) Collapse

71)

D) Annual growth rate

72) True or False? Exponential growth cannot continue indefinitely. After only a relatively small

72)

73) Given log10 2 = 0.3010 and log10 3 = 0.4771, find log10 18 without using a calculator. A) 0.2872 B) 1.2552 C) 1.0791 D) 0.5286

73)

74) Suppose a radioactive substance has a half-life of 1000 years. What fraction will be left after 2000

74)

number of doublings, exponentially growing quantities reach impossible proportions. A) True B) False

years?

A) 1 4

B) 8

C) 4

D) 1 8

75) The doubling time of a city's population is 24 years. How long does it take for the population to quadruple. A) 244 years

B) 224 years

C) 4 years

75)

D) 48 years

Solve.

76) Use the magic penny parable to determine how much money you would have after 17 days. A) $655.36 B) $2,621.44 C) $1,310.72 D) $171,798,691.84

76)

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growing suburban town (based on a current population of 100,000). 77) Use the average growth rate between 1970 and 2000, which was about 1.5%. 77) A) 47 years; population in 50 years = 210,151

B) 49 years; population in 50 years = 243,803 C) 42 years; population in 50 years = 156,142 D) 57 years; population in 50 years = 181,145 Provide an appropriate response. 78) In 2000, the population of Littletown was 4 thousand. Use the given doubling time to predict the population in 2060. Assume a doubling time of 23 years. A) 5,520 thousand B) 24.4 thousand C) 6.1 thousand D) 9.9 thousand Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 79) The value of your house is rising by 29% per year. If it is worth $379,205 today, what will it be worth in three years? A) Exponential; $814,035.20 B) Linear; $709,113.35

C) Exponential; $500,147.36

D) Linear; $599,143.90 9

78)

79)

Provide an appropriate response. 80) The half-life of a drug in the bloodstream is 9 hours. By what factor does the concentration of the drug decrease in 13 hours? A) 0.14 B) 0.37 C) 2.72 D) 0.05

80)

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growing suburban town (based on a current population of 100,000). 81) Use the current annual growth rate which is about 2.8%. 81) A) 20 years; population in 50 years = 229,740

B) 27 years; population in 50 years = 527,803 C) 25 years; population in 50 years = 400,000 D) 35 years; population in 50 years = 303,143 Provide an appropriate response. 82) Consider a population that begins growing exponentially at a base rate of 4% per year and then follows a logistic growth pattern. If the carrying capacity is 44 million, find the actual growth rate when the population is 10 million. A) 2.78% B) 3.31% C) 3.49% D) 3.09%

83) In 2000, the population of Littletown was 5 thousand. Use the given doubling time to predict the

82)

83)

population in 2100. Assume a doubling time of 42 years. A) 135.7 thousand B) 5.2 thousand

C) 26.0 thousand

D) 21,000 thousand

Solve.

84) Using the chessboard parable, find the total number of grains when all squares up to and including 11 are filled. A) 512 grains

B) 20 grains

C) 1,024 grains

D) 2,047 grains

Provide an appropriate response. 85) The number of cells in a tumor doubles every 6.8 months. If the tumor begins as a single cell, how many cells will there be after 5 years? A) 1,156 cells B) 2 cells C) 453 cells D) 408 cells Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 86) The value of your car is decreasing by 14% per year. If the car is worth $8,095 today, what will it be worth in two years? A) Exponential; $7,001.37 B) Linear; $10,361.60

C) Exponential; $5,987.06

84)

85)

86)

D) Linear; $9,228.30

Provide an appropriate response. 87) True or False? Our town is growing with a doubling time of 30 years, so its population will triple in 90 years. A) False B) True

87)

Use the decibel scale to answer the question. 88) How does the intensity of sound from a concert speaker at a distance of 20 meters compare to the intensity at a distance of 140 meters? A) Factor of 196 weaker at 140 m. B) Factor of 49 weaker at 140 m.

C) Factor of 7 weaker at 140 m.

88)

D) Factor of 70 weaker at 140 m.

Use the pH scale to answer the question.

89) What is the pH of a solution with a hydrogen ion concentration of 10-10 mole per liter? Is this solution an acid or a base? A) pH = 7; neutral

89)

B) pH = 10; base D) pH = 11; base

C) pH = 4; acid

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 90) The population of Scoville is increasing at a rate of 301 people per year. If the population is 423 today, what will it be in three years? A) Exponential; 27,271,324 people B) Linear; 1,326 people

C) Exponential; 75,687,268 people

90)

D) Linear; 1,570 people

Provide an appropriate response. 91) The initial population of a town is 98,068 and it grows with a doubling time of 45 years. What will the population be in 36 years? A) 3,530,448 people B) 170,746 people

C) 98,093 people

91)

D) 7,060,896 people

Use the earthquake magnitude scale to answer the question. 92) How much energy, in joules, is released by an earthquake of magnitude 7.4? A) 3.1 × 1015 joules B) 3.0 × 1015 joules

C) 7.9 × 1019 joules

92)

D) 6.3 × 1011 joules

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growing suburban town (based on a current population of 100,000). 93) Use the average growth rate between 1850 and 1950, which was about 1.4%. 93) A) 60 years; population in 50 years = 174,110

B) 52 years; population in 50 years = 229,740 C) 50 years; population in 50 years = 200,000 D) 45 years; population in 50 years = 151,572 Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 94) During the worst periods of inflation in America, the price of food increased at a rate of 8% per month. If your food bill was $500 one month during this period, what was it two months later? A) Exponential; $583.20 B) Linear; $1,080.00

C) Linear; $580.00

D) Exponential; $540.80

94)

Provide an appropriate response. 95) True or False? Birth rates have increased rapidly throughout the world during the past 50 years. A) True B) False

96) True or False? Bases have a pH Lower than 7. A) True

95)

96) B) False

Use the decibel scale to answer the question. 97) What is the loudness, in decibels, of a sound 26 trillion times as loud as the softest audible sound? A) 161 dB B) 188 dB C) 107 dB D) 134 dB Provide an appropriate response. 98) A nation of 100 million people is growing at a rate of 3% per year. Use the exact double time formula to determine what the population will be in 38 years. A) 307 million B) 175 million C) 220 million D) 102 million

97)

98)

Solve.

99) Use the bacteria parable to determine what fraction of the bottle is full at 11:53. A) 1 full 28

B) 11 full

C) 1 full 26

99) D) 1 full 27

Provide an appropriate response. 100) True or False? An earthquake of magnitude 6 will do twice as much damage as an earthquake of magnitude 3. A) False B) True Use the earthquake magnitude scale to answer the question. 101) How many times as much energy is released by an earthquake of magnitude 6 as by one of magnitude 4? A) 104 times as much energy B) 103 times as much energy

C) 102 times as much energy

100)

101)

D) 106 times as much energy

Solve.

102) Using the chessboard parable, how many grains of wheat should be placed on square 6 of the chessboard? A) 64 grains

B) 10 grains

C) 16 grains

D) 32 grains

Provide an appropriate response. 103) True or False? Repeated doubling, in which each doubling occurs in the same amount of time, is a hallmark of linear growth. A) False B) True

102)

103)

Answer Key Testname: CHAPTER 8

1) C 2) C 3) B 4) C 5) A 6) D 7) A 8) D 9) C 10) B 11) A 12) D 13) B 14) D 15) A 16) C 17) B 18) A 19) A 20) D 21) B 22) A 23) A 24) B 25) C 26) A 27) B 28) B 29) A 30) A 31) B 32) C 33) A 34) B 35) B 36) D 37) A 38) B 39) C 40) B 41) D 42) B 13

Answer Key Testname: CHAPTER 8

43) C 44) D 45) B 46) B 47) D 48) A 49) A 50) C 51) D 52) C 53) A 54) B 55) B 56) B 57) A 58) B 59) D 60) D 61) A 62) B 63) C 64) C 65) A 66) A 67) C 68) B 69) B 70) B 71) C 72) B 73) B 74) A 75) D 76) C 77) A 78) B 79) A 80) B 81) C 82) D 83) C 84) D 14

Answer Key Testname: CHAPTER 8

85) C 86) C 87) A 88) B 89) B 90) B 91) B 92) A 93) C 94) A 95) B 96) B 97) D 98) A 99) D 100) A 101) B 102) D 103) A

Exam

Chapter 9

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. In the following situation, state whether two variables are related in a way that might be described by a function. If so, identify the independent and dependent variables. 1) You make a list of the titles of books in a public library and their copyright year. 1) A) Independend variable, copyright year; dependent variable, book title

B) does not describe a function C) Independend variable, book title; dependent variable, copyright year 2) You are taking a road trip in a car and want to know how far you've traveled (read the odometer)

at various times during your trip. A) Independend variable, time; dependent variable, distance traveled

B) does not describe a function C) Independend variable, distance traveled; dependent variable, time SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Plot and label the given points. 3) (-6, -5), (-3, 4)

4) (1, 1), (-2, -6)

5) (5, -5), (-1, 4)

6) (6, 6), (-1, 1)

For the given function: a) Describe an appropriate domain and range for the function. b) Make a rough sketch of a graph of the function. c) Briefly discuss the validity of your graph as a model of the true function. 7) (miles ran per week, 5K time)

For the given graph: a) In words, describe the function shown on the graph. b) Find the slope of the graph and express it as a rate of change (be sure to include units). c) Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

Plot and label the given points. 10) (0, 6), (0, -2)

10)

11) (1, 5), (4, -2)

11)

12)

13)

15) (hours worked, yearly wages)

14) 15)

16)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a short statement that expresses a possible function between the given variables. 17) (price of a television, demand for television) A) As the price of a television increases, the demand generally decreases.

17)

B) As the demand of a television increases, the price generally decreases. C) As the demand of a television decreases, the price generally increases. D) As the price of a television increases, the demand generally increases. 18) (weight of a bag of oranges, price of the bag of oranges) A) As the price of the bag of oranges decreases, the weight of the bag increases. B) As the weight of the bag of oranges decreases, the price of the bag increases. C) As the price of the bag of oranges increases, the weight of the bag decreases. D) As the weight of the bag of oranges increases, the price of the bag increases.

18)

Provide an appropriate response. 19) A certain drug is eliminated from the bloodstream exponentially with a half-life of 60 hours. Suppose that a patient receives an initial dose of 10 milligrams of the drug at midnight. How much of the drug is in the patient's blood at noon the next day? A) 4.35 mg B) 0.31 mg C) 8.71 mg D) 0.87 mg Write an equation for the linear function and use it to answer the given question. 20) You can purchase a motorcycle for $6,648 or lease it for a down payment of $653 and $240 per month. Find an equation that describes how the cost of the lease depends on time. How long can you lease the motorcycle before you've paid more than its purchase price. A) L = 653 + 240m; 24 months B) L = 653 + 240m; 30 months

C) L = 653 - 240m; 24 months

19)

20)

D) L = 653 - 240m; 30 months

Create the required linear function an use it to answer the question. 21) Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 786. Based on these two data points, create a linear equation for the function that describes how score varies as a function of time. A) s = 3.735t - 499.5 B) s = -4.15t + 495.5

C) s = 4.15t + 495.5

D) s = 3.735t + 499.5

21)

Provide an appropriate response. 22) The population of a town with an initial population of 73,607 is decreasing at a rate of 2.2% per year. Make a graph of the exponential function.

Year

23) In the algebraic equation of a line, the y-intercept is denoted by the letter ______. A) x B) m C) y D) b Solve the equation for the unknown quantity x. 24) 4x = 26

A) 1.57

22)

23)

24)

B) 0.43

C) 3.53

Provide an appropriate response. 25) The _____ the rate of change, the narrower the slope. A) more independent B) more dependent

C) smaller

D) greater

D) 2.35

25)

Solve the equation for the unknown quantity x. 26) 44x = 29

A) 0.61

26)

B) 3.64

C) 1.62

D) 1.65

Provide an appropriate response. 27) True or False? A negative slope means a line falling right. A) False B) True Create the required linear function an use it to answer the question. 28) In 1995 the United States recovered 20% of its municipal solid wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Based on these two data points, create a linear equation for the function that describes how P varies as a function of time. A) P = -0.6t + 7 B) P = 0.3t - 17 C) P = 0.6t + 24 D) P = 0.6t + 17 Provide an appropriate response. 29) True or False? The rate of change is equal to the slope of the graph. A) True B) False

27)

28)

29)

30) If prices increase at a monthly rate of 0.7%, by what percentage do they increase in a year? A) 8.4% B) 6.5% C) 10.9% D) 8.7%

30)

31) Cars sold

31)

Year Crafty Bill's Cool Car Sales opened as a used car sales lot in 2001. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2003? A) 650 cars B) 500 cars C) 600 cars D) 250 cars

Write an equation for the linear function and use it to answer the given question. 32) Normaltown High School's pool record for the 100-yard freestyle was 48.1 in 1990. Assume that the record falls at a constant rate of 0.05 second per year. What does the model predict for the record in 2,023? A) R = 48.1t + 0.05; 1,587.35 seconds B) R = 48.1 - 0.05t; 46.45 seconds

C) R = 48.1 + 0.05t; 49.75 seconds

D) R = 48.1t - 0.05; 1,587.25 seconds

Provide an appropriate response. 8

32)

33) The given table represents a function. Make a clear graph of the function. Date Average High Temperature Jan. 1 44° F Feb. 1 37° F Mar. 1 47° F Apr. 1 60° F May 1 68° F June 1 79° F July 1 82° F Aug. 1 87° F Sep. 1 83° F Oct. 1 73° F Nov. 1 56° F Dec. 1 48° F Dec. 31 41° F

33)

Write a short statement that expresses a possible function between the given variables. 34) (number of SUVs on road, air quality) A) As the number of SUVs on the road decreases, the quality of the air generally deteriorates.

34)

B) As the quality of the air deteriorates, the number of SUVs on the road increases. C) As the quality of the air deteriorates, the number of SUVs on the road decreases. D) As the number of SUVs on the road increases, the quality of the air generally deteriorates. Provide an appropriate response. 35) What is comprised of the values of the independent variable? A) Model B) Periodic function

C) Range

35)

D) Domain

36) Q = Q0 × 0.5t/Thalf is the equation for ________. A) growth or decay C) doubling time

36) B) half-life D) None of the above.

37) A computer is purchased for $4,400. Its value each year is about 77% of the value the preceding year. Find the value of the computer after 5 years. A) $706.14 B) $1,190.99

C) $917.06

38) The general shape of an exponential decay function is a ______. A) rising line B) rising curve C) falling curve

37)

D) $16,940.00 38) D) falling line

39) The following graph represents a function. Identify the independent and dependent variables and

39)

describe the domain and range.

A) The independent variable is age and the dependent variable is time, measured in years. The domain is the years between 1980 and 2004. The range is the ages between 0 and 82. B) The independent variable is time, measured in years, and the dependent variable is age. The domain is the years between 1980 and 2004. The range is the ages between 0 and 82. C) The independent variable is time, measured in years, and the dependent variable is age. The domain is the ages between 0 and 82. The range is the years between 1980 and 2004. D) The independent variable is age and the dependent variable is time, measured in years. The domain is the ages between 0 and 82. The range is the years between 1980 and 2004.

Write a short statement that expresses a possible function between the given variables. 40) (grade of hill, speed of sled) A) If you are coasting down a hill on a sled, the wider the hill, the slower you will coast.

40)

B) If you are coasting down a hill on a sled, the steeper the hill, the slower you will coast. C) If you are coasting down a hill on a sled, the narrower the hill, the faster you will coast. D) If you are coasting down a hill on a sled, the steeper the hill, the faster you will coast. Provide an appropriate response. 41) True or False? A linear function has a constant rate of change and a straight-line graph. A) False B) True Solve the equation for the unknown quantity x. 42) 5 × 7x = 35

A) 15.85

41)

42)

B) 0.09

C) 1

D) 7.04

The given situation involves a rate of change that you may assume to be constant. Write a statement that describes how one variable varies with respect to another, give the rate of change numerically (with units), and use the rate of change rule to answer the questions. 43) You drive along the highway at a constant speed of 49 miles per hour. How far do you travel in 43) 3.7 hours? In 6.1 hours? Write a statement that describes how one variable varies with respect to another. A) Your distance traveled changes with respect to time at a rate of 49 miles per hour. The rate of change is 49 mi/hr. In 3.7 hours, you travel 135.975 miles. In 6.1 hours, you travel 224.175 miles. B) Your distance traveled changes with respect to time at a rate of 49 miles per hour. The rate of change is 49 mi/hr. In 3.7 hours, you travel 226.625 miles. In 6.1 hours, you travel 373.625 miles. C) Your distance traveled changes with respect to time at a rate of 49 miles per hour. The rate of change is 49 mi/hr. In 3.7 hours, you travel 90.65 miles. In 6.1 hours, you travel 149.45 miles. D) Your distance traveled changes with respect to time at a rate of 49 miles per hour. The rate of change is 49 mi/hr. In 3.7 hours, you travel 181.3 miles. In 6.1 hours, you travel 298.9 miles.

Provide an appropriate response. 44) True or False? After 50 years, a population growing at a rate of 2% per year will have grown by twice as many people as a population growing at a rate of 1% per year. A) False B) True

45) There are currently 78 million cars in a certain country, decreasing by 7.9% annually. How many

44)

45)

years will it take for this country to have 50 million cars? Round to the nearest year. A) 28 years B) 4 years C) 42 years D) 6 years

Write an equation for the linear function and use it to answer the given question. 46) In the town of Oak Forest, a 3% local sales tax and a 6% state sales tax are charged on all retail sales. Let p be the before-tax amount of a purchase in dollars. Let T be the after-tax amount of the purchase. Find a linear equation that describes how T varies with p. What is the total price of an item that costs $46 before taxes? A) T = 0.09p + 1; $5.14 B) T = 0.97p; $44.62

C) T = 1.09p; $50.14

46)

D) T = 0.91p; $41.86

Provide an appropriate response. 47) True or False? An exponential function grows (or decays) by a different relative amount per unit time. A) True B) False Write an equation for the linear function and use it to answer the given question. 48) The cost of renting a car is a flat $29, plus an additional 0.07 cents per mile that you drive. How far can you drive for $97? A) r = 29m - 0.07; 3 miles B) r = 29 + 0.07m; 971 miles

C) r = 29m + 0.07; 3 miles

D) r = 29 - 0.07m; 1,800 miles

47)

48)

Provide an appropriate response. 49) True or False? The slope is defined as the amount that the graph runs horizontally for a given distance that it rises vertically. A) False B) True

50) The given table represents a function. Identify the independent and dependent variables, and

49)

50)

describe the domain and range.

Date Average High Temperature Jan. 1 44° F Feb. 1 37° F Mar. 1 49° F Apr. 1 59° F May 1 70° F June 1 80° F July 1 81° F Aug. 1 87° F Sep. 1 84° F Oct. 1 73° F Nov. 1 57° F Dec. 1 48° F Dec. 31 40° F

A) The variables are (temperature, time) or (temperature, date). The domain is all

temperatures between 37° and 87° and the range is all days over the course of a year.

B) The variables are (time, temperature) or (date, temperature). The domain is all days over

the course of a year. The range is temperatures between 44° and 40°. C) The variables are (temperature, time) or (temperature, date). The domain is all temperatures between 44° and 40° and the range is all days over the course of a year. D) The variables are (time, temperature) or (date, temperature). The domain is all days over the course of a year. The range is temperatures between 37° and 87°.

Solve the equation for the unknown quantity x. 51) log10x = -1.4

A) -15.4

51) C) 0.2466

B) -14

Provide an appropriate response. 52) What is comprised of the values of the dependent variable? A) Domain B) Model

C) Range

D) Periodic function

D) 0.0398

52)

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 53) y = 5x + 2 A) slope = 1 ; y intercept = (2, 0) B) slope = 5; y intercept = (0, 2) 5

D) slope = 1 ; y intercept = (0, 2)

C) slope = 5; y intercept = (2, 0)

53)

54) y = -6x - 3

54)

A) slope = -6; y intercept = (-3, 0)

B) slope = -6; y intercept = (0, -3)

C) slope = - 1 ; y intercept = (0, -3)

D) slope = - 1 ; y intercept = (-3, 0)

Write an equation for the linear function and use it to answer the given question. 55) You can rent time on computers at the local copy center for a $5 setup charge and an additional $2 for every 5 minutes. How much time can you rent for $20? A) r = 5t - 0.4; 4.08 minutes B) r = 5t + 0.4; 3.92 minutes

C) r = 5 - 0.4t; 62.5 minutes

D) r = 5 + 0.4t; 37.5 minutes

55)

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 56) y = -5x + 3 A) slope = -5; y intercept = (3, 0) B) slope = - 1 ; y intercept = (0, 3) 5

56)

D) slope = - 1 ; y intercept = (3, 0)

C) slope = -5; y intercept = (0, 3)

Draw a graph of the function and use the graph to answer the question. 57) During the month of January, the depth of the snow, at the base of one ski resort, decreased by 2 inches each day. On December 31st there was a base of 68 inches. Graph the equation and use the graph to estimate the depth of snow on January 28th.

57)

A) 40 inches

B) 17 inches

C) 20 inches

D) 12 inches

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 58) y = -x + 6 A) slope = 1; y intercept = (6, 0) B) slope = -1; y intercept = (0, 6)

58)

D) slope = -1; y intercept = (6, 0)

C) slope = 1; y intercept = (0, 6)

Provide an appropriate response. 59) The population of a town with an initial population of 66,333 is decreasing at a rate of 3.5% per year. Create a table showing the value of the quantity Q for the first 5 years or growth or decay.

B) Year Population 0 66,333 1 65,172 2 64,032 3 62,911 4 61,810 5 60,728

Year Population 0 66,333 1 64,011 2 61,771 3 59,609 4 57,523 5 55,509

D) Year Population 0 66,333 1 61,690 2 57,371 3 53,355 4 49,621 5 46,147

Year Population 0 66,333 1 68,655 2 71,058 3 73,545 4 76,119 5 78,783

59)

60) True or False? The demand for basketball tickets is a function of their price. A) True B) False

60)

Write an equation for the linear function and use it to answer the given question. 61) The price of a particular model car is $14,819 today and rises with time at a constant rate of $1,237 per year. How much will a new car cost in 2.4 years? A) p = 14,819t - 1,237; $34,328.60 B) p = 14,819 - 1,237t; $11,850.20

C) p = 14,819 + 1,237t; $17,787.80

D) p = 1,237 + 14,819t; $36,802.60

Provide an appropriate response. 62) True or False? If you create a graph showing how heart rate depends on running speed, the domain should be heart rates from 60 to 180. A) True B) False

63) What is a mathematical representation of a function that provides detailed information but can become unwieldy? A) Graph

61)

B) Domain

C) Equation

62)

63)

D) Data table

64) The following graph represents a function. Describe the function in words.

64)

A) The function shows a steadily decreasing average age of death between 1980 and 2004. B) The function shows a steadily increasing average age of death between 1980 and 2004. C) The function shows that the average age of death increases between 1980 and 1992 and does not change between 1992 and 2004.

D) The function shows that the average age of death per year does not change between 1980 and 2004.

Solve the equation for the unknown quantity x. 65) log10x = 5.5

A) 316,227.77

65)

B) 60.5

C) 534,145.74

D) 55

Provide an appropriate response. 66) The population of a town with an initial population of 62,423 is decreasing at a rate of 2.4% per year. Create an exponential function of the form Q = Q0 × (1 + r)t. A) Q = 62,423 × (1.024)t B) Q = 62,423 × (0.976)t

C) Q = 62,423 × (-1.4)t

66)

D) Q = 62,423 × (1.048)t

67) The population of a town with an initial population of 52,595 grows at a rate of 4.2% per year.

67)

Create a table showing the value of the quantity Q for the first 5 years or growth or decay.

B) Year Population 0 52,595 1 57,013 2 61,802 3 66,993 4 72,621 5 78,721

Year Population 0 52,595 1 273,494 2 1,422,169 3 7,395,278 4 38,455,444 5 199,968,311

D) Year Population 0 52,595 1 54,804 2 57,106 3 59,504 4 62,003 5 64,608

Year Population 0 52,595 1 50,386 2 48,270 3 46,242 4 44,300 5 42,440

68) A certain drug is eliminated from the bloodstream exponentially with a half-life of 48 hours.

68)

Suppose that a patient receives an initial dose of 20 milligrams of the drug at midnight. Estimate when the drug concentration will reach 20% of its initial level. A) 63 hours B) 46 hours C) 111 hours D) 159 hours

Create the required linear function an use it to answer the question. 69) Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 784. Based on these two data points, create a linear equation for the function that describes how score varies as a function of time. Use this function to predict an average score for persons taking a 45-hour review course. Round your answer to the tenths place. A) 681.5 B) 695.5 C) 685.7 D) 674.2

70) In 1995 the United States recovered 25% of its municipal wastes through recycling, up from 17% in 1990. Let P represent the percentage recycled and t the number of years since 1990. Based on these two data points, create a linear equation for the function that describes how P varies as a function of time. Use this function to predict the percentage recycled in 2007. A) 44.2% B) 45.9% C) 42.3% D) 40.6%

Draw a graph of the function and use the graph to answer the question.

69)

70)

71) The cost of tuition at one community college is $300 plus $125 per credit. Graph the equation, and find the cost if a student registers for 15 credits.

A) $1,125

B) $1,925

C) $2,175

71)

D) $2,325

Provide an appropriate response. 72) Between 1998 and 2002, the average rate of inflation for a particular country was about 2% per year. If a cart of groceries cost $68 in 1998, what did it cost in 2002? A) $73.61 B) $75.08 C) $79.55 D) $72.16

73) The population of a town with an initial population of 57,499 grows at a rate of 3.2% per year.

72)

73)

Create an exponential function of the form Q = Q0 × (1 + r)t.

A) Q = 57,499 × (0.968)t C) Q = 57,499 × (4.2)t

B) Q = 57,499 × (0.936)t D) Q = 57,499 × (1.032)t

Solve the equation for the unknown quantity x. 74) 11x = 48

A) 2.42

74)

B) 1.61

C) 0.62

D) 1.08

Provide an appropriate response. 75) The process of measuring the ages of rocks, bones, pottery, or other solid objects that contain radioactive elements is called ________. A) radioactive decay B) doubling time

C) half-life

D) radioactive measuring

75)

76) The population of a town with an initial population of 52,900 grows at a rate of 3.2% per year.

76)

Make a graph of the exponential function.

Year

Solve the equation for the unknown quantity x. 77) 11x/2 = 43

A) 0.32

77)

B) 1.18

C) 3.14

D) 2.09

The given situation involves a rate of change that you may assume to be constant. Write a statement that describes how one variable varies with respect to another, give the rate of change numerically (with units), and use the rate of change rule to answer the questions. 78) A gas station owner finds that for every penny increase in the price of gasoline, she sells 1,555 78) fewer gallons of gas per week. How much more or less gas will she sell if she raises the price by 10 cents per gallon? If she decreases the price by 2 cents per gallon? A) At a particular gas station, sales decrease with respect to price by 1,555 gallons per cent. The rate of change is -1,555 gallons per cent. If the price is increased by 10 cents per gallon, the change in gas sales is -15,550 gallons. If the price is decreased by 2 cents, gas sales increase by 3,110 gallons. B) At a particular gas station, sales decrease with respect to price by 1,555 gallons per cent. The rate of change is -1,555 gallons per cent. If the price is increased by 10 cents per gallon, the change in gas sales is -19,437.5 gallons. If the price is decreased by 2 cents, gas sales increase by -3,887.5 gallons. C) At a particular gas station, sales decrease with respect to price by 1,555 gallons per cent. The rate of change is 1,555 gallons per cent. If the price is increased by 10 cents per gallon, the change in gas sales is 11,662.5 gallons. If the price is decreased by 2 cents, gas sales increase by 2,332.5 gallons. D) At a particular gas station, sales decrease with respect to price by 1,555 gallons per cent. The rate of change is 1,555 gallons per cent. If the price is increased by 10 cents per gallon, the change in gas sales is 7,775 gallons. If the price is decreased by 2 cents, gas sales increase by -1,555 gallons.

Create the required linear function an use it to answer the question. 79) Suppose that you were 18 inches long at birth and 4 feet tall on your tenth birthday. Based on these two data points, create a linear equation for the function that describes how height varies with age. Use the equation to predict the height at age 7 and 42. A) h = 18 - 3a; -3 inches; -108 inches B) h = 18 + 6.6a; 39 inches; 295.2 inches

C) h = 18 + 11.4a; 72.6 inches; 496.8 inches

D) h = 18 + 3a; 39 inches; 144 inches

Solve the equation for the unknown quantity x. 80) log10(6 + x) = 1

A) 16

79)

80)

B) 6

C) -6

D) 4

Write an equation for the linear function and use it to answer the given question. 81) The Math Club plans to pay a visitor $63 to speak at a fundraiser. Tickets will be sold for $2 each. Find an equation that gives the profit/loss for the event as it varies with the number of tickets sold. How many people must attend the event for the club to break even. A) p = 63 - 2n; 63 people B) p = -63 + 2n; 63 people

C) p = -63 + 2n; 32 people

81)

D) p = 63 + 2n; 32 people

Provide an appropriate response. 82) True or False? Exponential functions are useful for modeling lottery numbers. A) True B) False

82)

83) A toxic radioactive substance with a density of 4 milligrams per square centimeter is detected in

83)

84) If prices of gold decrease at a monthly rate of 0.5%, by what percentage do they decrease in a year. A) 5.8% B) 6% C) 7.3% D) 6.2%

84)

85) What is the most compact mathematical representation of a function? A) Data table B) Graph C) Equation

85)

the ventilating ducts of a nuclear processing building that was used 37 years ago. If the half-life of the substance is 19 years, what was the density of the substance when it was deposited 37 years ago? A) 1.04 mg/cm2 B) 15.43 mg/cm2 C) 38.57 mg/cm2 D) 5.71 mg/cm2

D) Domain

Answer Key Testname: CHAPTER 9

1) B 2) A 3)

Answer Key Testname: CHAPTER 9

7) Answers may vary.

a) The domain of the function is the number of miles ran per week between 0 and 80 miles. The range consists of 5K times ranging between which typically range between 14 and 32 minutes. b)

c) The function should be roughly decreasing. Times will definitely vary based on sex, age, and size of the individual. However, typically the more miles an individual runs, the better their time will be. 8) a) As the length of the race increases, the average speed decreases. b) -0.8 (km/hr)/km hour. c) The model is a rough approximation.

Answer Key Testname: CHAPTER 9

9) Answers may vary.

a) The domain of the function consists of the typical sizes of all trucks from about 6 ft tall to 10 ft tall. The range consists of the average fuel mileage for trucks of various sizes. b)

c) This function should be roughly decreasing, because we expect fuel mileage to decrease as the size of the truck increases. However, the function probably would not give a good model because of the many exceptions (length and weight of truck, tall trucks with excellent fuel mileage and shorter trucks with poor fuel mileage).

10)

11)

12) a) Snow depth increases with time.

b) 4 in. per day. c) Good model if snowfall rate is constant for 5 days.

Answer Key Testname: CHAPTER 9

13) a) The number of students sick with the flu increases with time.

b) 5 students sick per day. c) Good model if the flu rate is constant for 5 weeks. 14) Answers may vary. a) The domain of the function is the number of hours spent studying for the exam between 0 and 20 and the range is the percentage scored on the exam between 0 and 100%. b)

c) The function should be roughly increasing. Typically, the more hours spent studying, the higher the percentage. However, there are many students who barely study and still perform well along with students who study often and still perform poorly. 15) Answers may vary. a) The domain of the function is the amount of hours worked per week between 10 and 60 hours and the range is yearly wages (in thousands of dollars) from $15K to $90K. b)

c) The function should be roughly increasing. Typically the more hours someone works, the more money they make. Any time over 40 hours, usually includes an overtime wage which raises the overall yearly wages dramatically. However, many people have a fixed salary regardless of how many hours they work, so this may not represent an appropriate model.

Answer Key Testname: CHAPTER 9

16) a) On a long trip, distance from home increases with time. b) 40 miles per hour. c) Good model if speed is constant for 8 hours.

17) A 18) D 19) C 20) A 21) C 22) C 23) D 24) D 25) C 26) A 27) B 28) D 29) A 30) D 31) A 32) B 33) D 34) D 35) D 36) B 37) B 38) C 39) B 40) D 41) B 42) C 43) D 44) A 45) D 46) C 47) B 48) B 49) A 50) D 51) D 52) C 53) B 54) B 55) D 56) C 30

Answer Key Testname: CHAPTER 9

57) D 58) B 59) B 60) A 61) C 62) B 63) D 64) B 65) A 66) B 67) C 68) C 69) A 70) A 71) C 72) A 73) D 74) B 75) A 76) D 77) C 78) A 79) D 80) D 81) C 82) B 83) B 84) A 85) C

Exam Name___________________________________

Chapter 10

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The fractal dimension of a coastline

A) is less than 1 C) is between 0 and 1

1) B) is between 1 and 2 D) is greater than 2

2) How long is the perimeter of a snowflake island? A) it is infinite C) 3 times the height

2) B) 2 times the height D) it is the same as the area

3) The Sierpinski sponge has a fractal dimension between A) 1 and 2 B) 2 and 3 C) 0 and 1

3) D) 3 and 4

4) Define a random iteration. A) an iteration that doesn't produce a fractal. B) an iteration with slight variations in every iteration. C) an iteration that is self-similar. 5) In fractal geometry, the perimeter of a region is A) unlimited; unlimited C) unlimited; limited

and the area is

B) limited; limited D) limited; unlimited

6) Define a fractal object. A) An object with several edges that can be revealed at larger scales. B) An object with many jagged edges. C) An object that can be magnified. D) An object that reveals new features at smaller scales.

7) Solving for fractal dimension, we use the rule that

A) log ab = log a + log b

B) log a = log a - log b

C) log a x = x log a

D) log(a + b) = log(a) log(b)

8) In fractal geometry, the shorter the ruler A) the more accurate the measurement C) the shorter the perimeter

B) the longer the perimeter D) the less accurate the measurement

9) The process of repeating a rule over and over to generate a self-similar fractal is called

A) repetition

B) interpretation

C) fractalization

D) iteration

10) Define a self-similar fractal. A) can be created by finding the fractal dimension B) has a fractal dimension between 0 and 1 C) looks similar to itself when examined at different scales D) has a fractal dimension greater than 2

10)

11) To create a Sierpinski triangle, start with a solid black triangle and iterate what rules? A) Connect the midpoints of the sides and remove the resulting inner triangle. B) Connect the endpoints of the sides and inserting an isosceles triangle. C) Draw an isosceles triangle extending from each side. D) Delete the middle third of each line segment of the triangle.

11)

12) What mathematical tool is helpful in finding the fractal dimension? A) iteration B) logarithm C) integration

12)

13) To create the Snowflake curve, the first step is to A) divide the line segment into three equal pieces B) use a smaller ruler C) divide the line segment in half D) find the fractal dimension

D) tangent

13)

Find the degree measure of the angle created by the given part of a circle. 14) 1 circle 60

A) 12°

B) 24°

C) 6°

14) D) 3°

Solve the problem. 15) A heat duct in the college library has a circular cross section with a radius of 11 inches and a length of 21 feet. How much paint (in square feet) is needed to paint the duct? A) 120.9 ft2 B) 60.4 ft2 C) 725.3 ft2 D) 1,450.7 ft2

16) Steve is 10% taller than Andy but proportioned in exactly the same way. If Andy's waist is 40 inches, what is Steve's waist? A) 44 in. B) 42 in.

C) 48 in.

D) 46 in.

Solve. Round your answer to the nearest tenth. 17) Find the area of a circle with a radius of 6.5 yards. A) 81.6 yd2 B) 530.7 yd2

C) 40.8 yd2

D) 132.7 yd2

15)

16)

17)

Solve.

18) Determine the area of a circular enclosure and a square enclosure made with 423 meters of fence. A) Circular: 9,707 m 2 ; square: 11,183 m 2 B) Circular: 14,240 m 2 ; square: 44,732 m 2 C) Circular: 9,707 m 2 ; square: 44,732 m 2 D) Circular: 14,240 m 2 ; square: 11,183 m 2 Find the fraction of a circle that encloses the given angle. 19) 18° A) 1 B) 1 20 10

18)

19) C) 1 25

D) 1 30

Provide an appropriate response. 20) In a right triangle, the square of the length of the hypotenuse is equal to the ________. A) area of the triangle

20)

B) square root of the sum of the other two side C) sum of the lengths of the other two sides D) sum of the squares of the other two sides Determine if the pair of triangles are similar.

21)

A) Similar

B) Not similar

Convert the given degree measure into degrees, minutes, and seconds of arc. 22) 140.0486° A) 140°47 5 B) 140°2 55 C) 140°2 47

22) D) 140°2 59

Use the formula relating angular size, physical size and distance. 23) A planet has an angular diameter of about 0.7° and a distance of about 135 million kilometers. What is its true diameter? A) 11.1 million kilometers B) 12.75 million kilometers

C) 1.65 million kilometers

23)

D) 3.3 million kilometers

Solve the problem. 24) The water reservoir for a city is shaped like a rectangular prism 359 meters long, 94 meters wide, and 12 meters deep at the end of the day, the reservoir is 90% full. How much water must be added overnight to fill the reservoir? A) 40,495 m 3 B) 536,561 m 3 C) 445,447 m 3 D) 131,609 m 3

24)

Provide an appropriate response. 25) How much does a road with a 22% grade rise for each horizontal foot? A) 0.176 ft B) 0.242 ft C) 0.22 ft

25) D) 0.198 ft

Solve.

26) Determine the area of a circular enclosure and a square enclosure made with 875 feet of fence. Use = 3.1416.

A) Circular: 60,926 ft2 ; square: 191,406 ft2 C) Circular: 41,533 ft2 ; square: 47,852 ft2

B) Circular: 60,926 ft2 ; square: 47,852 ft2 D) Circular: 41,533 ft2 ; square: 191,406 ft2

Refer to the given map. Assume that the length of each east-west block is block is

26)

1 mile and the length of each north-south 8

1 mile. 4

27) Find the straight-line distance between the bus stop and the library. A) 1.35 mi B) 1.62 mi C) 1.44 mi

27) D) 1.85 mi

Solve the problem. 28) If you magically tripled in size, by what factor has your arm length increased? A) 3 B) 27 C) 9 D) 2 Find the dimension of the object and state whether or not it is a fractal. 29) In measuring the length of the object, when you reduce the length of your ruler by a factor of 4 the number of length elements increases by a factor of 4. A) The dimension is 4 and the object is a fractal.

28)

29)

B) The dimension is 1 and the object is ordinary (non-fractal). C) The dimension is 3 and the object is ordinary (non-fractal). D) The dimension is 2 and the object is ordinary (non-fractal). Find the perimeter and area of the figure. 30) A square with sides of length 1.9 yards A) P = 3.8 yd, A = 7.22 yd2

30) B) P = 17.6 yd, A = 7.22 yd2

C) P = 7.22 yd, A = 3.61 yd2

D) P = 7.6 yd, A = 3.61 yd2

Provide an appropriate response. 31) What is the approximate grade of a path that rises 658 feet every mile? A) 9.97% B) 0.75% C) 0.37%

31) D) 12.46%

The two triangles below are similar. Find the missing lengths.

32)

32) 16

18 24

A) x = 30

B) x = 40

C) x = 32

D) x = 24

33)

33) 26

5 24

A) x = 10

13 12

B) x = 15

C) x = 7

D) x = 5

Use the formula relating angular size, physical size and distance. 34) A planet has an angular diameter of about 0.3° and a distance of about 68 million kilometers. What is its true diameter? A) 2.4 million kilometers B) 0.71 million kilometers

C) 0.36 million kilometers

34)

D) 2.75 million kilometers

Find the perimeter and area of the figure. 35) A rectangle with a length of 2 yards and a width of 7 yards A) P = 10 yd, A = 14 yd2 B) P = 8 yd, A = 28 yd2

C) P = 9 yd, A = 28 yd2

35)

D) P = 18 yd, A = 14 yd2

Convert the given degree measure into degrees, minutes, and seconds of arc. 36) 32.51° A) 32°30 24 B) 32°30 42 C) 32°30 36

36) D) 32°30 51

Find the perimeter.

37)

15 m

11 m

A) 39 m

B) 41 m

C) 82.5 m

D) 30 m

Find the degree measure of the angle created by the given part of a circle. 38) 3 circle 5

A) 216°

B) 60°

C) 270°

38) D) 108°

Solve the problem. 39) City A is at about latitude 59°S and longitude 28°W. City B is at about latitude 21°N and longitude28°W. About how far apart are the two cities? A) 2,660 mi B) 8,000 mi C) 3,800 mi D) 5,600 mi Find the perimeter and area of the figure. 40) A square with sides of length 2.9 feet A) P = 21.6 ft, A = 16.82 ft2

39)

40) B) P = 5.8 ft, A = 16.82 ft2 D) P = 16.82 ft, A = 8.41 ft2

C) P = 11.6 ft, A = 8.41 ft2

Solve the problem. 41) Suppose you build an architectural model of a new office complex using a scale factor of 57. How will the height of the actual office complex compare to the height of the scale model? A) 29 times as great B) 114 times as great

C) 3,249 times as great

41)

D) 57 times as great

42) Suppose you build an architectural model of a new concert hall using a scale factor of 31. How will the volume of the actual concert hall compare to the volume of the square model? A) 29,791 times as great B) 961 times as great

C) 93 times as great

D) 31 times as great

42)

The two triangles below are similar. Find the missing lengths.

43)

A) x = 8; y = 14 C) x = 25.7142857; y = 36

B) x = 8.75; y = 12.25 D) x = 10.5; y = 14

Find the area of the triangle.

44)

44) 41 ft

37 ft

50 ft A) 684.5 ft2

B) 758.5 ft2

C) 1,850 ft2

Provide an appropriate response. 45) How many dimensions does a point have? A) 0 B) 3

D) 925 ft2

45) C) 2

D) 1

Find the dimension of the object and state whether or not it is a fractal. 46) You generate the object from a line segment by deleting the middle third of each line segment of the current figure. A) The dimension is greater than 2 and the object is ordinary (non-fractal).

46)

B) The dimension is equal to 1 and the object is ordinary (non-fractal). C) The dimension is between 1 and 2 and the object is fractal (Cantor set). D) The dimension is less than 1 and the object is fractal (Cantor set). Use the formula relating angular size, physical size and distance. 47) What is the angular size of a quarter viewed from a distance of 30 yards? A) 2.8° B) 0.12° C) 0.05°

D) 1.91°

Provide an appropriate response. 48) How many dimensions does a plane have? A) 2 B) 1

D) 3

47)

48) C) 0

Solve. Round your answer to the nearest tenth. 49) Find the circumference of a circle with a diameter of 30 feet. A) 94.2 ft B) 706.5 ft C) 188.4 ft

49) D) 47.1 ft

50) Find the area of a circle with a diameter of 38 feet. A) 119.3 ft2 B) 4,534.2 ft2

50) C) 238.6 ft2

Find the fraction of a circle that encloses the given angle. 51) 2° A) 1 B) 1 120 135

51) C) 1

D) 1

180

Solve. Round your answer to the nearest tenth. 52) Find the circumference of a circle with a radius of 4.5 yards. A) 14.1 yd B) 28.3 yd C) 63.6 yd Refer to the given map. Assume that the length of each east-west block is block is

D) 1,133.5 ft2

52) D) 5.7 yd 1 mile and the length of each north-south 8

1 mile. 4

53) Find the straight-line distance between the bus stop and the theater. A) 1.27 mi B) 1.33 mi C) 1.50 mi

53) D) 1.58 mi

Solve the problem. 54) A competition swimming pool is 50 meters long, 26 meters wide, and 3 meters deep. How much water does the pool hold? A) 65,000 m 3 B) 3,900 m 3 C) 450 m 3 D) 33,800 m 3

54)

Find the area in acres of the property under the given assumptions. Refer to the figure.

55) The stream frontage is 631 feet in length and the property line is 2,340 feet in length. A) 8.16 acre B) 32.64 acre C) 16.32 acre D) 24.48 acre

55)

Find the dimension of the object and state whether or not it is a fractal. 56) In measuring the area of the object, when you reduce the length of your ruler by a factor of 6, the number of length elements increases by a factor of 24. A) The dimension is 0.564 and the object is fractal.

56)

B) The dimension is 18 and the object is ordinary (non-fractal). C) The dimension is 2.774 and the object is fractal. D) The dimension is 1.774 and the object is fractal. Solve the problem. 57) Find the area of the window. Round to the nearest tenth.

57)

10 dm

3 dm

A) 32.4 dm2

B) 33.5 dm2

C) 58.3 dm2

D) 44.1 dm2

58) A toy ball has a diameter of 4.6 inches. What are its volume and surface area? A) 50.9 in.3 ; 66.4 in.2 B) 52.3 in.3 ; 71.7 in.2 C) 52.2 in.3 ; 119.3 in.2 D) 117.2 in.3 ; 152.8 in.2

58)

59) A semi-circular transom above a door is to contain a stained glass window. If the stained glass

59)

window costs $0.95 per square inch, how much will the window cost?

28 in. | A) $292.33

B) $584.67

C) $2,338.67

60) If you magically doubled in size, by what factor has your weight increased? A) 1 B) 8 C) 4

D) $1,169.34 60) D) 2

Find the area of the triangle.

61)

25 ft 30 ft A) 375 ft2

B) 312.5 ft2

C) 187.5 ft2

D) 750 ft2

Solve the problem. 62) Steve is 5% taller than Andy but proportioned in exactly the same way. If Andy is 72 inches tall, how tall is Steve? A) 76 in. B) 83 in. C) 79 in. D) 72 in.

62)

Find the area of the triangle.

63)

63) 40 m

44 m 20.5 m

A) 800 m 2

B) 410 m 2

C) 820 m 2

D) 880 m 2

64)

64) 23 cm

20 cm

36.5 cm A) 200 cm2

B) 230 cm2

C) 730 cm2

D) 365 cm2

Refer to the given map. Assume that the length of each east-west block is block is

1 mile and the length of each north-south 8

1 mile. 4

65) Find the shortest possible walking distance (following the streets) between the grocery store and the library. A) 1.0 mi

B) 0.50 mi

C) 1.25 mi

65)

D) 0.75 mi

Provide an appropriate response. 66) True or False? Longitude measures positions east or west position. A) True B) False

66)

Find the perimeter and area of the figure. 67) A square with sides of length 1.8 feet A) P = 6.48 ft, A = 3.24 ft2

67) B) P = 3.6 ft, A = 6.48 ft2 D) P = 17.2 ft, A = 6.48 ft2

C) P = 7.2 ft, A = 3.24 ft2

Refer to the given map. Assume that the length of each east-west block is block is

1 mile and the length of each north-south 8

1 mile. 4

68) Find the shortest possible walking distance (following the streets) between the bus stop and the grocery store. A) 1.38 mi

B) 1.25 mi

C) 1.63 mi

D) 1.50 mi

68)

Find the perimeter.

69)

69) 14 ft

7 ft

15 ft

A) 35 ft

B) 29 ft

C) 52.5 ft

D) 36 ft

Solve the problem. 70) (i) In general terms, how does the surface-area-to-volume ratio of a mouse compare to that of a giraffe? (ii) Which animal must maintain a higher rate of metabolism to replace the heat lost through the skin? A) (i) The surface-area-to-volume ratio of a mouse is equal to the surface-area-to-volume ratio of a giraffe. (ii) Both animals must maintain the same rate of metabolism. B) (i) The surface-area-to-volume ratio of a mouse is lower than the surface-area-to-volume ratio of a giraffe. (ii) The giraffe must maintain a higher rate of metabolism. C) (i) Cannot compare the two because one type of creature is a mammal and the other is not. (ii) Cannot compare the two because one type of creature is a mammal and the other is not. D) (i) The surface-area-to-volume ratio of a mouse is higher than the surface-area-to-volume ratio of a giraffe. (ii) The mouse must maintain a higher rate of metabolism. Provide an appropriate response. 71) What is the slope of a 2 in 13 roof? A) 2 = 0.13 B) 13 = 0.87 15 15

70)

71) C) 13 = 6.5 2

D) 2 = 0.15 13

Find the perimeter.

72)

72) 23 cm

22 cm 28 cm

A) 72 cm

B) 74 cm

C) 308 cm

Convert the given degree measure into degrees, minutes, and seconds of arc. 73) 176.28° A) 176°17 48 B) 176°16 48 C) 176°14 28

D) 73 cm

73) D) 176°16 28

Provide an appropriate response. 74) Determine which surface is steeper between a roof with a pitch of 1 in 3 or a roof with a slope of 3 . 5

B) a roof with a slope of 3

A) a roof with a pitch of 1 in 3

74)

Solve.

75) Determine the area of a circular enclosure and a square enclosure made with 1,930 yards of fence. Use

75)

= 3.1416.

A) Circular: 202,065 yd2 ; square: 232,806 yd2 B) Circular: 202,065 yd2 ; square: 931,225 yd2 C) Circular: 296,417 yd2 ; square: 232,806 yd2 D) Circular: 296,417 yd2 ; square: 931,225 yd2

Refer to the given map. Assume that the length of each east-west block is block is

1 mile and the length of each north-south 8

1 mile. 4

76) Find the shortest possible walking distance (following the streets ) between the bus stop and the theater. A) 0.75 mi

B) 1.0 mi

C) 1.50 mi

Convert the given degree measure into degrees, minutes, and seconds of arc. 77) 262.2219° A) 262°14 18 B) 262°13 19 C) 262°18 22

76)

D) 1.25 mi

77) D) 262°13 22

Find the dimension of the object and state whether or not it is a fractal. 78) In measuring the length of the object, when you reduce the length of your ruler by a factor of 6, the number of length elements increases by a factor of 7. A) The dimension is 1.086 and the object is fractal.

78)

B) The dimension is 2.086 and the object is fractal. C) The dimension is 0.921 and the object is fractal. D) The dimension is 1 and the object is ordinary (non-fractal). Solve the problem. 79) Suppose you build an architectural model of a new office complex using a scale factor of 62. How will the amount of paint needed for the exterior of the actual office complex compare to the amount of paint needed for the scale model? A) 124 times as much B) 62 times as much

C) 238,328 times as much

D) 3,844 times as much

79)

80) Steve is 17% taller than Andy but proportioned in exactly the same way. If Andy is 187 pounds, how much does Steve weigh? A) 383 lb B) 300 lb

C) 340 lb

80)

D) 263 lb

81) Suppose you build an architectural model of a new concert hall using a scale factor of 21. How

81)

will the height of the actual concert hall compare to the height of the scale model. A) 21 times as great B) 441 times as great

C) 11 times as great

D) 42 times as great

82) If you magically doubled in size, how much more material will be required for your new set of clothes? A) 8

B) 2

C) 4

D) 1

Provide an appropriate response. 83) Who was the first mathematician to summarize many of the ideas of geometry? A) Newton B) Pythagoras C) Pascal D) Euclid Solve the problem. 84) City A is nearly at the same longitude as City B, but City A's latitude is 43°S while City B's latitude is 26°S. About how far away is City A from City B? A) 1,190 mi B) 1,700 mi C) 6,900 mi D) 4,830 mi Solve. Round your answer to the nearest tenth. 85) Find the area of a circle with a diameter of 7 centimeters. A) 153.9 cm2 B) 38.5 cm2 C) 44 cm2

D) 22 cm2

Convert the given angle measure into degrees and decimal fractions of a degree. 86) 314°6'46'' A) 314.113° B) 314.173° C) 314.073°

D) 314.123°

D) 55 times as many

83)

84)

85)

86)

Solve the problem. 87) You build an architectural model of a new office complex using a scale factor of 55. Suppose you wanted to fill both the scale model office complex and the actual office complex with marbles. How many times the number of marbles required for the model would be required for the actual building? A) 166,375 times as many B) 3,025 times as many

C) 165 times as many

82)

87)

Determine if the pair of triangles are similar.

88)

A) Similar

B) Not similar

Provide an appropriate response. 89) True or False? The farther away an object is located from you, the smaller it will appear in angular size. A) True B) False Use the formula relating angular size, physical size and distance. 90) What is the angular size of a quarter viewed from a distance of 15 yards? A) 3.82° B) 0.23° C) 0.11° Find the fraction of a circle that encloses the given angle. 91) 40° A) 1 B) 1 12 4

89)

90) D) 5.6°

91) C) 1 9

D) 1 8

Convert the given degree measure into degrees, minutes, and seconds of arc. 92) 236.47° A) 236°28 47 B) 236°11 47 C) 236°29 11

D) 236°28 12

Convert the given angle measure into degrees and decimal fractions of a degree. 93) 47°35' A) 47.58° B) 47.59° C) 47.64°

D) 47.54°

92)

93)

Refer to the given map. Assume that the length of each east-west block is block is

1 mile and the length of each north-south 8

1 mile. 4

94) Find the straight-line distance between the grocery store and the library. A) 0.63 mi B) 0.48 mi C) 0.56 mi

94) D) 0.75 mi

Find the dimension of the object and state whether or not it is a fractal. 95) In measuring the volume of the object, when you reduce the length of your ruler by a factor of 6 the number of length elements increases by a factor of 216. A) The dimension is 1 and the object is ordinary (non-fractal).

95)

B) The dimension is 2 and the object is ordinary (non-fractal). C) The dimension is 6 and the object is a fractal. D) The dimension is 3 and the object is ordinary (non-fractal). Provide an appropriate response. 96) If a roof with a pitch of 1 in 10 rises in the horizontal direction for 1.3 feet, how high is it vertically? A) 0.12 ft B) 1.18 ft C) 13 ft D) 1.3 ft Solve the problem. 97) Find the area of the skating rink. Round to the nearest tenth. 42 yd

97)

9 yd

A) 632.3 yd2

B) 1,264.7 yd2

C) 1,010.3 yd2

96)

D) 886.7 yd2

Find the dimension of the object and state whether or not it is a fractal. 98) In measuring the volume of the object, when you reduce the length of your ruler by a factor of 5, the number of length elements increases by a factor of 60. A) The dimension is 2.544 and the object is fractal.

98)

B) The dimension is 3.544 and the object is fractal. C) The dimension is 55 and the object is ordinary (non-fractal). D) The dimension is 0.393 and the object is fractal. Solve the problem. 99) Earth has a radius of approximately 6400 kilometers, and Venus has a radius of approximately 6,500 kilometers (assuming that the planets are spherical). (i) Compute the surface area and volume for both planets. (ii) Which planet has the larger surface-area-to-volume ratio? A) (i) Surface area of Earth is about 5.15 × 108 square kilometers, volume of Earth is about

99)

1.10 × 1012 cubic kilometers, surface area of Venus is about 5.31 × 108 square kilometers, volume of Venus is about 1.15 × 1012 cubic kilometers

(ii) Venus has the larger surface-area-to-volume ratio. B) (i) Surface area of Earth is about 5.31 × 108 square kilometers, volume of Earth is about 1.15 × 1012 cubic kilometers, surface area of <a> is about 5.15 × 108 square kilometers, volume of Venus is about 1.10 × 1012 cubic kilometers

(ii) Earth has the larger surface-area-to-volume ratio. C) (i) Surface area of Earth is about 5.31 × 108 square kilometers, volume of Earth is about

1.15 × 1012 cubic kilometers, surface area of Venus is about 5.15 × 108 square kilometers, volume of Venus is about 1.10 × 1012 cubic kilometers

(ii) Venus has the larger surface-area-to-volume ratio. D) (i) Surface area of Earth is about 5.15 × 108 square kilometers, volume of Earth is about

1.10 × 1012 cubic kilometers, surface area of Venus is about 5.31 × 108 square kilometers, volume of Venus is about 1.15 × 1012 cubic kilometers (ii) Earth has the larger surface-area-to-volume ratio.

Refer to the given map. Assume that the length of each east-west block is block is

1 mile and the length of each north-south 8

1 mile. 4

100) Find the shortest possible walking distance (following the streets) between the bus stop and the library. A) 1.25 mi

B) 1.50 mi

C) 2.0 mi 17

D) 1.75 mi

100)

Provide an appropriate response. 101) The word geometry means __________. A) triangle forming

101) B) shape measure D) earth measure

C) mountain shape

Solve. Round your answer to the nearest tenth. 102) Find the circumference of a circle with a diameter of 5 feet. A) 15.7 ft B) 7.9 ft C) 19.6 ft Convert the given angle measure into degrees and decimal fractions of a degree. 103) 201°9'51'' A) 201.174° B) 201.124° C) 201.224° Convert the given degree measure into degrees, minutes, and seconds of arc. 104) 81.91° A) 81°64 26 B) 81°54 36 C) 81°54 26

102) D) 31.4 ft

103) D) 201.164°

104) D) 81°64 36

Find the degree measure of the angle created by the given part of a circle. 105) 1 circle 4

A) 90°

B) 120°

C) 72°

105) D) 45°

Find the perimeter and area of the figure. 106) A parallelogram with sides of length of 3.5 feet and 7 feet, and a distance between the 7-foot sides of 0.6 foot. A) P = 21 ft, A = 4.2 ft2 B) P = 21 ft, A = 6.1 ft2

C) P = 6.1 ft, A = 0.5 ft2

106)

D) P = 6.1 ft, A = 0.9 ft2

Solve the problem. 107) Suppose you build an architectural model of a new concert hall using a scale factor of 28. How will the surface area of the actual concert hall compare to the surface area of the scale model? A) 784 times as great B) 21,952 times as great

C) 56 times as great

107)

D) 28 times as great

Provide an appropriate response. 108) True or False? Grade is the term used when expressing the rise over run of a road as a percentage. A) False B) True

109) How many dimensions does a cube have? A) 4 B) 1

108)

109) C) 3

D) 2

Solve.

110) Suppose you are designing a cardboard box that must have a volume of 35 cubic feet. The cost of the cardboard is $7 per square foot. How much will the material for each box cost? A) $224.70 B) $299.60 C) $599.19 D) $449.39

110)

Solve the problem. 111) Find the latitude and longitude of the location on Earth precisely opposite the point located at latitude 52°N, longitude 122°E. A) 52°N, 58°E B) 52°N, 122°W C) 52°S, 58°E D) 52°S, 58°W

111)

Find the area in acres of the property under the given assumptions. Refer to the figure.

112) The stream frontage is130 feet in length and the property line is 436 feet in length. A) 0.31 acre B) 0.62 acre C) 1.24 acre D) 0.93 acre

112)

Solve.

113) A 12-foot fence on the property line would cast a 30-foot shadow on the shortest day of the year,

113)

and the north side of the house is set back 60 feet from the property line. Find the maximum allowed height of the house. A) 42 ft B) 36 ft C) 24 ft D) 30 ft

Find the dimension of the object and state whether or not it is a fractal. 114) In measuring the area of the object, when you reduce the length of your ruler by a factor of 3 the number of length elements increases by a factor of 9. A) The dimension is 3 and the object is ordinary (non-fractal).

114)

B) The dimension is 1 and the object is ordinary (non-fractal). C) The dimension is 2 and the object is ordinary (non-fractal). D) The dimension is 3 and the object is a fractal. Provide an appropriate response. 115) Optimization problems seek what type of solution? A) Best possible B) Largest

116) How many dimensions does a line have? A) 1 B) 2

115) C) Average

D) Smallest 116)

C) 0

D) 3

Find the area of the triangle.

117)

117) 34 m 24 m

A) 744 m 2

31 m

B) 527 m 2

C) 372 m 2 19

D) 480.5 m 2

Convert the given angle measure into degrees and decimal fractions of a degree. 118) 13°7'44'' A) 13.189° B) 13.129° C) 13.139° Solve the problem. 119) If you magically tripled in size, by what factor has your waist size increased? A) 3 B) 9 C) 2

118) D) 13.089°

119) D) 27

120) A driveway is shaped like a parallelogram. How much asphalt (in square yards) is needed to

120)

pave the driveway?

7.75 yd

2 yd

A) 15.5 yd2

B) 8 yd2

C) 31 yd2

D) 7.75 yd2

Provide an appropriate response. 121) True or False? In Euclidean geometry, a triangle with three acute angles is impossible to construct. A) True B) False

122) True or False? A geometric line is formed by the shortest path between any 2 points. A) True B) False Refer to the given map. Assume that the length of each east-west block is block is

121)

122)

1 mile and the length of each north-south 8

1 mile. 4

123) Find the straight-line distance between the bus stop and the grocery store. A) 0.96 mi B) 1.43 mi C) 1.06 mi

123) D) 1.22 mi

Provide an appropriate response. 124) Determine which surface is steeper between a road with a 24% grade or a road with a pitch of 1 in 4. A) a road with a pitch of 1 in 4 B) a road with a 24% grade

124)

Find the perimeter.

125)

125) 21 yd

21 yd

A) 62 yd

B) 220.5 yd

C) 42 yd

D) 63 yd

Provide an appropriate response. 126) True or False? Two triangles are similar if they have the same shape, but not necessarily the same size. A) False B) True

126)

Solve.

127) A 15-foot fence on the property line would cast a 40-foot shadow on the shortest day of the year,

127)

and the north side of the apartment building is set back 70 feet from the property line. Find the maximum allowed height of the apartment building. A) 35.75 ft B) 26.25 ft C) 38.5 ft D) 41.25 ft

Provide an appropriate response. 128) True or False? A circle is an example of a solid. A) True

128) B) False

Answer Key Testname: CHAPTER 10

1) B 2) A 3) B 4) B 5) C 6) D 7) C 8) B 9) D 10) C 11) A 12) B 13) A 14) C 15) A 16) A 17) D 18) D 19) A 20) D 21) B 22) B 23) C 24) A 25) C 26) B 27) A 28) A 29) B 30) D 31) D 32) C 33) A 34) C 35) D 36) C 37) B 38) A 39) D 40) C 41) D 42) A 22

Answer Key Testname: CHAPTER 10

43) B 44) D 45) A 46) D 47) C 48) A 49) A 50) D 51) D 52) B 53) A 54) B 55) C 56) D 57) B 58) A 59) A 60) B 61) A 62) A 63) B 64) D 65) D 66) A 67) C 68) D 69) D 70) D 71) D 72) D 73) B 74) B 75) C 76) C 77) B 78) A 79) D 80) B 81) A 82) C 83) D 84) A 23

Answer Key Testname: CHAPTER 10

85) B 86) A 87) A 88) A 89) A 90) C 91) C 92) D 93) A 94) C 95) D 96) D 97) C 98) A 99) D 100) D 101) D 102) A 103) D 104) B 105) A 106) A 107) A 108) B 109) C 110) D 111) D 112) B 113) B 114) C 115) A 116) A 117) C 118) B 119) A 120) A 121) B 122) A 123) C 124) A 125) D 126) B 24

Answer Key Testname: CHAPTER 10

127) D 128) B

Exam

Chapter 11

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Which regular polygon can be used to make a tiling with a single polygon? A) heptagon B) hexagon C) dodecahedron

2) The golden ratio is a(n) A) rational number. C) whole number.

1) D) octagon 2)

B) irrational number. D) natural number

3) What is the first principle of perspective? A) All lines that are parallel in the real scene and perpendicular to the canvas must intersect at

the principal vanishing point of the painting. B) All parallel lines never intersect, they remain the same distance apart.

C) All shapes and sizes must remain equal, regardless of their distance from the viewer. D) None of these. 4) What is one way to decide if two numbers follow a Fibonacci sequence? A) if their sum is the same as their difference B) if each number is a multiple of the next C) if each number is prime D) if their ratio is approximately the same as the golden ratio

5) When making a tiling using only regular hexagons A) the tiles do not fill all of the space, there is some overlap of the tiles. B) the tiles do not fill all of the space, there are gaps between the hexagons. C) the tiles fill all of the space, with no overlaps and no gaps. D) the tiles fill all of the space, but there is some overlap of the tiles.

6) The golden ratio divides a line into how many pieces? A) two B) three C) four

7) What fraction is approximately equal to the golden ratio? A) 1 2

B) 8 5

C) 3 5

8) Which regular polygon can be used to make a tiling? A) triangle B) pentagon C) parallelogram

D) one 7) D) 1 5 8) D) octagon

9) On a painting using perspective there is a row of 6-story buildings extending from the

foreground, all the way to the vanishing point. The buildings in the background A) appear smaller than the ones in the foreground.

B) appear to be the same size as the ones in the foreground. C) appear larger than the ones in the foreground. D) None of these. 10) What types of instruments create music digitally? A) guitars B) synthesizers

10) C) trombones

11) Which symbol do we use to denote the golden ratio? A) B) C) 12) Which item is not related to the golden ratio? A) logarithmic spiral C) the golden pitch

D) pianos 11) D) 12)

B) Fibonacci sequences D) the golden rectangle

13) What question led Greek scholars to formulating the golden ratio? A) How are pitch and vibration related? B) What is the square root of 2? C) How to find ? D) What is the best way to divide a line?

13)

14) In mathematics, the word symmetry is used A) to describe an operation that changes appearance. B) when a solution to an equation is unknown. C) to draw an obtuse angle. D) to describe an operation that leaves something unchanged.

14)

15) The golden ratio is an example of the use of A) multiplication. B) symmetry.

15) C) perspective.

16) The golden ratio was used in A) Greek architecture. C) the discovery of gold.

D) proportion. 16)

B) the value of D) the building of the atomic bomb.

17) The vanishing point of a picture with perspective is A) the point where parallel lines meet. B) the point where two perpendicular lines intersect. C) the point where you cannot see anything on the picture. D) the point where two curves intersect.

17)

18) One of the most basic qualities of sound is A) octave. B) analog.

18) C) string.

D) pitch.

19) Which subject was not a part of the quadrivium - the standard curriculum in medieval universities? A) geometry

B) music

C) astronomy

20) Which letter is an example of reflective symmetry? A) G B) R

19)

D) history 20)

C) K

21) Which of the following is a method for storing digital music? A) vinyl records B) floppy disk C) sheet music

D) Q 21) D) compact disk

22) The number of different tilings with irregular polygons is A) zero; you cannot make a tiling using irregular polygons. B) unlimited; you can make many different tilings using irregular polygons. C) limited; you can only make 1 different tiling using irregular polygons. D) limited; you can only make 3 different tilings using irregular polygons.

22)

23) Which music principle did the Greeks discover? A) the shorter the string, the lower the pitch B) the shorter the string, the higher the pitch C) the longer the string, the shorter the pitch D) the longer the string, the higher the pitch

23)

24) Which letter is an example of rotation symmetry? A) R B) T

24) C) C

D) S

25) Which of the following is an example of exponential growth? A) the better the quality of sound B) the increase in frequencies in scale C) the change in height of a newborn baby D) the number of notes in a song

25)

26) What are the most pleasing combinations of notes? A) fourths C) consonant tones

26)

27) Which of these is not a type of picture of music? A) digital C) analog

B) first harmonics D) fifths 27) B) color D) All of the above

28) When an object can be shifted, say to the left or right, and still remains the same, this is an example of

A) reflection

28)

symmetry.

B) rotation

C) translation

29) Which of the following is not a type of symmetry? A) rotation B) repetition

D) relation 29)

C) translation 3

D) All of these.

30) In how many ways does the golden ratio occur in a pentagram? A) at least ten B) eight C) five

30) D) none

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Form a tiling from the given figure using translations and reflections.

31)

Provide an appropriate response. 32) Draw an object with translation symmetry.

32)

Form a tiling from the given figure using translations and reflections.

33)

34)

Find the frequencies of the first 6 notes of the scale that starts at the given note. 35) B above middle C; this B has a frequency of 491

35)

Form a tiling from the given figure using translations and reflections.

36)

Provide an appropriate response. 37) Draw an object with reflection symmetry.

37)

38) Draw an object with rotation symmetry.

38)

Find the frequencies of the first 6 notes of the scale that starts at the given note. 39) F# above middle C; this F# has a frequency of 368

39)

Form a tiling from the given figure using translations and reflections.

40)

Provide an appropriate response. 41) Draw two cubes, one with perspective and one without.

41)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify all of the symmetries in the following figure.

42)

A) It has reflection symmetries; it can be reflected across a vertical line through its center, a

horizontal line through its center, or either of its diagonals, and its appearance remains the same. B) It has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its appearance remains the same. C) It has reflection symmetries; it can be reflected across a vertical line through its center, a horizontal line through its center, or either of its diagonals, and its appearance remains the same. It also has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its appearance remains the same. D) None of these.

Solve.

43) Given 1.3 inches is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation A) 2.11 in. or 0.80 in. B) 2.11 in. or 1.25 in.

C) 3.41 in. or 2.02 in.

43)

= 1.62.

D) 3.41 in. or 0.50 in.

44) Given 0.07 centimeters is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation = 1.62. A) 0.11 cm or 23.14 cm B) 0.18 cm or 37.43 cm

C) 0.11 cm or 0.04 cm

D) 0.18 cm or 0.03 cm

44)

Identify all of the symmetries in the following figure.

45)

A) It has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its appearance remains the same. It also has translation symmetry.

B) It has reflection symmetries; it can be reflected across a vertical line through its center or a

horizontal line through its center, and its appearance remains the same. It also has rotation symmetry; it can be rotated through 180° and its appearance remains the same. C) It has reflection symmetries; it can be reflected across a vertical line through its center, a horizontal line through its center, or either of its diagonals, and its appearance remains the same. It also has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its appearance remains the same. D) None of these.

46)

A) It has rotation symmetry with angles of 360° ÷ 5 = 72° and multiples of 72°. It can also be reflected across five lines through its center and retain its appearance. B) It has rotation symmetry with angles of 360° ÷ 5 = 72° and multiples of 72°.

C) It has rotation symmetry; it can be rotated through 270° and its appearance remains the same.

D) None of these. Provide an appropriate response. 47) Starting at middle D with a frequency of 292 cps, find the frequency of the note a an octave and a fourth above middle D. A) 779 B) 774 C) 761 D) 801

47)

48) Starting with a tone having a frequency of 536 cycles per second, find the frequency of the tone that is three octaves higher. A) 4,288 cps B) 2,144 cps

C) 1,608 cps

D) 287,296 cps

49) Starting at middle E with a frequency of 328 cps, find the frequency of the note 36 half-steps above middle E. A) 2,624

B) 2,660

C) 2,619

B) 1,320 cps

C) 5,280 cps

49)

D) 2,588

50) Starting with a tone having a frequency of 660 cycles per second, find the frequency of the tone that is two octaves higher. A) 435,600 cps

48)

50)

D) 2,640 cps

Solve.

51) Given 2.6 inches is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation A) 6.81 in. or 1.01 in. B) 4.21 in. or 0.62 in.

C) 4.21 in. or 1.60 in.

51)

= 1.62.

D) 6.81 in. or 0.99 in.

Provide an appropriate response. 52) Starting with middle A, at a frequency of 437 cycles per second, find the frequency of the next octave of A in the circle of fifths. A) 521 B) 55,936 C) 36,708 D) 27,968

53) Starting with a tone having a frequency of 114 cycles per second, find the frequency of the tone that is three octaves higher. A) 456 cps B) 342 cps

C) 12,996 cps

52)

53)

D) 912 cps

54) The circle of fifths is generated by starting at a particular musical note and stepping upward by

54)

55) Given 5.4 kilometers is one side of a golden rectangle, find the length of the other side. Notice that

55)

intervals of a fifth. By what factor does the frequency of a tone increase if it is raised by two fifths? A) 2.24 B) 3.32 C) 1.14 D) 7.94

Solve. the other side could be either longer or shorter than the given side. Use the approximation = 1.62. A) 8.75 km or 0.30 km B) 8.75 km or 3.33 km

C) 14.15 km or 0.49 km

D) 14.15 km or 2.06 km

Provide an appropriate response. 56) Starting with a tone having a frequency of 143 cycles per second, find the frequency of the tone that is four octaves higher. A) 572 cps B) 20,449 cps C) 1,144 cps D) 2,288 cps

56)

57) Starting with a tone having a frequency of 121 cycles per second, find the frequency of the tone that is two octaves higher. A) 363 cps

B) 14,641 cps

C) 968 cps

D) 484 cps

58) Starting with a tone having a frequency of 140 cycles per second, find the frequency of the tone that is one octave higher. A) 280 cps

B) 420 cps

C) 560 cps

B) 390

C) 274

B) 650

C) 419

59)

D) 385

60) Starting at middle A with a frequency of 437 cps, find the frequency of the note a fifth above middle A. A) 677

58)

D) 19,600 cps

59) Starting at middle D with a frequency of 292 cps, find the frequency of the note five half-steps above middle D. A) 412

57)

60)

D) 655

Identify all of the symmetries in the following figure.

61)

A) It has rotation symmetry; it can be rotated through 180° and its appearance remains the same. It also has translation symmetry (if imagined to extend in both directions).

B) It has translation symmetry (if imagined to extend in both directions). It also has reflection symmetry (across a horizontal line between the jagged lines).

C) It has reflection symmetries; it can be reflected across a vertical line through its center, a

horizontal line through its center, or either of its diagonals, and its appearance remains the same. D) None of these.

Solve.

62) A line is subdivided according to the golden ratio, with the smaller piece having a length of 7 meters. What is the length of the entire line? A) 11.2 m B) 14 m

C) 36.4 m

D) 18.2 m

62)

Answer Key Testname: CHAPTER 11

1) B 2) B 3) A 4) D 5) C 6) A 7) B 8) A 9) A 10) B 11) B 12) C 13) D 14) D 15) D 16) A 17) A 18) D 19) D 20) C 21) D 22) B 23) B 24) D 25) B 26) C 27) B 28) C 29) B 30) A 31)

Answer Key Testname: CHAPTER 11

32) Possible answer:

33)

34)

35) Note

B C C# D D# E Frequency 491 520 551 583 618 655

36)

Answer Key Testname: CHAPTER 11

37) Possible answer:

38) Possible answer:

39) Note

F# G G# A A# B Frequency 368 390 413 437 463 491

40)

41) Possible answer:

42) C 43) A 11

Answer Key Testname: CHAPTER 11

44) C 45) B 46) B 47) A 48) A 49) A 50) D 51) C 52) B 53) D 54) A 55) B 56) D 57) D 58) A 59) B 60) D 61) B 62) D

Exam

Chapter 12

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Consider the following preference schedule. First B Second A Third C 9

C B A 8

A C B 7

A B C 4

If the winner is selected by a Borda count, which of the following fairness criteria is violated? A) Fairness Criterion 4 B) Fairness Criterion 3

C) Fairness Criterion 2

D) None of these

2) Which of the following voting methods always satisfies Fairness Criterion 2? A) Sequential runoff B) Borda count C) Plurality D) Pairwise comparison

3) Consider the following preference schedule.

First C Second A Third B 11

B C A 9

B A C 7

A C B 6

If the winner is selected by a Borda count, which of the following fairness criteria is violated? A) Fairness Criterion 2 B) Fairness Criterion 4

C) Fairness Criterion 3

D) None of these

4) Which method of apportionment was vetoed by George Washington? A) Webster's method B) Hill-Huntington method C) Jefferson's method D) Hamilton's method

5) Consider the following preference schedule.

First B A C D Second D B A C Third A D B B Fourth C C D A 16 10 7 5 If the winner is decided by pairwise comparisons, which of the following fairness criteria is violated? A) Fairness Criterion 2 B) Fairness Criterion 3

C) Fairness Criterion 1

D) None of these

6) Which of the following best describes how the modified quota is found? A) Divide the state's population by the standard quota B) Divide the state's population by the standard divisor C) Divide the state's population by the modified divisor D) Trial and error

7) Which method of apportionment can lead to an occurrence of the population paradox? A) Hill-Huntington method B) Webster's method C) Hamilton's method D) Jefferson's method

8) Which of the following best describes how the modified divisor is found? A) Trial and error B) Divide the state's population by the modified quota C) Divide the state's population by the standard quota D) Divide the state's population by the standard divisor

9) Which of the following voting methods does not always satisfy Fairness Criterion 1? A) Borda count B) Sequential runoff C) Pairwise comparison D) Plurality

10) Consider the following preference schedule.

10)

First B A C D Second D B A C Third A D B B Fourth C C D A 16 10 7 5 If the winner is decided by a Borda count, which of the following fairness criteria is violated? A) Fairness Criterion 4 B) Fairness Criterion 3

C) Fairness Criterion 2

D) None of these

11) Consider the following preference schedule. First C Second A Third B 11

B C A 9

B A C 7

11)

A C B 6

If the winner is selected by sequential runoffs, which of the following fairness criteria is violated? A) Fairness Criterion 3 B) Fairness Criterion 2

C) Fairness Criterion 4

D) None of these

12) Consider the following preference schedule.

12)

First A B C D Second D D B B Third B A D C Fourth C C A A 15 10 7 6 If the winner is decided by pairwise comparisons, which of the following fairness criteria is violated? A) Fairness Criterion 3 B) Fairness Criterion 2

C) Fairness Criterion 4

D) None of these

13) Which of the following is the geometric mean of x and y? A) x2 + y2

B) x + y

13)

C) xy

D) xy

14) Which method of apportionment never leads to a violation of the quota criterion? A) Jefferson's method B) Hamilton's method C) Webster's method D) Hill-Huntington method

14)

15) Consider the following preference schedule.

15)

First A B C D Second D D B B Third B A D C Fourth C C A A 15 10 7 6 If the winner is decided by a Borda count, which of the following fairness criteria is violated? A) Fairness Criterion 2 B) Fairness Criterion 3

C) Fairness Criterion 1

D) None of these

16) Which of the following best describes the relationship between the standard divisor and the modified divisor? A) The quantities are unrelated.

16)

B) The modified divisor is bigger. D) The standard divisor is bigger.

C) The two quantities are equal. 17) Consider the following preference schedule.

17)

First A B C D Second D D B B Third B A D C Fourth C C A A 15 10 7 6 If the winner is decided by plurality, which of the following fairness criteria is violated? A) Fairness Criterion 4 B) Fairness Criterion 3

C) Fairness Criterion 1

D) All of these

18) Which of the following quantities does not vary from state to state? A) Number of Representatives B) Minimum quota C) Standard divisor D) Standard quota

18)

19) Which method of apportionment compares a modified quota to a geometric mean? A) Hill-Huntington method B) Jefferson's method C) Hamilton's method D) Webster's method

19)

20) Which of the following quantities varies from state to state? A) Standard divisor B) Standard quota C) Number of Senators D) Modified divisor

20)

21) Which of the following voting methods always satisfies Fairness Criterion 2? A) Sequential runoff B) Pairwise comparison C) Borda count D) Plurality

21)

22) Consider the following preference schedule.

22)

First B Second A Third C 9

C B A 8

A C B 7

A B C 4

If the winner is selected by sequential runoffs, which of the following fairness criteria is violated? A) Fairness Criterion 1 B) Fairness Criterion 3

C) Fairness Criterion 2

D) None of these

23) Consider the following preference schedule.

23)

First B A C D Second D B A C Third A D B B Fourth C C D A 16 10 7 5 If the winner is decided by plurality, which of the following fairness criteria is violated? A) Fairness Criterion 3 B) Fairness Criterion 2

C) Fairness Criterion 4

D) All of these

24) Which of the following voting methods does not always satisfy Fairness Criterion 3? A) Borda count B) Sequential runoff C) Pairwise comparison D) Plurality

24)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether the statement makes sense. Explain your reasoning. 25) Our state has 5 districts. 30% of the state's Republicans live in my district.

25)

Provide an appropriate response. 26) What has happened if the population paradox has occurred?

26)

Decide whether the statement makes sense. Explain your reasoning. 27) These days most congressional races are decided by small margins.

27)

Provide an appropriate response. 28) Explain briefly what Fairness Criterion 1 means and give a voting method that may violate this criterion.

28)

The table shows election data for a hypothetical state in two different years (before and after redistricting). The table shows the vote counts for all House districts in the state in each of the two years. Votes for parties other than Republican and Democrat are neglected. Find the percentage of votes cast for Republican and Democratic House candidates before and after redistricting. Find the percentage of House seats that were won by Republican and Democratic candidates before and after redistricting. Did the distribution of House seats better reflect the distribution of votes before or after redistricting?

29)

29) Votes for Republican Votes for Democratic candidates (1000s) candidates (1000s) Before redistricting 2165 1087 After redistricting 2248 1286

Republican seats 13 16

Democratic seats 10 8

Decide whether the statement makes sense. Explain your reasoning. 30) Since our state is evenly divided between Democrats and Republicans, I figure that each of the congressional races will be decided by a small margin.

30)

Solve the problem. 31) Refer to the figure, which shows the distribution of voters in a state with 14 Democratic voters and 11 Republican, and five voters per district.

31)

Draw district boundaries so that two Democrats and three Republican are elected. You may draw districts with any shape you wish, as long as the district is contiguous.

Decide whether the statement makes sense. Explain your reasoning. 32) Martin demanded a second election because he lost to Simon in a close Borda count vote. In the second election, the voters did not change their preferences but one of the other losing candidates dropped out. Martin won the second election.

32)

33) Districts which are decided by a small margin are less likely to elect representatives with

33)

Solve the problem. 34) Devise a preference schedule with three candidates in which candidate A has a plurality of the votes, but loses by the sequential runoff method.

34)

extreme partisan views than those which are decided by large margins.

Decide whether the statement makes sense. Explain your reasoning. 35) The total number of teachers in a school district is larger this year than last. nevertheless, using the Webster apportionment method, one of the schools was assigned fewer teachers than last year.

35)

36) Sunil and his brother live in different states. The population of Sunil's state has been

36)

37) Alison won the majority of the vote but not the plurality.

37)

growing fast while the population of his brother's state has been fairly stable. nevertheless, using the Hill-Huntington apportionment method last year Sunil's state lost a seat while his brother's state gained a seat.

Solve the problem. 38) Given that there are 30 voters and 4 candidates, complete the following preference schedule so that the Borda count method violates Fairness Criterion 1. First Second Third Fourth

38)

B C C DD D CB A AA B 16 ? ?

Provide an appropriate response. 39) Explain briefly what Fairness Criterion 2 means and give a voting method that satisfies it.

40) What has happened if the Alabama paradox has occurred? Solve the problem. 41) Refer to the figure, which shows the geographical distribution of voters in a state with 64 voters and eight districts. The voters are half Democrat and half Republican. Assume that district boundaries must follow the grid lines shown in the figure and that each district must be contiguous.

39) 40)

41)

Draw boundaries expected to result in the election of four Democratic and four Republican representatives.

Decide whether the statement makes sense. Explain your reasoning. 42) Using the Hamilton apportionment method, a state was given 14 seats even though its standard quota was 15.12.

42)

43) Our state has 10 districts and 350,000 Democrats. I figure that roughly 35,000 Democrats

43)

44) Sunil and his brother live in different states. The population of Sunil's state has been

44)

live in each district.

growing fast while the population of his brother's state has been fairly stable. Nevertheless, using the Hamilton apportionment method last year Sunil's state lost a seat while his brother's state gained a seat.

Provide an appropriate response. 45) Briefly summarize Arrow's Impossibility Theorem. 7

45)

46) Explain briefly what Fairness Criterion 4 means and give a voting method that may

46)

violate this criterion.

Decide whether the statement makes sense. Explain your reasoning. 47) In the mayoral election, a top-two runoff system was used and all four of the fairness criteria were satisfied. Solve the problem. 48) Construct a preference schedule for 39 voters and 5 candidates where the majority candidate wins 4 pairwise comparison points and another candidate wins 3 pairwise points. Provide an appropriate response. 49) Describe briefly how approval voting works.

47)

48)

49)

Decide whether the statement makes sense. Explain your reasoning. 50) In an election there were four candidates - Karine, Dave, Rajan, and Amy. Karine won fewer votes than Dave or Rajan, yet in a sequential runoff, she won the election.

51) Using the Webster apportionment method, a state was given 19 seats even though its

50)

51)

standard quota was 20.08.

Solve the problem. 52) Devise a preference schedule with three candidates in which the top-two runoff system violates Fairness Criterion 3. Explain.

52)

Decide whether the statement makes sense. Explain your reasoning. 53) Using the Hamilton apportionment method, a state was given 15 seats even though its standard quota was 15.92.

53)

Solve the problem. 54) Refer to the figure, which shows the geographical distribution of voters in a state with 64 voters and eight districts. The voters are half Democrat and half Republican. Assume that district boundaries must follow the grid lines shown in the figure and that each district must be contiguous.

54)

Draw boundaries expected to result in the election of five Democratic and three Republican representatives.

Provide an appropriate response. 55) Explain what is meant by the fractional remainder. Decide whether the statement makes sense. Explain your reasoning. 56) Last year a mathematician came up with a new apportionment system which would be guaranteed to avoid the Alabama, population, and new states paradoxes, and which would never violate the quota criterion.

55)

56)

57) The defendant was found not guilty even though 11 of the 12 jurors voted for conviction.

57)

Solve the problem. 58) Refer to the figure, which shows the distribution of voters in a state with 14 Democratic voters and 11 Republican, and five voters per district.

58)

Draw district boundaries so that three Democrats and two Republican are elected. You may draw districts with any shape you wish, as long as the district is contiguous.

Decide whether the statement makes sense. Explain your reasoning. 59) Toni lost the election in a sequential runoff even though she received the majority of the first-place votes.

59)

60) The 64 senators who were in favor of the bill were unable to end the filibuster so the bill

60)

61) In Debra's town, a new voting system will be used which will be guaranteed to always

61)

did not pass.

satisfy all four of the fairness criteria.

Solve the problem. 62) Construct a preference schedule for 41 voters and 4 candidates that has a Condorcet candidate that fails to be elected by both the Borda count method and the plurality method. Decide whether the statement makes sense. Explain your reasoning. 63) Carmen won in a Borda count vote. In a second election, some voters ranked her higher than in the first election without changing the order of the other candidates. Nevertheless she lost the second election.

62)

63)

64) In the last election 52% of the people voted for a Republican but Republicans won only

64)

65) A school district decides to add new teachers after a new school opens in the district. They

65)

66) Darren lost in a plurality vote even though he is favored in pairwise races over every

66)

35% of our state's seats in the House of Representatives.

use the Jefferson apportionment method to determine how many teachers each school should get. They are surprised to find that as a result of adding the new school, one of the existing schools loses a teacher.

other candidate.

Solve the problem. 67) Given that there are 30 voters and 3 candidates, complete the following preference schedule so that the Borda count method violates Fairness Criterion 1.

67)

First B C C Second C B A Third A A B 16 ? ?

Provide an appropriate response. 68) What has happened if the new states paradox has occurred? Solve the problem. 69) Devise a preference schedule with three candidates in which the Borda count method violates Fairness Criterion 1. Explain. Decide whether the statement makes sense. Explain your reasoning. 70) This time around the Democrats are redrawing the boundaries of the districts. It would be to their advantage to draw the boundaries in such a way that all districts have roughly the same number of Republicans. 10

68)

69)

70)

Provide an appropriate response. 71) Explain briefly what Fairness Criterion 3 means and give a voting method that satisfies it.

71)

Decide whether the statement makes sense. Explain your reasoning. 72) My district is shaped like a horseshoe.

72)

73) Stephanie won by approval voting even though more than half of the voters disapproved

73)

74) Alex won by the Borda method, but Tom won by the method of sequential runoffs.

74)

75) In the U.S. presidential election, the candidate that wins the majority of the popular vote

75)

76) The population of my state is roughly 12,647,000 and it has 22 districts. There are 850,000

76)

Solve the problem. 77) Devise a preference schedule with three candidates in which candidate A has a majority of the votes, but loses by the Borda count method.

77)

Decide whether the statement makes sense. Explain your reasoning. 78) Pierre won fewer votes than Anthony or Carol, yet in a single runoff, Pierre won the election.

78)

of her.

does not always become president.

people in my district.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 79) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

P T P R R R R S T S S S T S P T P R P T 15 30 18 17 10

S P R T 2

Which choice wins using the method of pairwise comparisons? A) T B) R C) S

D) P

79)

Use the Hill-Huntington method to find the apportionment. 80) Use the Hill-Huntington method to apportion eleven seats among State X, State Y, and State Z. The populations of the states are State X, 4.0 million; State Y, 6.5 million; and State Z, 5.2 million. The current assignment of ten seats gives State X two seats, State Y four seats, and State Z four seats. Assign the eleventh and twelfth seats. A) Eleventh seat: State Y; Twelfth seat: State Y

80)

B) Eleventh seat: State X; Twelfth seat: State Y C) Eleventh seat: State X; Twelfth seat: State Z D) Eleventh seat: State Y; Twelfth seat: State Z Solve the problem. 81) Refer to the following preference schedule. First Second Third Fourth

C D B A 18

A B C D 12

B D A C 9

B C D A 5

81)

D A B C 3

Find the winner by a runoff of the top two candidates. A) A B) B C) D

D) C

82) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next

82)

year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

P T P R R R R S T S S S T S P T P R P T 15 30 18 17 10

S P R T 2

Which option is selected using the plurality method? A) S B) R C) T

D) P

83) Refer to the following preference schedule. If the plurality method is used to determine the winner, is Fairness Criterion 2 satisfied? First AB AC Second B A C B Third C C B A 7 10 4 8 A) Yes

B) No

83)

84) Consider an election in which the votes were cast as follows. How many of Quincy's votes would

84)

Plaxton need to win the runoff election? Candidate Number of Votes Plaxton 260 Quincy 297 Rasputin 281 A) 138 B) 142

C) 22

D) 160

85) Refer to the following preference schedule. If the winner is decided by sequential runoffs, is

85)

Fairness Criterion 2 satisfied? First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 A) Yes

B) No

86) Refer to the following preference schedule. If the Borda count method is used to determine the

86)

winner, is Fairness Criterion 2 satisfied? First B C DAC Second A A C D D Third C D A C A Fourth D B B B B 15 11 9 5 1 A) Yes

B) No

Determine whether the specified paradox occurs. 87) A town has 13 police officers to be apportioned among 3 precincts based on the population of each precinct. The populations for the current and previous years are given in the following table. Precinct 1 2 3 Previous Year Population 930 738 415 Current Year Population 975 750 421 Does the population paradox occur using Hamilton's method of apportionment? A) Yes B) No

87)

Make the requested preference schedule. 88) Eight voters are asked to rank 3 brands of automobiles: A, B, and C. The eight voters turn in the following ballots showing their preferences in order:

88)

C B A A C B B A B C B B B C A B A A C C A A C C Make a preference schedule for these ballots.

B) First AB B C Second B A C B Third C C A A 3 2 1 2

First AB B C Second B A C A Third C C A B 3 1 2 2

D) First AB B C Second B A C A Third C C A B 3 2 1 2

First AB B C Second B A C B Third C C A A 3 1 2 2

Use the Hill-Huntington method to find the apportionment. 89) Use the Hill-Huntington method to apportion eleven seats among State P, State Q, and State R. The populations of the states are State P, 0.75 million; State Q, 1.2 million; and State R, 1.5 million. A) P: 2; Q: 3; R: 6 B) P: 2; Q: 5; R: 4 C) P: 2; Q: 4; R: 5 D) P: 3; Q: 4; R: 4 Find the standard quota asked for. Round your answer to two decimal places if necessary. 90) A small city has 45 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table.

89)

90)

Precinct 1 2 3 4 5 6 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174 Find the standard quota for the Third Precinct. A) 5.47 B) 4.59

C) 6.76

D) 5.16

Determine whether the specified paradox occurs. 91) A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province. Does the Alabama paradox occur using Hamilton's method if the number of judges is increased from 300 to 301? A) Yes B) No

91)

Solve the problem. 92) Refer to the following preference schedule. If the Borda count method is used to determine the winner, is Fairness Criterion 1 satisfied? First AB B A ACB Second B C D B C B D Third C D C D D D A Fourth D A A C B A C 8 7 4 10 8 6 8 A) Yes

B) No

93) Refer to the following preference schedule. First Second Third Fourth

C D B A 18

A B C D 12

B D A C 9

B C D A 5

Find the plurality winner. A) A

92)

93)

D A B C 3

B) B

C) C

D) D

Use Hamilton's method to find the apportionment. 94) A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use Hamilton's method to apportion the seats. State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

A) State

a b c d e Number of Representatives 29 35 141 23 22

B) State

a b c d e Number of Representatives 29 35 141 23 21

C) State

a b c d e Number of Representatives 28 35 142 23 22

D) State

a b c d e Number of Representatives 28 35 143 23 21

94)

Use Jefferson's method to find the apportionment. 95) A small country consists of 7 provinces with the following populations:

95)

Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province. Find the apportionment for province G using Jefferson's method. A) 55 B) 56 C) 54 D) 53

Solve the problem. 96) If Jefferson's method is used to apportion 132 legislative seats to four states with the populations given in the table, then a violation of the quota criterion occurs. State Population

96)

a b c d 17,180 7,500 49,400 5,820

The apportionment for which state violates the quota criterion? A) c B) b C) a

D) d

97) Consider an election in which the votes were cast as follows. How many of Umprey's votes would

97)

Stewart need to win the runoff election? Candidate Number of Votes Stewart 237 Tilley 403 Umprey 181 A) 167

B) 174 D) Stewart cannot win the runoff election.

C) 173

98) Refer to the following preference schedule. If the Borda count method is used to determine the

98)

winner, is Fairness Criterion 1 satisfied? First AB A C Second B A C B Third C C B A 7 10 12 8 A) Yes

B) No

Use Jefferson's method to find the apportionment. 99) The table below gives the populations of four districts A, B, C, and D, among which a total of 20 seats are to be apportioned. District A B C D Population 544,000 183,000 229,000 98,000 How many seats does district A receive using Jefferson's method? A) 10 B) 12 C) 11

D) 9

99)

Solve the problem. 100) Refer to the following preference schedule. First Second Third Fourth

A C B D 14

B C D A 12

D C A B 10

C B A D 7

100)

C B D A 6

Find the winner by the method of pairwise comparisons. A) A B) B C) D

D) C

Answer the question. 101) A proposed amendment to the U.S. Constitution has passed both the House and the Senate with the required 2/3 super majority. Each state holds a vote on the amendment and it receives a majority vote in 35 of the 50 states. Is the Constitution amended? A) Yes B) No Solve the problem. 102) Refer to the following preference schedule. First Second Third Fourth

C D B A 18

A B C D 12

B D A C 9

B C D A 5

101)

102)

D A B C 3

Find the winner of a sequential runoff. A) A B) D

C) C

D) B

Provide an appropriate response. 103) Suppose there are two candidates in a hypothetical U.S. Presidential election. Gonzales wins 46,936,349 popular votes and 314 electoral votes, while Kemper wins 46,932,073 popular votes and 224 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Gonzales or Kemper.) A) Kemper wins the popular vote and becomes President.

103)

B) Gonzales wins the popular vote and becomes President. C) Gonzales wins the popular vote, but Kemper becomes President. D) Kemper wins the popular vote, but Gonzales becomes President. Determine whether any of the listed candidates has a majority. 104) Four candidates running for senate receive votes as follows: Edwards: 99,144, Fong: 38,556, Goodman: 16,524, Haddad: 27,540 A) Yes B) No

104)

Solve the problem. 105) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

105)

C S J 8

Determine the winner using the Borda count method. A) Clark B) Jones and Smith tie.

C) Smith

D) Jones

Provide an appropriate response. 106) Suppose there are two candidates in a hypothetical U.S. Presidential election. Roberts wins 46,946,982 popular votes and 243 electoral votes, while Simpson wins 46,285,073 popular votes and 295 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Roberts or Simpson.) A) Roberts wins the popular vote and becomes President.

106)

B) Simpson wins the popular vote and becomes President. C) Roberts wins the popular vote, but Simpson becomes President. D) Simpson wins the popular vote, but Roberts becomes President. Use Jefferson's method to find the apportionment. 107) The table below gives the populations of four districts A, B, C, and D, among which a total of 60 seats are to be apportioned.

107)

District A B C D Population 256,500 143,000 89,000 51,500 How many seats does district A receive using Jefferson's method? A) 29 B) 28 C) 26

D) 27

Use Webster's method to find the apportionment. 108) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Webster's method. A) 25 B) 26 C) 24

D) 23

108)

Find the standard quota asked for. Round your answer to two decimal places if necessary. 109) A small country consists of seven states; there are 164 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

109)

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the standard quota for state C. A) 30.49 B) 36.79

C) 37.45

D) 33.42

Solve the problem. 110) Refer to the following preference schedule. If the Borda count method is used to determine the winner, is Fairness Criterion 1 satisfied? First B C DAC Second A A C D D Third C D A C A Fourth D B B B B 28 11 9 5 1 A) Yes

110)

B) No

Make the requested preference schedule. 111) Ten voters are asked to rank 3 brands of shoes: A, B, and C. The ten voters turn in the following ballots showing their preferences in order: C B B C B B C B C B B C A B C A B C B C A A C A A C A A A A Make a preference schedule for these ballots.

B) First B B CC Second A C B A Third C A A B 2 3 4 1

First B B C Second A C A Third C A B 2 4 4

D) First B B C Second A C B Third C A A 2 4 4

First B B CC Second A C B A Third C A A B 2 3 3 2

111)

Solve the problem. 112) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the preliminary nonbinding ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

112)

C S J 8

A second election is then held, which yields the following preference schedule: First J S Second S J Third C C 7 11

J C S 3

C S J 8

If the method of pairwise comparisons is used to determine the winner, is Fairness Criterion 3 satisfied? A) yes B) no

Use Webster's method to find the apportionment. 113) West End school district is purchasing 50 new computers to be distributed among the five schools in the district. The computers will be apportioned based on the school population of each school as given in the table below. Use Webster's method to apportion the computers.

113)

School a b c d e Population 210 165 160 175 190

A) School

a b c d e Number of Computers 11 9 10 10 10

B) School

a b c d e Number of Computers 11 10 9 10 10

C) School

a b c d e Number of Computers 12 9 9 10 10

D) School

a b c d e Number of Computers 12 9 10 10 9

Determine which state is more poorly represented. 114) State A with a population of 491,598 and 9 representatives or state B with a population of 264,186 and 9 representatives. A) State B

B) State A C) The two have equal representation.

114)

Solve the problem. 115) Refer to the following preference schedule. First Second Third Fourth

C D B A 18

A B C D 12

B D A C 9

B C D A 5

115)

D A B C 3

Find the winner by a Borda count. A) D B) B

C) A

D) C

116) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A),

116)

Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference schedule. First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 Which choice is the winner of a sequential runoff? A) Florida B) Hawaii

C) San Antonio

D) Alaska

117) If Jefferson's method is used to apportion 250 legislative seats to five states with the populations

117)

given in the table, then a violation of the quota criterion occurs. State Population

a b c d e 912,000 1,117,000 4,537,000 739,000 695,000

The apportionment for which state violates the quota criterion? A) b B) c C) a

D) e

Determine whether the specified paradox occurs. 118) A country with two states has 16 seats in the legislature. The population of each state (in thousands) is given by: State A B Population 134 52

Total 186

A third state is added with 3 additional seats as shown below. State A B C Population 134 52 38

Total 224

Does the new states paradox occur using Hamilton's method of apportionment? A) Yes B) No

118)

Use Hamilton's method to find the apportionment. 119) A small country consists of 7 provinces with the following populations:

119)

Solve the problem. 120) Refer to the following preference schedule. First Second Third Fourth

A C B D 14

B C D A 12

D C A B 10

C B A D 7

120)

C B D A 6

Find the winner by a Borda count. A) A B) C

C) B

D) D

121) Refer to the given preference schedule. If the plurality method is used to determine the winner

121)

and D drops out, is Fairness Criterion 4 satisfied? First Second Third Fourth

A B A A C B D C C C A B C D D B B A B C C D A A A D D D D D B B C C A B 3 7 5 8 7 4 6 6 4 A) Yes

B) No

Find the standard quota asked for. Round your answer to two decimal places if necessary. 122) The table below gives the populations of four districts A, B, C, and D, among which a total of 60 seats are to be apportioned. District A B C D Population 256,500 143,000 89,000 51,500 Find the standard quota for District A. A) 9000 B) 28.50

C) 2.09

D) 4300

122)

Solve the problem. 123) Jackson Associates is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference schedule.

123)

First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 Which choice wins using the Borda count method? A) Hawaii B) Alaska

C) Florida

D) San Antonio

124) Refer to the following preference schedule. First Second Third Fourth Fifth

124)

C D E E A B D B A B E C A C D 18 22 15

Find the winner by a runoff of the top two candidates. A) C B) D C) B

D) E

Use Jefferson's method to find the apportionment. 125) West End school district is purchasing 50 new computers to be distributed among the five schools in the district. The computers will be apportioned based on the school population of each school as given in the table below. Use Jefferson's method to apportion the computers. School a b c d e Population 210 165 160 175 190

A) School

a b c d e Number of Computers 11 10 9 10 10

B) School

a b c d e Number of Computers 12 9 9 10 10

C) School

a b c d e Number of Computers 11 9 10 10 10

D) School

a b c d e Number of Computers 12 9 10 10 9

125)

Use Webster's method to find the apportionment. 126) A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table.

126)

Precinct 1 2 3 4 5 6 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174 Find the apportionment for the Seventh Precinct using Webster's method. A) 7 B) 4 C) 5

D) 6

Solve the problem. 127) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

P T P S S S S R T R R R T R P T P S P T 45 90 54 51 30

127)

R P S T 6

Which choice wins using the Borda count method? A) T B) S

C) P

D) R

128) Refer to the following preference schedule. If the Borda count method is used to determine the

128)

winner, is Fairness Criterion 2 satisfied? First AB AC Second B A C B Third C C B A 7 10 4 8 A) Yes

B) No

129) Refer to the given preference schedule. If candidate D drops out, does the Borda count method satisfy Fairness Criterion 4? First Second Third Fourth

A B A A C B D C C C A B C D D B B A B C C D A A A D D D D D B B C C A B 3 7 5 8 7 4 6 6 4 A) Yes

B) No

129)

130) If Jefferson's method is used to apportion 200 legislative seats to four states with the populations

130)

given in the table, then a violation of the quota criterion occurs. State Population

a b c d e 4590 1515 2015 1120 1110

The apportionment for which state violates the quota criterion? A) e B) a C) d

D) b

131) Refer to the following preference schedule. First Second Third Fourth

C D A B 18

B A C D 12

A D B C 9

A C D B 5

131)

D B A C 3

Find the winner of a sequential runoff. A) A B) C

C) B

D) D

132) The Mathematics Department is holding an election for department chair. Each member ranks the

132)

candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

C S J 8

Determine the winner using the plurality method. A) Smith

C) Jones

B) Clark D) Jones and Smith tie.

Determine whether any of the listed candidates has a majority. 133) Four candidates running for mayor receive votes as follows: Ito: 39,717, Johnson: 17,652, Kennedy: 8,826, Lieberman: 13,239 A) Yes B) No

133)

Answer the question about the preference schedule. 134) If candidate E withdrew from the election (and voters for the other candidates were moved up in the table), how many votes would the other four candidates receive? Preference Schedule for an election. First A B E D E Second C E C B A Third E A B E C Fourth B D A A B Fifth D C D C D Voters 12 5 11 4 15 A) A-27, B-5, C-0, D-4 B) A-27, B-5, C-11, D-4

C) A-12, B-5, C-0, D-4

D) A-12, B-5, C-11, D-4

Solve the problem. 135) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

T P T R R R R S P S S S P S T P T R T P 15 30 18 17 10

D) R

136) Refer to the following preference schedule. A C B D 14

B C D A 12

D C A B 10

C B A D 7

135)

S T R P 2

Which choice wins using the method of pairwise comparisons? A) P B) S C) T

First Second Third Fourth

134)

136)

C B D A 6

Find the winner by a runoff of the top two candidates. A) A B) D C) C

D) B

Find the standard quota asked for. Round your answer to two decimal places if necessary. 137) A school district receives a grant to purchase 42 new computers to be apportioned among the 6 schools in the district based on the student population of each school. The student populations are given in the following table. School A B C D E F Population 314 211 197 243 279 325 Find the standard quota for school A. A) 8.41 B) 9.71

C) 10.6

D) 11.05

137)

Answer the question. 138) A criminal conviction in a particular state requires a vote by 2/3 of the jury members. On a 16-member jury, 11 jurors vote to convict. Will the defendant be convicted? A) Yes B) No Provide an appropriate response. 139) Suppose there are two candidates in a hypothetical U.S. Presidential election. Smith wins 53,647,684 popular votes and 259 electoral votes, while Furuya wins 53,984,510 popular votes and 276 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Smith or Furuya.) A) Furuya wins the popular vote and becomes President.

138)

139)

B) Smith wins the popular vote, but Furuya becomes President. C) Furuya wins the popular vote, but Smith becomes President. D) Smith wins the popular vote and becomes President. Determine whether the specified paradox occurs. 140) A city has 204 police officers to be apportioned among 4 precincts based on the population of each precinct. The populations are given in the following table.

140)

Precinct 1 2 3 4 Population 3462 7470 4265 5300 Does the Alabama paradox occur using Hamilton's method if the number of police officers is increased from 204 to 205? A) Yes B) No

Use Hamilton's method to find the apportionment. 141) West End school district is purchasing 50 new computers to be distributed among the five schools in the district. The computers will be apportioned based on the school population of each school as given in the table below. Use Hamilton's method to apportion the computers. School a b c d e Population 210 165 160 175 190

A) School

a b c d e Number of Computers 11 9 10 10 10

B) School

a b c d e Number of Computers 11 10 9 10 10

C) School

a b c d e Number of Computers 12 9 9 10 10

D) School

a b c d e Number of Computers 12 9 10 10 9

141)

Solve the problem. 142) Suppose that candidates A and C have moderate political positions, while candidate B is quite liberal. Voter opinions about the candidates are as follows: 28% want A as their first choice, but would also approve of C. 40% want B as their first choice, and approve of neither A nor C. 27% want C as their first choice, but would also approve of A 5% want C as their first choice, and approve of neither A nor B. Which candidate wins by an approval vote? A) A B) B C) C D) There is a tie.

143) Refer to the following preference schedule. If the Borda count method is used to determine the

142)

143)

winner, is Fairness Criterion 1 satisfied? First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 A) Yes

B) No

Find the standard quota asked for. Round your answer to two decimal places if necessary. 144) A university has 24 scholarships to be apportioned among the engineering students based on the enrollment in each department. There are three departments: Mechanical Engineering (M), Electrical Engineering (E), and Civil Engineering (C). The number of students in each department is given in the following table.

144)

Department M E C Enrollment 233 297 153 Find the standard quota for the Mechanical Engineering Department. A) 7.02 B) 8.19 C) 7.53

D) 7.86

Solve the problem. 145) Refer to the following preference schedule. First Second Third Fourth

A C B D 14

B C D A 12

D C A B 10

C B A D 7

Find the plurality winner. A) C

145)

C B D A 6

B) D

C) B

D) A

Demographic data for a hypothetical state is given. Use the information to solve the problem. 146) A state has 20 representatives and a population of 16 million; party affiliations are 70% Republican and 30% Democrat. If districts are drawn randomly, what would be the most likely distribution of House seats? A) 13 Republicans, 7 Democrats B) 6 Republicans, 14 Democrats

C) 14 Republicans, 6 Democrats

D) 15 Republicans, 5 Democrats

Make the requested preference schedule. 147) Eight voters are asked to rank 4 brands of ice cream: A, B, C, and D. The eight voters turn in the following ballots showing their preferences in order: B C A D

C A D B

C D A B

B C A D

C D A B

B A C D

146)

147)

C A D B

Make a preference schedule for these ballots.

B) First B B CC Second A C B D Third C A D A Fourth D D A B 1 2 2 3

First B B CC Second A C A D Third C A D A Fourth D D B B 1 2 3 2

D) First B B CC Second A C B D Third C A D A Fourth D D A B 1 2 3 2

First B B CC Second A C A D Third C A D A Fourth D D B B 1 2 2 3

Solve the problem. 148) Consider an election in which the votes were cast as follows. What percentage of Simpson's votes would Gomez need to win the runoff election? Candidate Percentage of Vote Hughes 41% Simpson 28% Gomez 31% A) 61.3% B) 67.9%

C) 71.4%

D) 19%

Provide an appropriate response. 149) Suppose there are two candidates in a hypothetical U.S. Presidential election. Atwood wins 53,720,827 popular votes and 262 electoral votes, while Jones wins 53,926,903 popular votes and 276 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Atwood or Jones.) A) Atwood wins the popular vote and becomes President.

B) Atwood wins the popular vote, but Jones becomes President. C) Jones wins the popular vote, but Atwood becomes President. D) Jones wins the popular vote and becomes President. 29

148)

149)

Answer the question. 150) Of the 100 Senators in the U.S. Senate, 62 support a new bill on environmental protection. The opposing Senators start a filibuster. Is the bill likely to pass? A) Yes B) No Find the standard quota asked for. Round your answer to two decimal places if necessary. 151) A small country consists of 7 provinces with populations as indicated in the table.

150)

151)

Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 400 federal judges to be apportioned according to the population of each province. Find the standard quota for province G. A) 72.68 B) 66.61 C) 56.93 D) 84.68

Solve the problem. 152) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference table.

152)

First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 Determine the winner using the plurality method. A) Hawaii B) San Antonio

C) Florida

D) Alaska

153) A condominium association is holding an election for president of the board of directors. Each

member ranks the candidates. The preference schedule below shows the results of the ballots with candidates Abbott (A), Blake (B), Cleary (C), and Downs (D). First Second Third Fourth

A B A A C B D C C C A B C D D B B A B C C D A A A D D D D D B B C C A B 3 7 5 8 7 4 6 6 4

Determine the winner using the Borda count method. A) Cleary B) Blake C) Abbott

D) Downs

153)

Use Hamilton's method to find the apportionment. 154) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

154)

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Hamilton's method. A) 26 B) 23 C) 25

D) 24

Determine whether the specified paradox occurs. 155) In a small country consisting of 5 provinces, 300 federal judges are apportioned according to the population of each province. The population of each province is shown for the first and sixth years.

155)

Province A B C D E First Year Population 25,312 8,911 11,451 33,611 15,932 Sixth Year Population 26,011 9,732 12,678 35,977 17,311 Does the population paradox occur using Hamilton's method of apportionment? A) Yes B) No

Solve the problem. 156) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the preliminary nonbinding ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

C S J 8

A second election is then held, which yields the following preference schedule: First J S Second S J Third C C 7 11

J C S 3

C S J 8

If the winner is decided by sequential runoffs, is Fairness Criterion 3 satisfied? A) yes B) no

156)

157) The Mathematics Department is holding an election for department chair. Each member ranks the

157)

candidates from first to third. The preference schedule below shows the results of the preliminary nonbinding ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

C S J 8

A second election is then held, which yields the following preference schedule: First J S Second S J Third C C 7 11

J C S 3

C S J 8

If the method of pairwise comparisons is used to determine the winner, is Fairness Criterion 3 satisfied? A) no B) yes

158) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A),

158)

Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference schedule. First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 Which choice wins using the method of pairwise comparisons? A) Alaska & Florida (tie) B) Alaska & Hawaii (tie)

C) Alaska

D) Florida & Hawaii (tie)

159) Suppose that candidates A and B have moderate political positions, while candidate C is quite liberal. Voter opinions about the candidates are as follows: 27% want A as their first choice, but would also approve of B. 3% want A as their first choice, and approve of neither B nor C. 75% want B as their first choice, but would also approve of A. 45% want C as their first choice, and approve of neither A nor B. If an election is held using the approval voting method, which candidate wins? A) C B) There is a tie. C) A D) B

159)

160) Refer to the following preference schedule. If the plurality method is used to determine the

160)

winner, is Fairness Criterion 2 satisfied? First B C DAC Second A A C D D Third C D A C A Fourth D B B B B 15 11 9 5 1 A) Yes

B) No

161) If Jefferson's method is used to apportion 131 legislative seats to six states with the populations

161)

given in the table, then a violation of the quota criterion occurs. State Population

a b c d e f 5672 8008 2400 6789 4972 20,000

The apportionment for which state violates the quota criterion? A) b B) d C) e

D) f

Use Webster's method to find the apportionment. 162) A small country consists of 7 provinces with the following populations:

162)

Solve the problem. 163) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J C Second C J Third S S 7 10

J S C 4

163)

S C J 8

Determine the winner using the method of pairwise comparisons. A) Jones B) Smith

C) Clark

D) Jones & Clark (tie)

164) Imagine that a small company has four shareholders who hold 26%, 25.5%, 25%, and 23.5% of the

company's stock. Assume that votes are assigned in proportion to shareholding. Also assume that decisions are made by strict majority vote. Does the individual with 23.5% hold any effective power in voting? A) no B) yes

164)

Determine whether any of the listed candidates has a majority. 165) Four candidates running for congress receive votes as follows: Alberts: 52,239, Brown: 14,247, Cassimatis: 37,992, D'Amico: 33,243 A) Yes B) No

165)

Determine which state is more poorly represented. 166) State A with a population of 312,903 and 9 representatives or state B with a population of 556,272 and 16 representatives. A) State A

166)

B) State B C) The two have equal representation. Answer the question. 167) A criminal conviction in a particular state requires a vote by 2/3 of the jury members. On an 11-member jury, 8 jurors vote to convict. Will the defendant be convicted? A) Yes B) No Use Jefferson's method to find the apportionment. 168) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

167)

168)

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Jefferson's method. A) 23 B) 26 C) 24

D) 25

Solve the problem. 169) The table below shows the population and number of electoral votes for three states. Rank the three states in order of increasing voting power. State Hawaii Nevada Vermont

Population 1,285,000 2,496,000 624,000

Electoral votes 4 5 3

A) Nevada, Hawaii, Vermont C) Nevada, Vermont, Hawaii

B) Hawaii, Vermont, Nevada D) Vermont, Hawaii, Nevada

169)

170) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next

170)

year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

P T P R R R R S T S S S T S P T P R P T 30 60 36 34 20

S P R T 4

Which choice wins using the Borda count method? A) R B) S

C) P

D) T

171) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next

171)

year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

S T S P P P P R T R R R T R S T S P S T 15 30 18 17 10

R S P T 2

Which choice wins using the Borda count method? A) R B) T

C) P

D) S

Determine whether the specified paradox occurs. 172) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown below for the first and sixth years.

172)

State A B C D E F G First Year Population 1283 2374 2725 2155 1592 2511 2017 Sixth Year Population 1347 2469 2847 2220 1640 2611 2078 Does the population paradox occur using Hamilton's method of apportionment? A) Yes B) No

Solve the problem. 173) Refer to the given preference schedule. If the plurality method is used to determine the winner and C drops out, is Fairness Criterion 4 satisfied? First J S Second S J Third C C 7 10 A) Yes

J C S 4

C S J 8

B) No

173)

174) The Mathematics Department is holding an election for department chair. Each member ranks the

174)

candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J C Second C J Third S S 7 10

J S C 4

S C J 8

Determine the winner using the Borda count method. A) Jones and Smith tie. B) Jones

C) Clark

D) Smith

175) If the population of the United States increased to 410 million and the number of representatives

175)

were set at the constitutional limit of one representative for every 30,000 people, how many representatives would there be in Congress? A) 13,667 representatives B) 1230 representatives

C) 1367 representatives

D) 7317 representatives

176) Consider an election in which the votes were cast as follows. How many of Burnaby's votes

176)

would Costello need to win the runoff election? Candidate Number of Votes Abbott 319 Burnaby 126 Costello 194 A) 63 B) 125

C) 68

D) 126

177) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next

year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First P T P R R S Second R R S T S P Third S S T S P R Fourth T P R P T T 45 90 54 51 30 6 Which choice is the winner of a sequential runoff? A) T B) R

C) S

D) P

177)

178) In an election, each member ranks the candidates from first to third. The preference schedule

178)

below shows the results of the preliminary nonbinding ballots with candidates Robbins (R), Kaplan (K), and Simpson (S). First K Second S Third R 16

S S K R R K 5 10

R K S 14

A second election is then held, which yields the following preference schedule: First K Second S Third R 16

K S R 5

S R K 10

R K S 14

If a run-off of the top two candidates is used to determine the winner, is Fairness Criterion 3 satisfied? A) no B) yes

179) Suppose that candidate A is quite conservative, while candidates B and C have moderate political positions. Voter opinions about the candidates are as follows: 35% want A as their first choice, and approve of neither B nor C. 29% want B as their first choice, but would also approve of C. 25% want C as their first choice, but would also approve of B. 11% want C as their first choice, and approve of neither A nor B. Which candidate wins by an approval vote? A) A B) B C) C

D) There is a tie.

180) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next

year's budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. First Second Third Fourth

T S T R R R R P S P P P S P T S T R T S 30 60 36 34 20

P T R S 4

Which choice wins using the method of pairwise comparisons? A) T B) R C) S

179)

D) P

180)

Make the requested preference schedule. 181) Ten voters are asked to rank 4 brands of cell phones: A, B, C, and D. The ten voters turn in the following ballots showing their preferences in order: A B D C

B C A D

B A C D

B C A D

A B C D

B A C D

B C A D

B A D C

B A C D

181)

A B C D

Make a preference schedule for these ballots.

B) First AAB B B Second B C A A C Third C B C D A Fourth D D D C D 2 2 2 1 3

First AAB B B Second B C A A C Third C B C D A Fourth D D D C D 2 1 3 1 3

D) First AAB B B Second B B A A C Third C D C D A Fourth D C D C D 2 2 2 1 3

First AAB B B Second B B A A C Third C D C D A Fourth D C D C D 2 1 3 1 3

Determine whether the specified paradox occurs. 182) A country with two states has 75 seats in the legislature. The population of each state (in thousands) is given by: State A B Population 3184 8475

Total 11,659

A third state is added with 2 additional seats as shown below. State A B C Population 3184 8475 330

Total 11,989

Does the new states paradox occur using Hamilton's method of apportionment? A) Yes B) No

182)

Solve the problem. 183) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

C S J 8

Who is the winner of a sequential runoff? A) Smith

B) Jones D) Jones and Clark tie.

C) Clark 184) Refer to the following preference schedule. First Second Third Fourth

C A B D 14

B A D C 12

D A C B 10

183)

A B C D 7

184)

A B D C 6

Find the winner by the method of pairwise comparisons. A) A B) B C) C

D) D

Determine whether the specified paradox occurs. 185) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table.

185)

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Does the Alabama paradox occur using Hamilton's method if the number of seats is increased from 160 to 161? A) Yes B) No

Solve the problem. 186) Refer to the following preference schedule. If the Borda count method is used to determine the winner, is Fairness Criterion 1 satisfied? First ACAA CB DCC Second C B B C D D B B A Third B A C D A A A D D Fourth D D D B B C C A B 3 7 5 8 11 4 6 9 7 A) Yes

B) No

186)

Use Webster's method to find the apportionment. 187) A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use Webster's method to apportion the seats.

187)

State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

A) State

a b c d e Number of Representatives 28 35 142 23 22

B) State

a b c d e Number of Representatives 29 35 141 23 22

C) State

a b c d e Number of Representatives 29 35 141 23 21

D) State

a b c d e Number of Representatives 28 35 143 23 21

Provide an appropriate response. 188) Suppose there are two candidates in a hypothetical U.S. Presidential election. Roberts wins 46,285,073 popular votes and 243 electoral votes, while Simpson wins 46,946,982 popular votes and 295 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Roberts or Simpson.) A) Simpson wins the popular vote and becomes President.

188)

B) Roberts wins the popular vote, but Simpson becomes President. C) Simpson wins the popular vote, but Roberts becomes President. D) Roberts wins the popular vote and becomes President. Solve the problem. 189) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First C J Second J C Third S S 7 10

C S J 4

S J C 8

Determine the winner using the Borda count method. A) Smith B) Jones

C) Jones and Smith tie.

D) Clark

189)

Determine whether the specified paradox occurs. 190) A country with two states has 16 seats in the legislature. The population of each state is given by:

190)

State A B Total Population 86,342 77,312 163,654 A third state is added with 5 additional seats as shown below. State A B C Total Population 86,342 77,312 53,792 217,446 Does the new states paradox occur using Hamilton's method of apportionment? A) Yes B) No

Use Hamilton's method to find the apportionment. 191) The table below gives the populations of four districts A, B, C, and D, among which a total of 60 seats are to be apportioned.

191)

District A B C D Population 256,500 143,000 89,000 51,500 How many seats does district A receive using Hamilton's method? A) 27 B) 26 C) 28

D) 29

Provide an appropriate response. 192) Suppose there are two candidates in a hypothetical U.S. Presidential election. Smith wins 53,647,684 popular votes and 259 electoral votes, while Furuya wins 52,984,510 popular votes and 276 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Smith or Furuya.) A) Furuya wins the popular vote, but Smith becomes President.

192)

B) Smith wins the popular vote and becomes President. C) Smith wins the popular vote, but Furuya becomes President. D) Furuya wins the popular vote and becomes President. 193) Suppose there are two candidates in a hypothetical U.S. Presidential election. Gonzales wins

46,936,349 popular votes and 224 electoral votes, while Kemper wins 46,932,073 popular votes and 314 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Gonzales or Kemper.) A) Gonzales wins the popular vote and becomes President.

B) Gonzales wins the popular vote, but Kemper becomes President. C) Kemper wins the popular vote and becomes President. D) Kemper wins the popular vote, but Gonzales becomes President.

193)

Solve the problem. 194) Refer to the following preference schedule. First A Second B Third C 11

A C B 8

B A C 16

B C A 17

C A B 20

194)

C B A 12

Find the winner by a runoff of the top two candidates. A) A B) C

C) B

D) No clear winner

Answer the question. 195) A criminal conviction in a particular state requires a vote by 4/5 of the jury members. On a 13-member jury, 10 jurors vote to convict. Will the defendant be convicted? A) Yes B) No Solve the problem. 196) Refer to the following preference schedule. First Second Third Fourth

195)

196)

A B B C D D B C D A A C C A C D C B D D A B B A 15 17 20 16 12 22

Find the winner by a runoff of the top two candidates. A) D B) A C) C

D) B

Find the standard quota asked for. Round your answer to two decimal places if necessary. 197) The faculty senate of a university has 55 senators to be apportioned among its four colleges based on the number of faculty in each college. The colleges are Liberal Arts (L), Sciences (S), Business (B), and Engineering (E). The number of faculty in each college is shown in the following table.

197)

College L S B E Number of Faculty 279 355 312 423 Find the standard quota for the College of Sciences. A) 15.96 B) 17.53

C) 14.26

D) 19.94

Answer the question. 198) Of the 100 Senators in the U.S. Senate, all but 46 support a new bill on environmental protection. The opposing Senators start a filibuster. Is the bill likely to pass? A) Yes B) No

198)

Solve the problem. 199) If the population of the United States increased to 390 million and the number of representatives remained at 435, how many Americans, on average, would each representative serve? A) 885,551 people per representative B) 896,552 people per representative

C) 169,650 people per representative

199)

D) 1,115,385 people per representative

200) Refer to the following preference schedule. If the Borda count method is used to determine the

200)

winner, is Fairness Criterion 1 satisfied? First J S Second S J Third C C 7 10 A) Yes

J C S 4

C S J 8

B) No

Determine which state is more poorly represented. 201) State A with a population of 654,264 and 12 representatives or state B with a population of 532,500 and 15 representatives. A) State A

201)

B) State B C) The two have equal representation. Solve the problem. 202) Suppose that candidates A and B have moderate political positions, while candidate C is quite conservative. Voter opinions about the candidates are as follows: 27% want A as their first choice, but would also approve of B. 28% want B as their first choice, but would also approve of A. 2% want B as their first choice, and approve of neither A nor C. 43% want C as their first choice, and approve of neither A nor B. Which candidate wins by an approval vote? A) A B) There is a tie. C) B D) C

203) Refer to the following preference schedule. First Second Third Fourth

C D B A 18

A B C D 12

B D A C 9

B C D A 5

202)

203)

D A B C 3

Find the winner by the method of pairwise comparisons. A) D B) B C) A

D) C

204) A condominium association is holding an election for president of the board of directors. Each

204)

member ranks the candidates. The preference schedule below shows the results of the ballots with candidates Abbott (A), Blake (B), Cleary (C), and Downs (D). First Second Third Fourth

A B A A C B D C C C A B C D D B B A B C C D A A A D D D D D B B C C A B 3 7 5 8 7 4 6 6 4

Determine the winner using the plurality method. A) Blake B) Abbott

C) Cleary

D) Downs

205) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A),

205)

Florida (F), San Antonio (S), or Hawaii (H). In a preliminary, nonbinding election, the employees rank the four possible sites. The results are depicted in the following preference schedule. First A H F A A H F Second H S S F H F A Third F A H H S S S Fourth S F A S F A H 5 7 4 7 5 6 8 Suppose that after the preliminary election the eight voters who voted FASH, in that order, change their votes to AHFS. The official vote is then held. If the Borda count method is used to determine the winner, is Fairness Criterion 3 satisfied? A) no B) yes

206) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J S Second S J Third C C 7 10

J C S 4

C S J 8

Determine the winner using the method of pairwise comparisons. A) Jones B) Jones & Clark (tie)

C) Clark

D) Smith

206)

207) Refer to the following preference schedule. First Second Third Fourth

A C B D 14

B C D A 12

D C A B 10

C B A D 7

207)

C B D A 6

Find the winner of a sequential runoff. A) C B) A

C) D

D) B

208) An election is held in which each member ranks the candidates from first to third. The preference

208)

schedule below shows the results of the preliminary nonbinding ballots with candidates A, B, and C. First B A Second A C Third C B 11 16

C B A 8

A second election is then held, which yields the following preference schedule: First B A Second A B Third C C 11 16

C B A 8

If a run-off of the top two candidates is used to determine the winner, is Fairness Criterion 3 satisfied? A) no B) yes

209) The Mathematics Department is holding an election for department chair. Each member ranks the

209)

candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First C J Second J C Third S S 7 10

C S J 4

S J C 8

Who is the winner of a sequential runoff? A) Jones

B) Clark D) Smith

C) Jones and Clark tie.

Use the Hill-Huntington method to find the apportionment. 210) City A, City B, and City C are together undertaking a road construction project. The nine-member committee has representatives allocated to the committee in proportion to the population in each city. City A has a population of 15,000, City B has a population of 18,000, and City C has a population of 19,000. Apportion the committee seats using the Hill-Huntington method. A) A: 4; B: 3; C: 2 B) A: 2; B: 3; C: 4 C) A: 3; B: 2; C: 4 D) A: 3; B: 3; C: 3 45

210)

Solve the problem. 211) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). In a preliminary, nonbinding election, the employees rank the four possible sites. The results are depicted in the following preference schedule.

211)

First A H F A A H F Second H S S F H F S Third F A H S S S A Fourth S F A H F A H 5 7 4 7 5 6 8 Suppose that after the preliminary election the four voters who voted FSHA, in that order, change their votes to HSAF. The official vote is then held. If the winner is decided by sequential runoffs, is Fairness Criterion 3 satisfied? A) no B) yes

212) Refer to the given preference schedule. If the Borda count method is used to determine the winner

212)

and C drops out, is Fairness Criterion 4 satisfied? First J S Second S J Third C C 7 10 A) Yes

J C S 4

C S J 8

B) No

Answer the question. 213) A proposed amendment to the U.S. Constitution has passed both the House and the Senate with the required 2/3 super majority. Each state holds a vote on the amendment and it receives a majority vote in all but 13 of the 50 states. Is the Constitution amended? A) Yes B) No Solve the problem. 214) Refer to the following preference schedule. First Second Third Fourth

C B D A 18

A D C B 12

D B A C 9

D C B A 5

213)

214)

B A D C 3

Find the winner by the method of pairwise comparisons. A) A B) C C) D

D) B

Use the Hill-Huntington method to find the apportionment. 215) Use the Hill-Huntington method to apportion nine seats among State X, State Y, and State Z. The populations of the states are state X, 4.0 million; State Y, 6.5 million; and State Z, 5.2 million. A) X: 2; Y: 4; Z: 3 B) X: 3; Y: 4; Z: 2 C) X: 3; Y: 3; Z: 3 D) X: 4; Y: 2; Z: 3

215)

Answer the question. 216) A criminal conviction in a particular state requires a vote by 3/4 of the jury members. On a 13-member jury, 8 jurors vote to convict. Will the defendant be convicted? A) Yes B) No Solve the problem. 217) The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference schedule below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). First J C Second C J Third S S 7 10

J S C 4

B) Jones D) Smith

C) Clark

Demographic data for a hypothetical state is given. Use the information to solve the problem. 218) A state has 10 representatives and a population of 8 million; party affiliations are 40% Republican and 60% Democrat. If districts could be drawn without restriction (unlimited gerrymandering), what would be the maximum and minimum number of Republican representatives who could be sent to Congress? A) 7, 1 B) 7, 0 C) 6, 1 D) 8, 0 Solve the problem. 219) Refer to the following preference schedule. C A B D 14

B A D C 12

D A C B 10

A B C D 7

A B D C 6

D) A

220) Refer to the following preference schedule. C B D A 18

A D C B 12

D B A C 9

D C B A 5

218)

219)

Find the winner by a runoff of the top two candidates. A) C B) B C) D

First Second Third Fourth

217)

S C J 8

Who is the winner of a sequential runoff? A) Jones and Clark tie.

First Second Third Fourth

216)

220)

B A D C 3

Find the winner by a runoff of the top two candidates. A) C B) A C) D

D) B

Provide an appropriate response. 221) Suppose there are two candidates in a hypothetical U.S. Presidential election. Atwood wins 53,720,827 popular votes and 276 electoral votes, while Jones wins 53,926,903 popular votes and 262 electoral votes. State who wins the popular vote and who becomes President. (Assume that all votes were cast for either Atwood or Jones.) A) Atwood wins the popular vote, but Jones becomes President.

221)

B) Jones wins the popular vote, but Atwood becomes President. C) Atwood wins the popular vote and becomes President. D) Jones wins the popular vote and becomes President. Use Jefferson's method to find the apportionment. 222) A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use Jefferson's method to apportion the seats.

222)

State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

A) State

a b c d e Number of Representatives 28 35 142 23 22

B) State

a b c d e Number of Representatives 28 35 143 23 21

C) State

a b c d e Number of Representatives 29 35 141 23 22

D) State

a b c d e Number of Representatives 29 35 141 23 21

Solve the problem. 223) Refer to the given preference schedule. If candidate C drops out, does the method of pairwise comparisons satisfy Fairness Criterion 4? First A B A C Second B A C B Third C C B A 7 10 4 8 A) Yes

B) No

223)

Answer the question about the preference schedule. 224) How many voters preferred Candidate C to Candidate D? Preference Schedule for an election. First A B E D E Second C E C B A Third E A B E C Fourth B D A A B Fifth D C D C D Voters 13 8 10 2 17 A) 10 B) 43 C) 40

224)

D) 27

Determine which state is more poorly represented. 225) State A with a population of 309,600 and 12 representatives or state B with a population of 504,000 and 14 representatives. A) State A

225)

B) State B C) The two have equal representation. Solve the problem. 226) Consider an election in which the votes were cast as follows. How many of Grafton's votes would Howard need to win the runoff election? Candidate Number of Votes Fuston 374 Grafton 118 Howard 245 A) 104

B) 124 D) Howard cannot win the runoff election.

C) 129

226)

Answer Key Testname: CHAPTER 12

1) A 2) D 3) D 4) D 5) D 6) C 7) C 8) A 9) A 10) D 11) D 12) D 13) D 14) B 15) D 16) D 17) A 18) C 19) A 20) B 21) B 22) B 23) C 24) B 25) Yes, the statement makes sense. There is no requirement that the voters of a particular party be evenly distributed

among the districts. In fact, due to gerrymandering, it is common that the voters of a particular party are concentrated in a few districts. 26) A slow-growing state gained a seat at the expense of a faster-growing state. 27) No, the statement does not make sense. As a result of redistricting, most congressional districts are decided by large margins today. Very few congressional races are competitive. 28) If a candidate receives a majority of the first-place votes, that candidate should be the winner; point system (Borda count) 29) Votes: Before redistricting: Republican 67%, Democrat 33%; After redistricting: Republican 64%, Democrat 36%; Seats: Before redistricting: Republican 57%, Democrat 43%; After redistricting: Republican 67%, Democrat 33%; The distribution of House seats better reflects the distribution of votes after redistricting. 30) No, the statement does not make sense. Even though the state is evenly divided between Democrats and Republicans, this does not mean that each district will be evenly divided. As a result of gerrymandering it is common for voters of a given party to be concentrated in a few districts.

Answer Key Testname: CHAPTER 12

31) Answers may vary. One possible answer is:

32) Yes, the statement makes sense. Using the Borda count method, fairness criterion 4 may be violated. This means that if a second election is held in which one of the losing candidates drops out and in which voters keep the same preferences, there is no guarantee that the same candidate will win. 33) Yes, the statement makes sense. In an election for a competitive seat, the parties have an incentive to produce candidates who will appeal to the large political middle. 34) Possible answer:

First A B C Second B C B Third C A A 10 5 4 35) No, the statement does not make sense. This would be an example of the Alabama paradox. The Webster apportionment method is not susceptible to this paradox. 36) No, the statement does not make sense. This would be an example of the population paradox which occurs when a slow-growing state gains a seat at the expense of a faster-growing state. The Hill-Huntington apportionment method is not susceptible to this paradox. 37) No, the statement does not make sense. If Alison won the majority of the vote (more than 50%), she must also have won more votes than any other candidate (the plurality of the vote). 38) Answers will vary. Possible solution: First Second Third Fourth

B C C DD D CB A AA B 16 9 5 39) If a candidate is favored over every other candidate in pairwise races, that candidate should be declared a winner; pairwise comparison 40) The total number of available seats increased, yet one or more states lost a seat as a result.

Answer Key Testname: CHAPTER 12

41) Answers may vary. One possible answer is:

42) No, the statement does not make sense. This would be a violation of the quota criterion, and the Hamilton

apportionment method cannot violate the quota criterion. 43) No, the statement does not make sense. Even though it is true that all districts within a particular state must have roughly equal populations, there is no requirement that the voters of a particular party be evenly distributed among the districts. In fact, due to gerrymandering, it is common that the voters of a particular party are concentrated in a few districts. 44) Yes, the statement makes sense. This is the population paradox and it occurs when a slow-growing state gains a seat at the expense of a faster-growing state. The Hamilton apportionment method is not immune to this paradox. 45) It is impossible to create a voting system that always satisfies all four fairness criteria. 46) Suppose that Candidate X is declared the winner of an election. If a second election is held in which voters do not change their preferences but one or more of the losing candidates drops out, then X should also win the second election. Possible answers are plurality, top-two runoff, sequential runoff, point system (Borda count), or pairwise comparison. 47) Yes, the statement makes sense. Even though Arrow's impossibility theorem says that no voting system can satisfy all four fairness criteria in all cases, it is possible for a voting system to satisfy all four fairness criteria in certain cases. 48) Answers will vary. Possible solution: First A B Second B D Third C E Fourth D C Fifth E A 20 19 49) Voters state whether or not they approve of each candidate, and the candidate with the most approval votes wins. 50) Yes, this is possible. If Karine won more votes than Amy, the first runoff would be between Karine, Dave, and Rajan. If Karine gained more votes than one of the other two as a result of Amy's elimination, it is possible for her to win. 51) Yes, the statement makes sense. This would be a violation of the quota criterion and the Webster apportionment method is not guaranteed to satisfy the quota criterion in all cases. 52) Possible answer: In the preference schedule below, A wins the election. However, if the two voters in the final column were to change their vote to ACB, A would lose and B would win. First A B C C Second C A B A Third B C A B 6 5 4 2

Answer Key Testname: CHAPTER 12

53) Yes, the statement makes sense. The state received its minimum quota. Under the Hamilton apportionment method, there is no guarantee that a state will receive more than its minimum quota even if its fractional remainder is large. For example if there are no extra seats after each state has been given its minimum quota. 54) Answers may vary. One possible answer is:

55) The fractional remainder is the fraction that remains in the standard quota after subtracting the minimum quota. 56) No, the statement does not make sense. It has been proved by mathematicians that such a system is impossible. 57) Yes, this is possible. Some states require a unanimous vote in order for a defendant to be found guilty. 58) Answers may vary. One possible answer is:

59) No, the statement does not make sense. The sequential runoff system always satisfies fairness criterion 1. This means that a candidate who wins the majority of the first-place votes will win the election.

60) No, the statement does not make sense. Only 60% of the senators are needed to end a filibuster and pass a bill. In this case more than 60% of the senators are in favor of the bill which is sufficient to end the filibuster.

61) No, the statement does not make sense. Arrow's impossibility theorem says that no voting system can satisfy all four fairness criteria in all cases. 62) Answers will vary. Possible solution:

First B C DAC Second A A C D D Third C D A C A Fourth D B B B B 15 11 9 5 1 63) No, the statement does not make sense. Using the Borda count method, fairness criterion 3 is always satisfied. This means that if Carmen won the first election, this result should still stand if some voters rank her higher in the second election without changing the order of the other candidates. 64) Yes, the statement makes sense. Depending on how the Republicans are distributed among the districts, it is possible for the percentage of seats won by Republicans to differ greatly from the percentage of Republican voters in the state. 65) No, the statement does not make sense. This would be an example of the new states paradox. The Jefferson apportionment method is not susceptible to this paradox. 53

Answer Key Testname: CHAPTER 12

66) Yes, the statement makes sense. Using the plurality method, fairness criterion 2 may be violated. This means that even if a candidate is favored in pairwise races over every other candidate, they may still lose the election by the plurality method. 67) Answers will vary. Possible solution: First B C C Second C B A Third A A B 16 8 6 68) The addition of seats for a new state changed the apportionment for existing states. 69) Possible answer: In the preference schedule below, B wins according to the Borda count, but A has the majority of first-place votes. First A B C Second B C B Third C A A 10 5 4 70) No, the statement does not make sense. It would be to the Democrats' advantage to draw the boundaries in such a way that most of the Republicans are concentrated in a few districts. 71) Suppose that Candidate X is declared the winner of an election. If a second election is held in which the only change is that some voters rank X higher than before, then X should also win the second election. Possible answers are plurality, point system (Borda count), or pairwise comparison. 72) Yes, the statement makes sense. This is possible. As a result of gerrymandering there can be strangely shaped districts. The only requirements are that the districts be contiguous and that all districts within a state have roughly the same population. 73) Yes, the statement makes sense. In the approval voting system the candidate with the most approval votes wins. That means only that Stephanie must have won more approval votes than any of the other candidates, not necessarily that more than 50% of the voters approved of her. 74) Yes, this is possible. The different methods do not always produce the same winner. 75) Yes, the statement makes sense. The candidate who receives the majority of the electoral votes wins the election. This may not be the candidate who wins the majority of the popular vote. 76) No, the statement does not make sense. All districts within a particular state must have very nearly equal populations. 77) Possible answer: First A B C Second B C B Third C A A 10 5 4 78) No, the statement does not make sense. In a single runoff there would be a runoff between the top two vote getters Anthony and Carol. Pierre would not be in the runoff.

79) A 80) B 81) B 82) D 83) B 84) D 54

Answer Key Testname: CHAPTER 12

85) A 86) B 87) A 88) D 89) C 90) A 91) B 92) B 93) C 94) C 95) A 96) A 97) B 98) A 99) C 100) D 101) B 102) A 103) B 104) A 105) C 106) C 107) A 108) C 109) A 110) B 111) C 112) A 113) C 114) B 115) B 116) D 117) B 118) A 119) B 120) B 121) B 122) B 123) C 124) A 125) B 126) C 55

Answer Key Testname: CHAPTER 12

127) B 128) A 129) A 130) B 131) C 132) C 133) B 134) B 135) A 136) C 137) A 138) A 139) A 140) A 141) C 142) C 143) B 144) B 145) D 146) C 147) D 148) B 149) D 150) A 151) A 152) D 153) C 154) D 155) B 156) A 157) B 158) B 159) C 160) B 161) D 162) B 163) C 164) A 165) B 166) C 167) A 168) C 56

Answer Key Testname: CHAPTER 12

169) A 170) A 171) C 172) B 173) B 174) C 175) A 176) D 177) A 178) A 179) C 180) C 181) D 182) A 183) A 184) A 185) B 186) A 187) A 188) A 189) B 190) B 191) C 192) C 193) B 194) C 195) B 196) D 197) C 198) B 199) B 200) B 201) A 202) C 203) B 204) C 205) A 206) D 207) A 208) B 209) A 210) D 57

Answer Key Testname: CHAPTER 12

211) B 212) A 213) B 214) C 215) A 216) B 217) C 218) B 219) D 220) C 221) B 222) B 223) A 224) C 225) B 226) D