TEST BANK for Using and Understanding Mathematics A Quantitative Reasoning Approach 7e Jeffrey Benne by StudyGuide

Using and Understanding Mathematics A Quantitative Reasoning Approach 7e Jeffrey Bennett, William Briggs (Test Bank All Chapters, 100% Original Verified, A+ Grade) Answers At The End Of Each Chapter Chapter 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 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. 1) Some dogs are adorable. 1)

Decide whether the statement makes sense. Explain your reasoning. 2) The premises are true and the conclusion is true, so the argument must be valid. 3) 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.

2) 3)

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. 4) I think term limits should be enacted for the Senate. A senator should not be allowed to 4) serve more than two consecutive terms, because professional politicians become too focused on getting reelected.

Draw a Venn diagram to represent the given information. 5) 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.

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 deregulation." 6) Draw a Venn diagram to determine whether the argument is valid. 7) Premise: No surfers speak French. Premise: Pierre speaks French. Conclusion: Pierre is not a surfer.

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 8) (Appeal to Emotion) A television commercial shows a happy, attractive family dining at 8) Ma & Pa's Restaurant. Describe how the sentence is ambiguous. 9) Our goal is to increase voter participation from 25% of the eligible voters, or 4000, to 50%. Identify the type of argument and determine its validity with a Venn diagram. 10) Premise: If you cut me, I bleed. Premise: I do not bleed. Conclusion: You did not cut me.

10)

Draw a Venn diagram to determine whether the argument is valid. 11) Premise: All snakes have fangs. Premise: Teri's pet does not have fangs. Conclusion: Teri's pet is not a snake.

11)

Provide an appropriate response. 12) IRS guidelines state that a married person under 65 years of age who can be claimed as a 12) 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. 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.

Decide whether the statement makes sense. Explain your reasoning. 14) Your conditional deductive argument is valid. Therefore, it must be an example of "Affirming the Hypothesis." 15) Your argument is sound, but it isn't valid.

14)

15)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 16) George Washington was the first president of the United States of America and France is in 16) Europe. The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 17) The grass is wet or the grass is dry. 17)

Use your knowledge of the listed sets to draw a A Venn diagram illustrating the relationships among them. 18) clothes, shirts, pants, shoes, fancy duds 18) 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. 19) Affirming the conclusion 19)

Use your knowledge of the listed sets to draw a A Venn diagram illustrating the relationships among them. 20) real numbers, integers, positive numbers, negative numbers, irrational numbers 20)

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. 21) Affirming the hypothesis 21)

Identify the type of argument and determine its validity with a Venn diagram. 22) Premise: If you try hard, then you will succeed. Premise: You did not try hard. Conclusion: You will not succeed. Decide whether the statement makes sense. Explain your reasoning. 23) The argument is weak, so its conclusion must be false. 24) 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.

22)

23) 24)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 25) Premise: 8 + 11 = 19 25) Premise: 12 + 7 = 19 Premise: 38 + 33 = 71 Conclusion: Whenever we add an even number and an odd number, the result is an odd number. Decide whether the statement makes sense. Explain your reasoning. 26) I did not convince my friend that I was right, so I must not have argued logically.

26)

A seemingly simple argument is given. Identify at least two hidden assumptions. 27) Cardiovascular exercise is important, because to be healthy you need a strong heart.

27)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 28) The House of Representatives voted to override the veto of the communications bill. 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? Decide whether the statement makes sense. Explain your reasoning. 30) 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 to represent the given information. 31) There are 12 girls and 15 boys in a kindergarten class. 8 of the girls and 10 of the boys are right handed.

29)

30)

31)

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. 32) Denying the conclusion 32)

The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 33) Cats reads books or dogs bark. 33)

34) There are 25 letters in the English alphabet or the letter c is a vowel.

34)

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. 35) truck drivers, employed, unemployed 35)

Identify the type of argument and determine its validity with a Venn diagram. 36) Premise: If you are hot, then you will sweat. Premise: James is hot. Conclusion: James will sweat.

36)

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. 37) doctors and poets 37)

Describe how the sentence is ambiguous. 38) Two stores with more than 1000 pieces of merchandise will have grand openings at the mall this weekend.

38)

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. 39) teachers, bowlers, and men 39)

A seemingly simple argument is given. Identify at least two hidden assumptions. 40) The campfire should be extinguished before we go fishing because the park ranger can cite us for illegal activities. Analyze the situation and explain how you would make a decision. 41) 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?

40)

41)

Provide an appropriate response. 43) IRS guidelines state that a married person under 65 years of age who can be claimed as a 43) 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. 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.

Draw a Venn diagram to determine whether the argument is valid. 44) Premise: All lawyers wear suits. Premise: Jack wears a suit. Conclusion: Jack is a lawyer.

44)

Decide whether the statement makes sense. Explain your reasoning. 45) The time I spend studying is a subset of the time I spend playing basketball.

45)

A seemingly simple argument is given. Identify at least two hidden assumptions. 46) I should not go outside, because it is raining.

46)

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. 47) beverages and soft drinks 47)

Provide an appropriate response. 48) 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.

48)

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. 49) athletes and high school students 49) The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 50) There are seven days in a week and there are 24 hours in a day. 50)

Identify the type of argument and determine its validity with a Venn diagram. 51) Premise: If you break curfew, then you will be punished. Premise: Thelma was punished. Conclusion: Thelma broke curfew.

51)

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. 52) motor vehicles and cars 52)

Analyze the situation and explain how you would make a decision. 53) You need a rental car for four days. The daily rate is $20 per day plus 20¢ per mile. The weekly rate is $100, and mileage is included. Which is the better option?

53)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 54) Springfield is the capital of Illinois and Chicago is the capital of Illinois. 54) 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. 55) Some singers are not children. 55)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 56) (Hasty Generalization) Isabelle had vegetarian food for lunch every day last week, so she 56) must be a vegetarian. 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. 57) astronauts and fathers 57)

A seemingly simple argument is given. Identify at least two hidden assumptions. 58) Jeremy needs a new bike, because the new models have a safer braking system. Decide whether the statement makes sense. Explain your reasoning. 59) 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.

58)

59)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 60) 7 + 8 = 15 and 5 × 3 = 20 60)

61) The sun is bigger than the moon and the sun rotates around the earth. A seemingly simple argument is given. Identify at least two hidden assumptions. 62) We should not vote for the incumbent because he has already been in office for three consecutive terms.

61)

62)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 63) Premise: Baseball, football, basketball, golf, hockey, and tennis are all played with a ball. 63) Conclusion: All sports are played with a ball. A seemingly simple argument is given. Identify at least two hidden assumptions. 64) All bills should be paid on time because a bad credit report will make it difficult to get a loan. 6

64)

Decide whether the statement makes sense. Explain your reasoning. 65) Your argument is valid, but it isn't sound.

65)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 66) (False Cause) Since I brought my umbrella, it didn't rain. 66) 67) (Straw Man) Mayor Brown opposes a tax increase to build new schools. His opponent in the upcoming election states: Mayor Brown is not concerned with improving the quality of education for our children.

67)

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. 68) Denying the hypothesis 68) 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. 69) Movies are entertaining. 69)

Decide whether the statement makes sense. Explain your reasoning. 70) I am very upset because the results of my biopsy were not positive for cancer.

70)

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

71)

72) 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.)

72)

73) Your argument has no fallacies, so your conclusion must be true.

73)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 74) Premise: Calvin Coolidge was over 35 years old when he became President of the United States. 74) 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. 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. 75) No dogs are cats. No gerbils are cats. All dogs have fleas. Some cats are thirsty. No thirsty 75) creatures have fleas. Question: Could a gerbil be a dog?

Draw a Venn diagram to represent the given information. 76) 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.

76)

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. 77) All cars have wheels. All trucks have wheels. Some toys have wheels. No grandmothers have 77) wheels. Question: Could a car be both a truck and a toy?

Analyze the situation and explain how you would make a decision. 78) Betty has to go to New Orleans on business. If she flies there and back on the same day her round 78) 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? Draw a Venn diagram to determine whether the argument is valid. 79) Premise: All clowns wear makeup. Premise: Bozo is a clown. Conclusion: Bozo wears makeup.

79)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 80) The state assembly repealed the ban on anti-smoking resolutions. 80) 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. 81) Some flight attendants are men. 81)

Provide an appropriate response. 82) Consider the following clause in a rental lease: 82) "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? 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. 83) salty things, sweet things, tangy things 83)

Analyze the situation and explain how you would make a decision. 84) 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? Describe how the sentence is ambiguous. 85) There was a 15% decrease in donations to the homeless shelter between 1996 and 2000, a year in which $50,000 was collected. Decide whether the statement makes sense. Explain your reasoning. 86) The answer to the question is a whole number but it is not an integer.

84)

85)

86)

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. 87) The dictator of a foreign country has enacted a ban on all firearms, citing prevention of 87) accidental deaths among children as the rationale. 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. 88) All horses are animals. 88) 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) even numbers and odd numbers 89)

Provide an appropriate response. 90) You mention to an acquaintance that you wish to buy a Rolex watch, but the model you're 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. 91) I know more of the names of the common fallacies in arguments than my father, so I can recognize fallacies better than he can. Analyze the situation and explain how you would make a decision. 92) 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?

90)

91)

92)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 93) Premise: I get lower grades than my best friend in math, chemistry, and English. 93) Conclusion: My friend is smarter than I am. Decide whether the statement makes sense. Explain your reasoning. 94) I drew a Venn diagram for two sets, and I only used one circle. Provide an appropriate response. 95) 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.

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) fish and birds 96)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 97) Premise: Monday is one of the days of the week. 97) 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." The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 98) The councilman does not oppose the anti-pollution measure. 98) Draw a Venn diagram to represent the given information. 99) In a survey of 80 pet owners, 50 had a dog, 33 had a cat, and 12 had both a cat and a dog. Analyze the situation and explain how you would make a decision. 100) 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?

99)

100)

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. 101) Beggars can't be choosers. 101) The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 102) 6 + 2 = 8 or 9 × 4 = 36 102)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 103) (Diversion) We've just remodeled the restaurant, so our food is delicious! 103) Decide whether the statement makes sense. Explain your reasoning. 104) The propositions "I am hungry" and "I am not hungry" are both true, since sometimes I am hungry and sometimes I am not hungry. A seemingly simple argument is given. Identify at least two hidden assumptions. 105) It is important to visit the dentist every 6 months to insure healthy teeth and gums.

104)

105)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the converse, inverse, or contrapositive off the proposition, as indicated. 106) If I pass, then I'll celebrate. (contrapositive) A) If I don't pass, then I won't celebrate. B) If I celebrate, then I'll pass. C) If I don't celebrate, then I didn't pass. D) If I pass, then I won't celebrate. Determine whether the statement is true or false. 107) If horses have six legs, then Benjamin Franklin was the first president of the United States. A) True B) False

106)

107)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 108) if q, then not r A) B) q r if q, then not r q r if q, then not r T T T T T F T F F T F T F T T F T T F F T F F T C) D) q r if q, then not r q r if q, then not r T T T T T F T F F T F T F T F F T F F F F F F F

108)

Decide whether the argument is inductive or deductive. 109) All U.S. Presidents have come from the contiguous 48 states. No person from Alaska can be President. A) Deductive B) Inductive Write the negation of the proposition. 110) Emily has brown eyes. A) Emily does not have brown eyes. C) Emily does not have green eyes.

109)

110)

B) Emily has green eyes. D) Jason has brown eyes.

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 111) -88 111) A) Whole numbers B) Integers C) Natural numbers D) Real numbers

Solve the problem. 112) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how 112) many people ordered cake.

A) 28

B) 7

C) 43

D) 21

The argument given or described involves some kind of fallacy. Identify the fallacy. 113) A television commercial shows two people who fall in love while wearing a certain brand of blue jeans. A) Limited choice B) Appeal to ignorance C) Hasty generalization D) Appeal to emotion Write the negation of the proposition. 114) She earns more than me. A) She earns less than me. C) She does not earn less than me.

B) She earns the same as me. D) She does not earn more than me.

Determine whether the statement is true or false. 115) If baseball is a sport, then the letter e is a consonant. A) True

B) False

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 116) p or q A) B) C) p q p or q p q p or q p q p or q T T T T T T T T T T F F T F T T F F F T T F T T F T F F F F F F F F F F

113)

114)

115)

116) p q p or q T T F T F F F T F F F T

Determine whether the statement is true or false. 117) If 9 + 2 = 19, then Canada is in North America. A) True

B) False

Write the negation of the proposition. 118) Some people don't like walking. A) Everyone likes walking. C) Nobody likes walking.

B) Some people don't like driving. D) Some people like walking.

117)

118)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 119) 2 119) A) Whole numbers B) Rational numbers C) Real numbers D) Natural numbers

Use braces to write the members of the set, or state that the set has no members. 120) The letters needed to spell the following words: tear, rate, rat, tea A) {tear, rate, rat, tea} B) {a, e, r, t} C) {t, e, a, r, r, a, t, e, r, a, t, t, e, a} D) {r, a, t}

120)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 121) r and not s A) B) r s p and not s r s r and not s T T F T T T T F T T F T F T F F T F F F F F F T C) D) r s r and not s r s r and not s T T T T T F T F F T F T F T F F T F F F F F F F

121)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 122) -10 122) A) Whole numbers B) Rational numbers C) Natural numbers D) Integers

Determine whether the statement is a proposition. 123) 0.8 = .08 A) Not a proposition

B) Proposition

The argument given or described involves some kind of fallacy. Identify the fallacy. 124) After getting new dishes, I started to sneeze. I must be allergic to the new dishes. A) Personal attack (ad hominem) B) Hasty generalization C) Circular reasoning D) False cause Decide whether the argument is inductive or deductive. 125) Every coach must know his sport well. Steve Spurrier is a football coach, so Steve Spurrier knows football well. A) Deductive B) Inductive Write the negation of the proposition. 126) Everyone is asleep. A) Nobody is asleep. C) Not everyone is asleep.

B) Everyone is awake. D) Nobody is awake.

123)

124)

125)

126)

Solve the problem. 127) The following Venn diagram describes the optional features ordered by new telephone customers in a 127) certain region. Use it to determine how many customers ordered call waiting.

A) 36

B) 40

C) 77

D) 76

Rephrase the statement as a conditional proposition with the form "if p, then q." 128) All chocolate is good. A) If it isn't good, then it's chocolate. B) If it's good, then it's chocolate. C) If it's chocolate, then it's good. D) If it isn't chocolate, then it isn't good.

128)

Solve the problem. 129) The following Venn diagram describes the cars on a used car lot. Use it to determine how many Fords are 129) on the lot.

A) 17

B) 20

C) 30

D) 23

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 130) 6.3 130) A) Integers B) Rational numbers C) Natural numbers D) Real numbers

Rephrase the statement as a conditional proposition with the form "if p, then q." 131) Being in California is sufficient for being in Los Angeles. A) If you are in California, then you are not in Los Angeles. B) If you are in California, then you are in Los Angeles. C) If you are in Los Angeles, then you might be in California. D) If you are in Los Angeles, then you are in California.

131)

State whether or is being used in the exclusive or inclusive sense in the given statement. 132) The insurance policy will not cover misuse or acts of God. A) Exclusive B) Inclusive

132)

Determine whether the statement is true or false. 133) If Florida is in the United States, then all rectangles are squares. A) True B) False

133)

Write the negation of the proposition. 134) Susie lives in a green house. A) Susie does not live in a house that is not green. B) Susie lives in a blue house. C) Susie does not live in a green house. D) Billy lives in a green house.

134)

The argument given or described involves some kind of fallacy. Identify the fallacy. 135) If Proposition Q fails, your children won't have good schools. A) Appeal to emotion B) Hasty generalization C) Appeal to ignorance D) Diversion (red herring) Rephrase the statement as a conditional proposition with the form "if p, then q." 136) Cats chase mice. A) If it is a cat, then it chases mice. B) If cats chase, then they chase mice. C) If cats, then mice. D) If a cat is chasing it, then it is a mouse. Determine whether the statement is a proposition. 137) Mary has a cat. A) Proposition

B) Not a proposition

Write the converse, inverse, or contrapositive off the proposition, as indicated. 138) If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive) A) If the sum of the interior angles of a geometric figure is not 180 degrees, then the figure is not a triangle. B) If a geometric figure is a triangle, then the sum of the interior angles is 180 degrees. C) If a geometric figure is not a triangle, then the sum of the interior angles is 180 degrees. D) If a geometric figure is not a triangle, then the sum of the interior angles is not 180 degrees. Determine whether the statement is true or false. 139) If Florida is in the United States, then all squares are rectangles. A) True B) False

135)

136)

137)

138)

139)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 140) -33.2 140) A) Natural numbers B) Rational numbers C) Integers D) Real numbers

State whether or is being used in the exclusive or inclusive sense in the given statement. 141) The prize is a new car or $10,000 cash. A) Inclusive B) Exclusive

141)

Decide whether the argument is inductive or deductive. 142) For any positive number p, -p = p. Therefore,|-94| = 94 A) Deductive B) Inductive

142)

Write the negation of the proposition. 143) Some athletes are musicians. A) Some athletes are not musicians. C) Not all athletes are musicians.

B) No athlete is a musician. D) All athletes are musicians.

Evaluate the validity of the chain of conditionals. 144) 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) Invalid B) Valid

143)

144)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 145) 0 145) A) Rational numbers B) Whole numbers C) Integers D) Natural numbers

Write the converse, inverse, or contrapositive off the proposition, as indicated. 146) If the sun shines, they will bask. (inverse) A) If they do not bask, then the sun does not shine. B) If they do not bask, then the sun shines. C) If the sun does not shine, then they will not bask. D) If they bask, then the sun shines.

146)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 147) (p or q) or r; p or (q or r) 147) A) No B) Yes Determine whether the statement is a proposition. 148) One inch is 2.54 meters. A) Proposition

B) Not a proposition

149) 2 + 5 = 8 A) Proposition

B) Not a proposition

148)

149)

Solve the problem. 150) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many 150) cookies have neither chocolate chips nor walnuts.

A) 17

B) 10

C) 3

D) 7

Decide whether the argument is inductive or deductive. 151) 7 + 17 = 24, 43 + 17 = 60, 41 + 13 = 54. Therefore, the sum of two prime numbers is even. A) Deductive B) Inductive Write the converse, inverse, or contrapositive off the proposition, as indicated. 152) If you received a refund of over $1000, then you cannot make a claim. (inverse) A) If you did not receive a refund of over $1000, then you can make a claim. B) If you can make a claim, then you received a refund of over $1000. C) If you cannot make a claim, then you did not receive a refund of over $1000. D) If you can make a claim, then you did not receive a refund of over $1000. State whether or is being used in the exclusive or inclusive sense in the given statement. 153) I don't know if I should wear my new skirt or my new dress tonight. A) Inclusive B) Exclusive Rephrase the statement as a conditional proposition with the form "if p, then q." 154) Having a computer is necessary for taking this class. A) If don't take this class, then you must not have a computer. B) If you take this class, then you must have a computer. C) If you have a computer, then you must take this class. D) If you take this computer, then you must have a class.

151)

152)

153)

154)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 155) 16 155) A) Real numbers B) Whole numbers C) Natural numbers D) Integers

Decide whether the argument is inductive or deductive. 156) Practice makes perfect. Therefore, if I practice, I'll be perfect. A) Deductive B) Inductive

156)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 5 157) 157) 9

A) Real numbers C) Integers

B) Natural numbers D) Rational numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 158) 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) Limited choice B) Circular reasoning C) Personal attack (ad hominem) D) Appeal to popularity Evaluate the validity of the chain of conditionals. 159) 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) Invalid B) Valid

158)

159)

Decide whether the argument is inductive or deductive. 160) Fresh fruit is expensive in winter. This is January, so these fresh strawberries will be expensive. A) Inductive B) Deductive

160)

State whether or is being used in the exclusive or inclusive sense in the given statement. 161) Shaun will win the race if he eats carbohydrates beforehand or if he has slept well. A) Exclusive B) Inclusive

161)

Decide whether the argument is inductive or deductive. 162) His last four at bats were strikeouts. Therefore, the next one will be a strikeout. A) Deductive B) Inductive

162)

Rephrase the statement as a conditional proposition with the form "if p, then q." 163) Attending practice is necessary for staying on the team. A) If you attend practice, then you must stay on the team. B) If you don't attend practice, then you must stay on the team. C) If you don't stay on the team, then you must not attend practice. D) If you stay on the team, then you must attend practice.

163)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 164) not (p and q); (not p) or q 164) A) Yes B) No Use braces to write the members of the set, or state that the set has no members. 165) The integers between 0 and 4 (not inclusive) A) {1, 2, 3, 4} B) {1, 2, 3} C) {0, 1, 2, 3, 4}

D) {0, 1, 2, 3}

165)

The argument given or described involves some kind of fallacy. Identify the fallacy. 166) Each of my brother's three dogs has fleas. Therefore, all dogs have fleas. A) Straw man B) Circular reasoning C) Hasty generalization D) False cause

166)

Rephrase the statement as a conditional proposition with the form "if p, then q." 167) Showing up at the party is sufficient to get a door prize. A) If you show up at the party, then you will get a door prize. B) If you don't show up at the party, then you will not get a door prize. C) If you get a door prize, then you don't have to show up at the party. D) If you got a door prize, then you showed up at the party.

167)

Determine whether the statement is true or false. 168) If a triangle is a parallelogram, then all rectangles are squares. A) True B) False

168)

Evaluate the validity of the chain of conditionals. 169) 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) Invalid B) Valid

169)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 170) -3 170) A) Whole numbers B) Real numbers C) Rational numbers D) Integers

Use braces to write the members of the set, or state that the set has no members. 171) The integers from 5 to 9 (inclusive) A) {6, 7, 8} B) {5, 6, 7, 8, 9} C) {5, 6, 7, 8}

D) {6, 7, 8, 9}

171)

Solve the problem. 172) The following Venn diagram describes the optional features ordered by new telephone customers in a 172) certain region. Use it to determine how many customers did not order caller ID.

A) 76

B) 67

C) 77

D) 103

Use braces to write the members of the set, or state that the set has no members. 173) The positive-integer powers of 3 A) {3, 6, 9, 12, 15, . . .} B) {1, 8, 27, 64, 125, . . .} C) {1, 3, 9, 27, 81, 243, . . .} D) {3, 9, 27, 81, 243, . . .}

173)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 174) p or q; not [(not p) and (not q)] 174) A) No B) Yes Use braces to write the members of the set, or state that the set has no members. 175) The whole numbers greater than 3 and less than 7 A) {4, 5, 6, 7} B) {3, 4, 5, 6} C) {4, 5, 6}

D) {3, 4, 5, 6, 7}

175)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 176) not (p and q); (not p) and (not q) 176) A) No B) Yes Rephrase the statement as a conditional proposition with the form "if p, then q." 177) I will lose weight if I diet. A) If I lose weight, then I will diet. B) If I diet, then I will gain weight. C) If I diet, then I will lose weight. D) If I don't diet, then I won't lose weight. Determine whether the statement is a proposition. 178) Do you like this color? A) Proposition

B) Not a proposition

The argument given or described involves some kind of fallacy. Identify the fallacy. 179) One candidate favors eliminating affirmative action programs. The other candidate states: My opponent doesn't think there's anything wrong with discrimination." A) Limited choice B) Straw man C) Hasty generalization D) Personal attack (ad hominem) Write the negation of the proposition. 180) Not all people like football. A) All people like football. C) Some people like football.

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

177)

178)

179)

180)

Draw a Venn diagram to represent the given information. 181) Patients in a (hypothetical) hospital on a single day were taking antibiotics (A), blood pressure medication 181) (BP), and pain medication (P) in the following numbers: A only BP only P only None

11 A and BP only 8 A and P only 22 BP and P only 6 All three

14 19 21

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

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 182) 3146 182) A) Whole numbers B) Integers C) Natural numbers D) Rational numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 183) 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) Straw man B) Diversion (red herring) C) False cause D) Appeal to force

183)

Write the converse, inverse, or contrapositive off the proposition, as indicated. 184) 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 beeps every thirty seconds. B) If you do not have to replace the battery, then the alarm does not beep 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 have to replace the battery, then the alarm does not beep every thirty seconds.

184)

Solve the problem. the 185) The following Venn diagram describes the cars on a used car lot. Use it to determine how many cars on185) lot are not red.

A) 55

B) 58

C) 38

D) 35

The argument given or described involves some kind of fallacy. Identify the fallacy. 186) You should brush your teeth every day because brushing your teeth is very important. A) Hasty generalization B) Circular reasoning C) Diversion (red herring) D) False cause Determine whether the statement is a proposition. 187) Not all flowers are roses. A) Proposition

B) Not a proposition

Evaluate the validity of the chain of conditionals. 188) 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 Determine whether the statement is a proposition. 189) Go fly a kite. A) Proposition

B) Not a proposition

186)

187)

188)

189)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 190) q and (not r) and s A) B) q r s q and (not r) and s q r s q and (not r) and s T T T T T T T F T T F F T T F F T F T F T F T T T F F F T F F F F T T F F T T F F T F F F T F F F F T F F F T F F F F F F F F F C) D) q r s q and (not r) and s q r s q and (not r) and s T T T F T T T F T T F T T T F F T F T F T F T T T F F F T F F T F T T F F T T F F T F F F T F F F F T F F F T F F F F F F F F F

190)

Solve the problem. 191) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many 191) chocolate chip cookies do not also have walnuts.

A) 25

B) 10

C) 15

D) 32

192) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how 192) many people ordered ice cream but not cake.

A) 36

B) 7

C) 21

Write the negation of the proposition. 193) No fifth graders play soccer. A) At least one fifth grader plays soccer. C) No fifth grader does not play soccer.

D) 15

B) Not all fifth graders play soccer. D) All fifth graders play soccer.

193)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 194) not (p or q); (not p)and (not q) 194) A) Yes B) No Use braces to write the members of the set, or state that the set has no members. 195) The days of the week A) {Saturday, Sunday} B) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} C) {Monday, Tuesday, Wednesday, Thursday, Friday} D) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

195)

Answer Key Testname: CHAPTER 1 1) 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. 2) 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.) 3) 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.) 4) 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. 5) Answers may vary. Possible answer:

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.

Answer Key Testname: CHAPTER 1 7)

The X represents Pierre. The conclusion follows necessarily from the premises, and the argument is valid. 8) 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. 9) 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). 10)

11)

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.

The X represents Teri's pet. The conclusion follows necessarily from the premises, and the argument is valid.

Answer Key Testname: CHAPTER 1 12) 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.) 13) The subject set is "positive numbers" and the predicate set is "negative numbers."

14) 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.) 15) 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.) 16) True. Both individual propositions are true, so the conjunction is true. 17) 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. 18) Answers may vary. One possibility:

Answer Key Testname: CHAPTER 1 19) 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. 20) 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. 21) 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.

22)

The argument is valid.

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.

Answer Key Testname: CHAPTER 1 23) 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.) 24) 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.) 25) Answers may vary. Possible answer: The premises are true. The argument is relatively strong, and the conclusion is true. 26) 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.) 27) Answers may vary. One possibility: Cardiovascular exercise leads to a strong heart. Being healthy is important. 28) 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. 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. 30) 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.) 31) Answers may vary. Possible answer:

32) 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. 33) True. Although cats do not read books, dogs do bark. The disjunction is false only if both individual propositions are false. 34) 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.

Answer Key Testname: CHAPTER 1 35)

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

36)

This region has no members.

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.

Answer Key Testname: CHAPTER 1 37)

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. 38) 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. 39)

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 40) Answers may vary. One possibility: An unattended campfire is illegal. Getting a citation from the park ranger would be a bad thing. 41) 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. 42) 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.

Answer Key Testname: CHAPTER 1

43) 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.) 44)

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. 45) 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.) 46) 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. 47)

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. 48) Answers may vary. One possibility: A "no" vote means that you believe that the state legislature should have the authority to restrict religious expression.

Answer Key Testname: CHAPTER 1 49)

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. 50) True. Both individual propositions are true, so the conjunction is true. 51)

52)

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.

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.

Answer Key Testname: CHAPTER 1 53) 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. 54) 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. 55) 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. 56) 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. 57)

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. 58) 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.

Answer Key Testname: CHAPTER 1 59) 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.)

60) False. The proposition 7 + 8 = 15 is true, but the proposition 5 × 3 = 20 is false. Since one of the individual propositions is false, the conjunction is false. 61) 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. 62) Answers may vary. One possibility: Four consecutive terms is too many. The incumbent is running in the election. 63) 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. 64) Answers may vary. One possibility: Paying bills late will result in bad credit. It is important to be able to get a loan. 65) 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.) 66) 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. 67) 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. 68) 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.

Answer Key Testname: CHAPTER 1 69) In standard form: All movies are things that are entertaining. The subject set is "movies" and the predicate set is "things that are entertaining."

70) 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.) 71) 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.) 72) 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.) 73) 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.) 74) 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.

Answer Key Testname: CHAPTER 1 75) 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. 76) Answers may vary. Possible answer:

Answer Key Testname: CHAPTER 1 77) 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. 78) 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. 79)

The X represents Bozo. The conclusion follows necessarily from the premises, and the argument is valid. 80) 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.

Answer Key Testname: CHAPTER 1 81) 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. 82) 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! 83)

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 84) 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. 85) It is unclear whether the year in which $50,000 was collected was 1996 or 2000. 86) 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.) 87) Answers may vary. One possibility: The dictator may believe that an unarmed populace is easier to control.

Answer Key Testname: CHAPTER 1 88) The subject set is "horses" and the predicate set is "animals."

89)

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. 90) 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. 91) 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.) 92) 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?

Answer Key Testname: CHAPTER 1 93) 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. 94) 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.) 95) 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. 96)

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. 97) 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. 98) 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. 99) Answers may vary. Possible answer:

Answer Key Testname: CHAPTER 1 100) 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? 101) In standard form: No beggars are choosers. The subject set is "beggars" and the predicate set is "choosers."

102) True. Both individual propositions are true. The disjunction is true if either or both propositions are true. 103) 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. 104) 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.) 105) Answers may vary. One possibility: Healthy teeth are important. Healthy gums are important. 106) C 107) A 108) B 109) B 110) A 111) B 112) A 113) D 114) D 115) B 116) B 117) A 118) A 119) C 120) B 121) D 42

Answer Key Testname: CHAPTER 1 122) D 123) B 124) D 125) A 126) C 127) D 128) C 129) D 130) B 131) B 132) B 133) B 134) C 135) A 136) A 137) A 138) D 139) A 140) B 141) B 142) A 143) B 144) B 145) B 146) C 147) B 148) A 149) A 150) D 151) B 152) A 153) B 154) B 155) C 156) A 157) D 158) C 159) A 160) B 161) B 162) B 163) D 164) B 165) B 166) C 167) A 168) A 169) B 170) B 171) B 43

Answer Key Testname: CHAPTER 1 172) B 173) D 174) B 175) C 176) A 177) C 178) B 179) B 180) A 181) D 182) C 183) B 184) A 185) A 186) B 187) A 188) B 189) B 190) B 191) C 192) D 193) A 194) A 195) D

Chapter 2 Exam 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) The container was big enough to hold a barrel of water, but it wasn't big enough to hold a barrel of petroleum.

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

3) I figured out the distance we had traveled by dividing our speed by the amount of time we had traveled.

4) We will need 1800 cubic feet of carpeting to cover the floors in our three-story house.

5) 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 .

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

7) I can walk on my hands for 5 meters before falling down, but my goal is to walk a full decimeter without losing my balance.

Solve the problem. 8) Paul and Saul ran a 50-meter race. When Paul crossed the finish line, Saul had run only 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?

9) Suppose that you have 10 white socks and 6 black socks in a clothes dryer. How many socks must you withdraw from the dryer (without looking) to be certain of having a pair of white socks?

10) 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.

10)

Decide whether the statement makes sense. Explain your reasoning. 11) Our utility company charges 10 cents per joule for the energy we use. Solve the problem. 12) 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? 1

11)

12)

13) You are considering buying 15 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale?

13)

14) 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?

14)

Decide whether the statement makes sense. Explain your reasoning. 15) I got pulled over by a police officer for speeding. I was going 150 kiloliters per second. 16) I donated 64 fluid ounces of blood today.

15) 16)

Solve the problem. 17) 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. 18) It takes you 84 seconds to walk from the first (ground) floor of a building to the fourth 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)?

17)

18)

Decide whether the statement makes sense. Explain your reasoning.

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

Solve the problem. 20) Abe, Boris, Cal, and David all proposed to Ellie on Friday. Abe proposed at 5:00, Boris 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?

19)

20)

21) A curved bridge rises over a river, so that the two endpoints of the bridge are 140 yards apart horizontally. You walk across the bridge with a device to measure its length and discover that the walking distance is 142 yards. Approximately how high does the bridge rise above the horizontal?

21)

22) A trader bought a stock for $20 and then sold it for $30. He bought it back for $38 and then sold it again for $48. How much did he gain or lose on these transactions?

22)

Decide whether the statement makes sense. Explain your reasoning. 23) 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. 24) 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? 2

23)

24)

25) 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. 26) I drove really far, almost 200 kilometers per hour. 27) 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. 28) 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?

25)

26) 27)

28)

29) 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?

29)

30) 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 350 feet above the horizontal. Approximately what is the walking distance along the bridge, in feet?

30)

Decide whether the statement makes sense. Explain your reasoning. 31) It is not recommended that you use approximations to solve a problem, because then your solution is only an approximation.

31)

32) To convert from Kelvin to Celsius, you subtract 273.15. For example, -100 K = -373.15 °C.

32)

33) If you complete the four-step problem-solving process carefully and thoroughly, then you will have no uncertainty about your final answer.

33)

Solve the problem. 34) Suppose that China's population policy is modified so that every family could have 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? 35) 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?

34)

35)

36) 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.

36)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the units you would expect for the given quantity. 37) The density of a meteor, found by dividing its mass in kilograms by its volume in cubic meters. A) kg/m 3 B) kg/m 2 C) kg3 /m D) m 3 /kg Write as a common fraction. 38) 0.745 149 A) 2000 Evaluate. 39)

149 B) 20

149 C) 2

149 D) 200

1 1 1 × × 4 5 6

15 2

1 120

C) Larger by a factor of 109

41)

1 60

1 26

40)

D) Larger by a factor of 1015

1 1 + 5 7

38)

39)

State how much larger or smaller the first unit is than the second. 40) gigagram, microgram A) Larger by a factor of 1012 B) Larger by a factor of 1018

Evaluate.

37)

41) 24 35

6 35

12 35

35 12

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 42) 45°C, into Fahrenheit A) 57°F B) 77°F C) 49°F D) 113°F

42)

Solve the problem. 43) A 14-gram object has a volume of 35 cubic centimeters. Find its density. A) 2.5 cm3 /g B) 490 g-cm3 C) 0.4 g/cm3

43)

D) 21 cm3

Evaluate. 44)

5 3 + 7 8

44) 112 61

61 56

61 28

56 61

Solve the problem. 45) Your electrical bill states that you used 770 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules. A) 277,200,000 joules B) 2,464,000,000 joules C) 246,400,000 joules D) 2,772,000,000 joules 46) 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) 6 grams B) 18 grams C) 40.5 grams D) 54 grams Carry out the indicated unit conversion. Round your answer, if appropriate. 47) Convert a distance of 48 feet into yards. A) 19 yards B) 32 yards C) 16 yards

D) 144 yards

Write as a common fraction. 48) 9.27 927 A) 100

927 D) 10

927 B) 1000

243 C) 25

Solve the problem. 49) A packing crate measures 5 feet by 11 feet by 9 feet. What is the area of its smallest side? A) 55 ft2 B) 495 ft3 C) 45 ft2 D) 99 ft2 50) 10-13 × 10-3 A) 10-10

B) 1039

51) How many cubic inches are in 17 cubic feet? A) 22,032 in.3 B) 793,152 in.3

C) 10-16

D) 1016

C) 2448 in.3

D) 29,376 in.3

Convert the measurement to the units specified. Round your answer to the nearest tenth. 52) 2900 square yards to square meters A) 3470.8 square meters B) 2651.8 square meters C) 3172.6 square meters D) 2424.8 square meters Solve the problem. 53) Your electrical bill states that you used 840 kilowatt-hours of energy in September. Determine your average power use, in watts. A) 1283.3 watts B) 1166.7 watts C) 1129 watts D) 1400 watts Answer the following question involving a conversion within the USCS system. 54) How many gallons are in 77 barrels of petroleum? A) 1.8 gal B) 3234 gal C) 2387 gal

D) 4004 gal

45)

46)

47)

48)

49)

50)

51)

52)

53)

54)

State how much larger or smaller the first unit is than the second. 55) gram, milligram A) Larger by a factor of 103 B) Smaller by a factor of 103 C) Larger by a factor of 106

Evaluate. 56)

55)

D) Smaller by a factor of 106

9 1 5 8

56) 77 40

67 40

19 10

17 10

Identify the units you would expect for the given quantity. 57) The price of pudding, found by dividing its cost in dollars by its weight in ounces. A) ounces per dollar B) ounce-dollars C) dollars per ounce D) dollar-ounces Answer the following question involving a conversion within the USCS system. 58) The container holds 3 gallons of water. How many fluid ounces is that? A) 96 fl oz B) 384 fl oz C) 768 fl oz Evaluate. 59)

57)

D) 192 fl oz

9 1 ÷ 2 5

58)

59) 45 4

9 10

9 5

45 2

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 60) -80°C, into Kelvin A) 193.15 K B) 129.15 K C) 93.15 K D) -353.15 K

60)

Solve the problem. 61) A field is 120 yards long and 90 yards wide. Find its area in square feet. A) 32,400 ft2 B) 291,600 ft2 C) 97,200 ft2

61)

Evaluate. 62)

D) 10,800 ft2

1 1 6 12

A) -

62) 1 6

1 6

1 12

D) -

1 12

Use units to help you answer the question. If necessary, round your answer to two decimal places. 63) 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 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

63)

State how much larger or smaller the first unit is than the second. 64) square decimeter, square kilometer A) Smaller by a factor of 103 B) Smaller by a factor of 104

64)

Answer the following question involving a conversion within the USCS system. 65) The baby weighs 7.4 pounds. How many ounces is that? A) 74 ounces B) 118.4 ounces C) 88.8 ounces

65)

C) Smaller by a factor of 108

D) Smaller by a factor of 106

D) 0.46 ounces

Use units to help you answer the question. If necessary, round your answer to two decimal places. 66) 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) $204.00 B) $741.82 C) $1870.00 D) $623.33 Carry out the indicated unit conversion. Round your answer, if appropriate. 67) Convert a weight of 12 pounds into ounces; there are 16 ounces in 1 pound. A) 96 ounces B) 192 ounces C) 384 ounces

D) 240 ounces

Convert the measurement to the units specified. Round your answer to the nearest tenth. 68) 37 liters to gallons A) 140 gallons B) 35 gallons C) 9.8 gallons D) 39.1 gallons Solve the problem. 69) 1010 - 104

A) 1,000,000

B) 10,000,010,000

C) 1,000,010,000

D) 9,999,990,000

70) There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms. A) 1 km3 = (1000 m)3 = 100,000 m 3 B) 1 m 3 = (1000 km)3 = 1,000,000 km3 C) 1 km3 = (1000 m)3 = 1,000,000,000 m 3

66)

67)

68)

69)

70)

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

Identify the units you would expect for the given quantity. 71) The price of gravel, found by dividing its total cost in dollars by its total weight in tons. A) cubic tons B) ton-dollars C) tons per dollar D) dollars per ton

71)

Carry out the indicated unit conversion. Round your answer, if appropriate. 72) Convert a distance of 14 miles into yards; there are 1760 yards in a mile. A) 26,320 yards B) 2464 yards C) 25,480 yards

72)

D) 24,640 yards

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 73) 370 K, into Celsius A) 296.85°C B) 196.85°C C) -67.59°C D) 96.85°C Identify the units you would expect for the given quantity. 74) The amount of electricity utilized, calculated by multiplying power in kilowatts by time in hours. A) kilowatts per hour B) hours per kilowatt C) kilowatts per second D) kilowatt-hours

73)

74)

Use units to help you answer the question. If necessary, round your answer to two decimal places. 75) Assume that you breathe once every 10 seconds. How many breaths do you take in 3 weeks? A) 181,440 B) 3024 C) 260,480 D) 25,920 Solve the problem. 76) A warehouse is 44 yards long and 25 yards wide with a height of 12 yards. What is the volume of the warehouse? A) 13,200 yd3 B) 1100 yd2 C) 13,200 ft3 D) 1100 ft2 Use units to help you answer the question. If necessary, round your answer to two decimal places. 77) Assuming that your heart beats 70 times per minute, how many times does your heart beat in 6 days? A) 201,600 B) 25,200 C) 604,800 D) 36,288,000 State how much larger or smaller the first unit is than the second. 78) centiliter, microliter A) Smaller by a factor of 1000 B) Larger by a factor of 10,000 C) Larger by a factor of 1000 D) Smaller by a factor of 10,000 Use units to help you answer the question. If necessary, round your answer to two decimal places. 79) 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) 864 acres B) 0.16 acres C) 1050 acres D) 11.14 acres

75)

76)

77)

78)

79)

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

80) How many Mexican pesos can you buy for $130? A) 1.56 pesos B) 10,832.9 pesos

C) 10.2115 pesos

D) 1654.9 pesos

Solve the problem. 81) 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) 0.05 g/100 ml B) 0.5 g/100 ml C) 0.25 g/100 ml D) 0.025 g/100 ml Carry out the indicated unit conversion. Round your answer, if appropriate. 1 82) Convert a lot size of acre to square feet (1 acre = 43,560 ft2 ). 6 A) 7260 square feet C) 737 square feet

B) 726 square feet D) 7370 square feet

80)

81)

82)

Evaluate. 83)

7 3 ÷ 3 7

84)

83) 7 3

49 9

C) 1

9 49

3 1 × 2 4

84) 1 4

3 8

1 8

3 16

Solve the problem. 85) 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 10,610 British pounds? A) $17,229.62 B) $19,981.17 C) $5495.98 D) $6533.64 Decide which of the two given prices is the better deal. 86) You can buy hair product in a 12-ounce bottle for $4.56 or in a 8-ounce bottle for $2.88. A) 12-ounce bottle for $4.56 B) 8-ounce bottle for $2.88 C) not enough information D) equal value Solve the problem. 87) You find a 2-pound nugget that is 50% gold. What is its purity in karats? A) 12 karats B) 50 karats C) 4.8 karats

D) 24 karats

Decide which of the two given prices is the better deal. 88) You can buy laundry product in a 28-ounce bottle for $6.44 or in a 24-ounce bottle for $4.80. A) not enough information B) equal value C) 24-ounce bottle for $4.80 D) 28-ounce bottle for $6.44 Solve the problem. 89) Find a conversion factor between square feet and square yards. Write it in three forms. A) 1 yd3 = (3 ft)3 = 27 ft3 B) 1 yd2 = (3 ft)2 = 9 ft2 C) 1 ft3 = (3 yd)3 = 27 yd3

State how much larger or smaller the first unit is than the second. 91) cubic micrometer, cubic meter A) Smaller by a factor of 1018 B) Smaller by a factor of 109 C) Smaller by a factor of 1012

A) 1011

86)

87)

88)

89)

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

90) A swimming pool 2 meters deep, 11 meters long, and 6 meters wide is filled with water. What volume of water does the pool contain? A) 153 m 3 B) 12 m 2 C) 132 m 3 D) 66 m 2

Solve the problem. 92) 105 × 106

85)

90)

91)

D) Smaller by a factor of 106

B) 1013

C) 1016

D) 1030

92)

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 93) 100°F, into Celsius A) 55.56°C B) 37.78°C C) 68.00°C D) 122.40°C Use units to help you answer the question. If necessary, round your answer to two decimal places. 94) Suppose you could spend $7 every hour, night and day. How much could you spend in a year? (Assume that there are 365 days in a year.) A) $3,679,200 B) $8760 C) $10,080 D) $61,320 Write as a common fraction. 95) 0.8 2 A) 25

8 11

8 9

4 5

Solve the problem. 96) How many cubic furlongs are in a cubic mile? (1 mile = 8 furlongs) A) 512 cubic furlongs B) 64 cubic furlongs C) 4096 cubic furlongs D) 8 cubic furlongs

3 B) 50

3 C) 500

3 D) 5000

Solve the problem. 106 99) 104 A) 1010

101)

B) 102

C) 10-2

2 15

97)

98)

D) 1024

2 ×5 15

95)

99)

100) A swimming pool 3 meters deep, 14 meters long, and 7 meters wide is filled with water. What is the area of the water's surface? A) 294 m 3 B) 21 m 2 C) 42 m 2 D) 98 m 2 Evaluate.

94)

96)

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 97) 70°F, into Celsius A) 56.67°C B) 21.11°C C) 38.00°C D) 38.89°C Write as a common fraction. 98) 0.0006 3 A) 50000

93)

100)

101) B)

1 3

3 2

2 3

Solve the problem. 102) An object has a total volume of 3 liters (which is 3000 cubic centimeters) and a mass of 2 kilograms. What is its density? Will it sink or float in water? A) 1.5 g/cm3 ; sink B) 0.67 g/cm3 ; sink C) 1.5 g/cm3 ; float

D) 0.67 g/cm3 ; float

102)

103) How many square inches are in 8 square yards? A) 288 in.2 B) 96 in.2

C) 10,368 in.2

D) 1152 in.2

104) Recently, one U.S. dollar was worth about 12.73 Mexican pesos. How much would 235 U.S. dollars be worth in Mexican pesos? A) $21.62 B) $18.46 C) $2568.55 D) $2991.55 Answer the following question involving a conversion within the USCS system. 105) A boat is moving at 48 miles per hour. What is its speed in knots (nautical miles per hour)? A) 57.2 knots B) 39.7 knots C) 55.2 knots D) 41.7 knots Solve the problem. 106) A supermarket in Japan sells soy milk for 379 yen per liter. If there are 83.23 yen per dollar, then what is the price in dollars per quart? A) $4.55 per quart B) $4.81 per quart C) $4.31 per quart D) $3.62 per quart 107) A column has a circular base with an area of 5 square feet and is 12 feet tall. What is its total volume? A) 300 ft3 B) 300 ft3 C) 60 ft3 D) 60 ft3 Convert the measurement to the units specified. Round your answer to the nearest tenth. 108) 11 cubic inches to milliliters A) 325.3 milliliters B) 0.4 milliliters C) 0.7 milliliters D) 180.2 milliliters Write as a common fraction. 109) 9.7 79 A) 100

79 B) 10

97 C) 10

97 D) 100

Use units to help you answer the question. If necessary, round your answer to two decimal places. 110) A paint mixture contains 16 gallons of base for every gallon of color. In 340 gallons of paint, how many gallons of color are there? A) 20 gal B) 113 gal C) 320 gal D) 170 gal Solve the problem. 111) You burn 900 Calories will exercising for 35 minutes. What is your average power while exercising, in watts? A) 1793.1 watts B) 2151.8 watts C) 1434.5 watts D) 2689.7 watts 112) 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 yd3 = (3 ft)3 = 27 ft3

104)

105)

106)

107)

108)

109)

110)

111)

112)

D) 1 yd2 = (36 in.)2 = 1296 in.2

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 6 113) 7 A) 0.854

103)

B) 1

C) 0.862

D) 0.857

113)

114) Which is worth most, 1 British pound, 1 Canadian dollar, 1 European euro, or 1 dollar? A) 1 dollar B) 1 British pound C) 1 European euro D) 1 Canadian dollar Solve the problem. 115) 104 + 108

A) 100,100,000 C) 1,000,000,000,000

B) 100,010,000 D) 10,010,000

Identify the units you would expect for the given quantity. 116) The gas mileage of a car, when you travel 4016 kilometers using 8 gallons of gas. A) $/gal B) km/gal C) 50 D) gal/km Solve the problem. 117) What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour? A) 60 cents B) 45 cents C) 30 cents D) 67 cents Carry out the indicated unit conversion. Round your answer, if appropriate. 118) Use a chain of conversions with familiar measures of time to convert 8 weeks into seconds. A) 201,600 seconds B) 4,838,400 seconds C) 691,200 seconds D) 80,640 seconds

114)

115)

116)

117)

118)

119) A fresh juice stand in Montreal sells a large glass of orange juice for 4.50 Canadian dollars. If you buy 4 glasses, how much have you spent in (U.S.) dollars? A) $23.76 B) $17.91 C) $18.09 D) $13.64 Convert the measurement to the units specified. Round your answer to the nearest tenth. 120) 39 pounds to grams A) 17,690.4 grams B) 86 grams C) 17.7 grams D) 85,995 grams

119)

120)

Decide which of the two given prices is the better deal. 121) The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 15-oz bottles for $4.13 Seven 18-oz bottles for $7.56 A) not enough information B) Five 15-oz bottles C) Seven 18-oz bottles D) equal value Convert the measurement to the units specified. Round your answer to the nearest tenth. 122) 99 kilometers per hour to miles per hour A) 71.6 miles per hour B) 61.5 miles per hour C) 138.2 miles per hour D) 159.3 miles per hour Carry out the indicated unit conversion. Round your answer, if appropriate. 123) 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) 1792 ounces B) 896 ounces C) 112 ounces D) 224 ounces State how much larger or smaller the first unit is than the second. 124) nanometer, meter A) Larger by a factor of 106 B) Larger by a factor of 109 C) Smaller by a factor of 106

Write as a common fraction. 125) 0.85 29 A) 5

122)

123)

124)

D) Smaller by a factor of 109

17 B) 2

17 C) 20

29 D) 50

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 427 126) 61 A) 8

121)

B) 6.1

C) 7

Answer the following question involving a conversion within the USCS system. 127) How many quarts are in 54 barrels of water? A) 1674 qt B) 2268 qt C) 9072 qt

126)

D) 6

D) 6696 qt

Use units to help you answer the question. If necessary, round your answer to two decimal places. 128) A stockbroker sold 45 shares of stock for $35.16 each. What was the total amount of the sale? A) $1582.1 B) $1582.20 C) $1582.31 D) $1582.3

125)

127)

128)

129) You return from a trip with 3700 Japanese yen. How much are your yen worth in dollars? A) $44.40 B) $2803.12 C) $290.64 D) $308,321 Convert the measurement to the units specified. Round your answer to the nearest tenth. 130) 28 feet to meters A) 91.8 meters B) 25.6 meters C) 8.5 meters D) 10.6 meters Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 101 131) 76 A) 1.139

B) 1.439

C) 0.752

B) 0.615

C) 0.072

135)

1 1 1 + + 3 4 5

47 60

132)

133)

D) 0.727

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 134) -25°C, into Fahrenheit A) 7°F B) -77°F C) 18.1°F D) -13°F Evaluate.

131)

D) 1562 people/mi2

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 8 133) 11 A) 0.8

130)

D) 1.329

Solve the problem. 132) A certain land area is 420,000 square miles, and it holds a population of 65.6 million people. Calculate the population density. A) 640 people/mi2 B) 64 people/mi2 C) 156 people/mi2

129)

134)

135) B)

49 60

43 60

3 4

Solve the problem. 136) A piece of land in Ottawa with an area of 0.5 square kilometers is priced at 5500 Canadian dollars. If there are 0.9976 Canadian dollars per (U.S.) dollar, then what is the price in dollars per square mile? A) $17,744.89 per square mile B) $28,556.85 per square mile C) $28,419.94 per square mile D) $4257.57 per square mile

136)

Identify the units you would expect for the given quantity. 137) A speed found by dividing a distance measured in meters by a time measured in seconds. A) meters per second B) meter-seconds C) seconds per meter D) square meters Convert the measurement to the units specified. Round your answer to the nearest tenth. 138) 8 kilometers to yards A) 22,658.9 yards B) 26,247.9 yards C) 8749.3 yards D) 67,976.8 yards Solve the problem. 105 139) 10-3 A) 108 140)

141) 102 × 10-5 A) 10-3

C) 102

B) 10-8

D) 10-15 140)

B) 10-5

C) 10-21

D) 105

B) 107

C) 10-7

D) 10-10

141)

Use units to help you answer the question. If necessary, round your answer to two decimal places. 142) 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) 1.45 gal B) 0.75 gal C) 1.33 gal D) 0.69 gal Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 7 143) 2 A) 14 144)

B) 3.5

C) 4.5

142)

143)

D) 2.5

16 41

A) 0.55

138)

139)

10-13 10-8

A) 10-104

137)

144) B) 2.563

C) 0.3

D) 0.39

Use units to help you answer the question. If necessary, round your answer to two decimal places. 145) A community garden contains 20 rectangular plots each measuring 4 yd by 10 yd. What is the total area available for gardening? A) 560 yd2 B) 800 yd2 C) 40 yd2 D) 820 yd2 Carry out the indicated unit conversion. Round your answer, if appropriate. 146) A car is driving at 240 miles per hour. What is its speed in miles per minute? A) 300 miles per minute B) 14,400 miles per minute C) 4 miles per minute D) 864,000 miles per minute

145)

146)

Answer the following question involving a conversion within the USCS system. 147) 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) 537.6 in.3 D) 268.8 in.3 148) If a horse ran 8 furlongs, how many yards did it run? A) 42,240 yd B) 1760 yd C) 7040 yd

D) 14,080 yd

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 615 149) 818 A) 0.759

B) 0.862

C) 0.562

D) 0.752

147)

148)

149)

Answer Key Testname: CHAPTER 2 1) 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.) 7 days 24 hr 60 min 60 sec × × × = (7 × 24 × 60 × 60) seconds, since all the other units cancel. 2) Makes sense. 1 wk × 1 wk 1 day 1 hr 1 min There are 604,800 seconds in a week. (Explanations will vary.) 3) 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.) 4) 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.) 5) 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.) 6) 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.) 7) 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.) 8) Paul 9) 8 socks 10) 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. 11) 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.) 12) 45.6 mi 13) 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. 14) 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. 15) Does not make sense. Kiloliters are a unit of volume, and speed is measured in units of distance divided by time. (Explanations will vary.) 16) 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.)

Answer Key Testname: CHAPTER 2 17) 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. 18) 252 seconds 19) 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.) 20) Cal's proposal 21) 11.9 yards 22) He gained $20 on the transactions. 23) 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.) 24) The surgeon is a woman. She is the mother of the patient. 25) 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." 26) 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.) 27) 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.) 28) 11 marbles 29) 68 in. 30) 5326.2 feet 31) 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.) 32) 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.) 33) 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.) 34) 1500 35) The number of yellow marbles in the red bucket is greater. 18

Answer Key Testname: CHAPTER 2 36) 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 37) A 38) D 39) B 40) D 41) C 42) D 43) C 44) B 45) D 46) C 47) C 48) A 49) C 50) C 51) D 52) D 53) B 54) B 55) A 56) B 57) C 58) B 59) D 60) A 61) C 62) C 63) D 64) C 65) B 66) D 67) B 68) C 69) D 70) C 71) D 72) D 73) D 74) D 75) A 76) A 77) C 78) B 79) A 80) D 81) B 82) A 83) B 84) B 19

Answer Key Testname: CHAPTER 2 85) A 86) B 87) A 88) C 89) B 90) C 91) A 92) A 93) B 94) D 95) D 96) A 97) B 98) D 99) B 100) D 101) D 102) D 103) C 104) D 105) D 106) C 107) D 108) D 109) C 110) A 111) A 112) B 113) D 114) B 115) B 116) B 117) C 118) B 119) C 120) A 121) B 122) B 123) B 124) D 125) C 126) C 127) D 128) B 129) A 130) C 131) D 132) C 133) D 134) D 20

Answer Key Testname: CHAPTER 2 135) A 136) B 137) A 138) C 139) A 140) B 141) A 142) C 143) B 144) D 145) B 146) C 147) C 148) B 149) D

Chapter 3 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 1) Any test for a disease has a certain rate of false positives (percentage of those who don't have the disease 1) 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 rate of false negatives C) The rate of false positives, the incidence of the disease D) The rate of false positives, the rate of false negatives, the incidence of the disease, the number of people being tested 2) 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 125% of yours. C) My salary is 25% less than yours. D) My salary is 20% less than yours.

3) In Slackville, the unemployment rate was 20% last year and this year it is 22%. Which of the following statements is correct? A) In absolute terms, the unemployment rate this year is 2 percentage points higher than last year and in relative terms it is 9.1% higher. B) In absolute terms, the unemployment rate this year is 10 percentage points higher than last year and in relative terms it is 2% higher. C) In absolute terms, the unemployment rate this year is 2 percentage points higher than last year and in relative terms it is 10% higher. D) In absolute terms, the unemployment rate this year is 2 percentage points higher than last year and in relative terms it is 2% higher.

Solve the problem. 4) John is 7 times as heavy as his dog. Determine which of the statement's below is true. A) John weighs 600% more than his dog. C) John weight is 600% of his dog's weight.

4) B) John's dog weighs 600% less than John. D) John weighs 700% more than his dog.

Answer the question. 5) Which of the statements below suggests an appropriate level of precision? A) The population of sperm whales worldwide is 817,213 B) The population of sperm whales worldwide is 817,200. C) The population of sperm whales worldwide is 817,210. D) The population of sperm whales worldwide is 800,000.

6) The average annual precipitation in Tewinville is 60 inches. In 2000, a particularly wet year, the 6) precipitation was 120 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) B and D C) B and C D) A and D 7) 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) Sun City had greater absolute growth in population, and also greater relative growth. B) Emeryville 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.

8) Which of the statements below suggests an appropriate level of precision? A) My temperature this morning is 37.612° F. B) My temperature this morning is 40° F. [to the nearest 10 degrees] C) My temperature this morning is 37.6127° F. D) My temperature this morning is 37.6° F.

Solve the problem. 9) Allison weighs 34% less than she did one year ago. Determine which of the statement's below is true. A) Allison's current weight is 66% of her weight one year ago. B) Allison's current weight is 134% of her weight one year ago. C) Allison's weight one year ago is 134% of her current weight . D) Allison's current weight is 34% of her weight one year ago. Answer the question. 10) Which of the statements below suggests an appropriate level of precision? A) Every day I drive a distance of 75.1341 miles to work. B) Every day I drive a distance of 80 miles to work. [to the nearest 10 miles] C) Every day I drive a distance of 75.134 miles to work. D) Every day I drive a distance of 76 miles to work. Solve the problem. 11) 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 500% of the value when she bought it. B) The value of her house today is 600% more than when she bought it. C) The value of her house today is 6 times what it was when she bought it. D) The value of her house today is 5 times what it was when she bought it.

10)

11)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 12) The weight of a grain of rice. 12) A) 0.0006 ounces B) 0.000001 ounces C) 0.006 ounces D) 0.01 ounces 2

Answer the question. 13) 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 an 3 inch gives your height as 70 inches. Which of these two measurement is more precise? Which is 8

13)

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

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 14) The total number of gallons of gasoline that will be used by American drivers in a year. 14) A) One hundred billion B) Ten billion C) Ten trillion D) One trillion 15) The total amount of money spent each year on food by Americans. A) Thirty trillion dollars B) Ten billion dollars C) One trillion dollars D) One hundred billion dollars Answer the question. 16) Suppose that a test for a disease correctly gives positive results for 95% of those having the disease 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 quite low B) It is about 50% C) It is very high D) It is 95%

15)

16)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 17) The total number of cups of coffee drunk last year by Europeans. 17) A) Ten billion B) Two trillion C) Two hundred billion D) Ten trillion Answer the question. 18) Which of the statements below suggests an appropriate level of precision? A) According to his bathroom scales, Enrique's weight is 194 lb. B) According to his bathroom scales, Enrique's weight is 194.1134 lb. C) According to his bathroom scales, Enrique's weight is 190 lb [to the nearest ten pounds] D) According to his bathroom scales, Enrique's weight is 194.113 lb. Solve the problem. 19) The retail cost of a computer is 32% more than its wholesale cost. Determine which of the statement's below is true. A) The wholesale cost of the computer is 68% of the retail price. B) The retail cost of the computer is 132% of the wholesale price. C) The retail cost of the computer is 32% of the wholesale price. D) The retail cost of the computer is 132% more than the wholesale price.

18)

19)

Answer the question. 20) 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) 8.8% B) 10% C) 95% D) 13.4%

20)

21) Of those who applied to the college, 40% were accepted and of those accepted, 10% enrolled. What percentage of those who applied, enrolled? A) 40% × 10% = 4% B) 40% - 10% = 30% C) 40% + 10% = 50% D) 40% × 10% = 0.4%

21)

22) In 2000 your salary increased by 5% . In 2001 you received a 5% pay cut. After the two changes, how does your salary compare to your original salary? A) It is higher. B) Cannot be determined from the information given C) It is unchanged. D) It is lower.

22)

23) 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

23)

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

24) Suppose that of the total amount collected in taxes by the U.S. government, 25% of it comes from families 24) with incomes greater than $200,000. If taxes are increased by 5% across the board, which of the following statements will be true? A) A family with an income greater than $200,000 will have to pay 25% more in taxes. B) 5% of the additional revenue will come from each income group. 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. 25) In 2000, the balance on Martin's credit card increased by 60%. In 2001, the balance increased by 20%. How does the balance at the end of 2001 compare to the balance at the beginning of 2000? A) It is 80% higher. B) It is 92% higher. C) It is 68% higher. D) It is 120% higher.

25)

26) 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 50% and the mean score for the second class is 70%. What can you say about the mean score for both classes combined? A) It is higher than 60%. B) It may be higher or lower than 60%, this cannot be determined from the information given. C) It is lower than 60%. D) It is equal to 60%.

26)

27) 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 thousand] B) 8314.1 people have enrolled for the college for next year. C) 8300 people have enrolled for the college for next year. [Number given to the nearest hundred] D) 8314 people have enrolled for the college for next year. Solve the problem. 28) The area of Jose's apartment is 53% 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 53% of the area of Alan's apartment. B) The area of Jose's apartment is 153% more than the area of Alan's apartment. C) The area of Jose's apartment is 153% of the area of Alan's apartment. D) The area of Alan's apartment is 53% less than the area of Jose's apartment. Answer the question. 29) In 2000 a company increased its workforce by 20%. In 2001 it decreased its workforce by 20%. 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 4% lower. B) It is unchanged. C) It is 4% higher. D) It is 2% lower.

27)

28)

29)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 30) The total number of steps an adult would take in walking from New York to San Francisco. 30) A) One million B) Ten million C) One hundred million D) One billion Answer the question. 31) 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) Though the median household income increased, prices increased by a greater percent, meaning that in real terms the median income actually decreased. B) It is not possible for both candidates to be right; one of them is obviously lying. C) 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. D) The incumbent is referring to the state economy, while the challenger is referring to the national economy. Solve the problem. 32) Cathy scored 4 times as much as Helen on the test. Determine which of the statement's below is true. A) Cathy's score was 300% of Helen's score. B) Helen's score was 300% less than Cathy's score. C) Cathy's score was 400% of Helen's score. D) Cathy's score was 400% more than Helen's score.

31)

32)

33) During the sale the price of the sofa was discounted by 20%. Determine which of the statement's below is true. A) The sale price of the sofa is 20% of the regular price. B) The sale price of the sofa is 80% of the regular price. C) The sale price of the sofa is 80% less than the regular price. D) The regular price of the sofa is 101% of the sale price.

33)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 34) The thickness of a compact disc. 34) A) 0.05 inches B) 0.1 inches C) 0.01 inches D) 0.005 inches Answer the question. 35) In the 1980s, the population of Pleasanton decreased by 10%. In the 1990s, its population increased by 20%. How does the population of Pleasanton at the end of the 1990s compare with its population in 1980? A) It is 30% higher. B) It is 12% higher. C) It is 8% higher. D) It is 10% higher.

35)

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. 36) The total number of breaths taken in his lifetime by a man who lives to be 80. 36) A) Three hundred million B) Ten billion C) Three billion D) Fifty million Answer the question. 37) 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 120,000. C) The number of people at the demonstration was 122,615. D) The number of people at the demonstration was 100,000 [to the nearest one hundred thousand].

37)

38) A researcher looks at the percentage of people having high blood pressure amongst those who exercise38) 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) The people in the "regular exercise" group probably started exercising because they have high blood pressure. B) Those that do not exercise regularly must be receiving some other treatment to lower their blood pressure. C) 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. D) Mistakes must have been made in measuring blood pressures.

39) A researcher looks at the percentage of people having high blood pressure amongst those who exercise39) 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) 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. B) In spite of exercising, people get older. C) 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. D) 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. 40) Which of the statements below suggests an appropriate level of precision? A) Worldwide there will be 100 million births next year. [to the nearest one hundred million] B) Worldwide there will be 133 million births next year. C) Worldwide there will be 133,147,763 births next year. D) Worldwide there will be 133.147 million births next year.

40)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 41) You use a tape measure to measure people's heights. 41)

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

42)

Use the Consumer Price Index below to answer the question.

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

43)

44) 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.

44)

45) Between 1990 and 2000, a college raised its annual tuition fees from $4490 to $6650. Find 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.

45)

Give an appropriate response. 46) The following table shows the deaths due to the same disease in two cities. Compute the death46) 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

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

Use the Consumer Price Index below to answer the question.

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

47)

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. 48) You estimate the speed of other cars by pulling up behind a car, driving at the same speed, 48) and looking at your speedometer.

Give an appropriate response. 49) Due to poor sales, a company eliminated a number of jobs. Twenty-five percent of the 300 49) 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.

Use the Consumer Price Index below to answer the question.

50) In 1992, Sue rented out her apartment for $750 per month. In 2000 she charged $800 per 50) 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. 51) An agency wishes to determine the number of unemployed people in a town. They 51) 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.

Use the Consumer Price Index below to answer the question.

by 52) The table below shows the federal hourly minimum wage in various years. Complete the table52) 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

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 53) The average income of 100 people is calculated by using the incomes which they reported 53) on credit card applications. These incomes are entered onto a computer and a statistical package is used to calculate the average income.

Give an appropriate response. 54) The tables below show the results of a study examining the incidence of breast cancer among 54) 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.

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, 60,000, 55) and 22,300 respectively.

Give an appropriate response. 56) 56) 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.

For the given measurement, briefly describe any likely sources of random error and any likely sources of systematic error. 57) The average weight of 100 college-age women, found by asking them their weight during 57) interviews conducted at their college.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Consumer Price Index below to answer the question.

58) What was the purchasing power of $1 in 1987 in terms of 1992 dollars? If necessary, round values to the nearest cent. A) $1.35 B) $1.19 C) $0.81 D) $1.24 Solve for the percentage in the problem. Round to the nearest tenth of a percent. 59) 3.3 cases is % of 23.7 cases. A) 7.2 B) 718.2 C) 0.1

D) 13.9

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 60) (3.3 × 1028) ÷ (1.1 × 10-26) A) 3.3 × 102

B) 3.3 × 1054

C) 3 × 102

D) 3 × 1054

Determine whether the source of error represents random or systematic error. 61) 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

58)

59)

60)

61)

Decide whether the statement is believable, given the precision with which it is stated. 62) Last year, the company made $545.2 in profits. A) Not believable at that precision B) Believable

62)

Answer the question. 63) Find the scale ratio for a map if 3 centimeters on the map represents 0.6 kilometer on the ground. A) 1 : 60,000 B) 1 : 20,000 C) 1 : 2,000 D) 1 : 200,000

63)

Determine ratio of A to B. Round as indicated. 64) A = 49 square centimeters is the area of a circle with diameter 14 centimeters. B = 196 square centimeters is the area of a square with sides of length <14 centimeters. (Do not round.) 7 4 A) B) C) D) 7 4

64)

Write the percentage as a fraction or decimal, as indicated. 65) Write as a fraction. 0.3125% 1 1 A) B) 320 32

65) C)

1 160

1 640

Solve the problem. 66) The table below shows the result of a polygraph test conducted on 2000 college students. Students were66) asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds Test finds student lying student truthful Total Has cheated 79 14 93 Has not cheated 207 1700 1907 Total 286 1714 2000 What percentage of those that were found to be truthful were actually lying ? A) 15.1% B) 10.9% C) 72.4%

D) 0.8%

Answer the question. 67) 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) 7.135 m C) 0.7135 m D) 0.007135 m Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 68) 958 people voted for the incumbent candidate out of 1772 voters. What percent voted for the incumbent? A) 185.0% B) 0.1% C) 54.1% D) 0.5%

67)

68)

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 69) (10 × 104 ) ÷ (5 × 106 ) A) -2.0 × 102 B) 2.0 × 102 C) -2.0 × 10-2 D) 2.0 × 10-2

69)

Write as a percent. 70) 0.53 A) 530%

70)

B) 5.3%

C) 0.053%

D) 53%

Solve the problem. 71) Suppose it cost $14.15 to fill a gas tank in 2000. How much would it have cost to fill the same tank in 1995? 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) $11.00 B) $12.22 C) $18.20 D) $10.00 State the number of significant digits and the implied precision of the given number. 72) 3.000505 minutes A) 4 significant digits, precise to the nearest 0.000001 minute B) 7 significant digits, precise to the nearest 0.0001 minute C) 4 significant digits, precise to the nearest 0.0001 minute D) 7 significant digits, precise to the nearest 0.000001 minute

71)

72)

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. 73) In her lifetime my grandmother saw about 6 × 107 hours of commercials on television. 73)

A) Yes

B) No

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. 74) The population of Placerville grew from 4740 a decade ago to 7040 today. 74) A) Absolute change: 2300 B) Absolute change: 2300 Percentage change: 32.7% Percentage change: 48.5% C) Absolute change: -2300 D) Absolute change: 32.7% Percentage change: 48.5% Percentage change: 2300

Restate the fact as indicated. 75) The speed of light is approximately 5,866,000,000,000 miles per year. Express this speed in miles per second. A) 11,160,578.4 miles per second B) 3100.2 miles per second C) 186,009.6 miles per second D) 4,460,000 miles per second Write the percentage as a fraction or decimal, as indicated. 76) Write as a fraction. 3800% A) 380 B) 19

75)

76) C) 38

D) 76

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 77) Last week, Brian earned $165 while Lucy earned $559. $165 is what percentage of $559? A) 70.5% B) 39.4% C) 29.3% D) 29.5%

77)

Use scientific notation to solve the problem. 78) 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 56 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) 8 × 10-7 liters B) 8 × 107 liters C) 1.4 × 107 liters

78)

D) 8 × 101.5 liters

Use the Consumer Price Index below to answer the question.

79) A book cost $35 in 1987. What was its price in 1994 dollars? If necessary, round values to the nearest dollar. A) $44 B) $50 C) $27 D) $46 True or false? 80) It is possible for one person's weight to be 161% less than another person's weight. A) True B) False Find the absolute and relative errors. 81) It took you one hour and 10 minutes to drive home, you estimated the time to be one hour and 23 minutes. A) absolute error: -13 minutes B) absolute error: 13 minutes relative error: -18.6% relative error: 1.9% C) absolute error: 13 minutes D) absolute error: 13 minutes relative error: 15.7% relative error: 18.6% Use scientific notation to perform the following operations. Leave your answer in scientific notation. 82) (20 × 10-2 ) ÷ (5 × 109 ) A) 8.0 × 10-11

C) 4.0 × 107

B) 4.0 × 10-11

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 83) % of 1810 sales is 22 sales. A) 22.2 B) 8227.3 C) 12.2

D) 8.0 × 107

D) 1.2

79)

80)

81)

82)

83)

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. 84) Last year my heart beat 4 × 107 times. 84)

A) No

B) Yes

Write the number in ordinary notation. 85) 5.677 × 10-5 A) 0.0005677

B) 0.000005677

C) -567,700

Write the number in scientific notation. 86) A company produces 732,000 small appliances in one year. A) 7.32 × 10-5 B) 73.2 × 104 C) 7.32 × 105

D) 0.00005677

D) 7.32 × 106

Restate the fact as indicated. 87) 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) 0.8 people per square mile C) 79 people per square mile D) 8 people per square mile Find the absolute and relative errors. 88) The length of the room is 11 feet but you measure it to be 11 feet and 5 inches. A) absolute error: 5 inches B) absolute error: -5 inches relative error: 3.6% relative error: -3.8% C) absolute error: 5 inches D) absolute error: 5 inches relative error: 3.8% relative error: 4.5% Write the number in ordinary notation. 89) 2 × 104 A) 2000

B) 20,000

C) 2,000,000

D) 200,000

C) 2.07 × 10-2

D) -2.07 × 103

C) 370,450

D) 3,704,500

Round to the indicated place value. 92) Round to the nearest hundredth: 12.55562 A) 12.57 B) 12.56

C) 12.556

D) 12.5556

Write the number in scientific notation. 93) 89,000,000 A) 8.9 × 106 B) 8.9 × 10-6

C) 8.9 × 107

D) 8.9 × 10-7

Write the number in scientific notation. 90) 0.00207 A) 2.07 × 10-4 B) 2.07 × 10-3 Write the number in ordinary notation. 91) 3.7045 × 105 A) 37,045

B) 185.225

85)

86)

87)

88)

89)

90)

91)

92)

93)

Solve the problem. 94) 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% Round to the indicated place value. 95) Round to the nearest thousandth: 1.4981 A) 1.498 B) 1.50

C) 1.49

Write the percentage as a fraction or decimal, as indicated. 96) Write as a decimal. 986% A) 0.986 B) 9.86

95)

96)

Write the number in ordinary notation. 97) 7.0289 × 10-7 A) -702890,000

D) 1.499

94)

B) 0.000000070289

C) 98.6

D) 9.87

C) 0.0000070289

D) 0.00000070289

Write the percentage as a fraction or decimal, as indicated. 98) Write as a decimal. 46% A) 0.046 B) 4.6

C) 0.46

D) 0.35

Write the number in scientific notation. 99) 0.0004 A) -4 × 104 B) 4 × 10-3

C) 4 × 10-4

D) 4 × 10-5

97)

98)

99)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 100) The average amount spent on food last year by the residents of your town was $3100 per person. 100) The population of your town is 41,480. What was the total amount spent on food last year by the residents of your town? A) $129,000,000 B) $128,600,000 C) $128,588,000 D) $130,000,000

Write as a percent. 101) 3.1 A) 31%

B) 0.31%

C) 0.0031%

D) 310%

101)

Use the Consumer Price Index below to answer the question.

102) In 1996, the federal minimum hourly wage was $3.50. Convert this to 2000 dollars. If necessary, round values to the nearest cent. A) $3.95 B) $3.19 C) $3.30 D) $3.84 Find the absolute and relative errors. 103) Your weight is 107 pounds but the scale indicates that it is 103 pounds. A) absolute error: 4 pounds B) absolute error: -4 pounds relative error: 3.7% relative error: -3.7% C) absolute error: -4 pounds D) absolute error: -4 pounds relative error: -3.9% relative error: -40% Round to the indicated place value. 104) Round to the nearest whole number: 720.553 A) 721 B) 720.6

C) 9.7

D) 9.5

Carry out the indicated operation and give your answer with the specified number of significant digits. 106) (4.9 × 10-9 ) ÷ (7.273 × 10-2 ); 3 significant digits A) 6.7 × 10-8

B) 7 × 10-8

C) 6.737 × 10-8

103)

104)

C) 720

105) Round to the nearest tenth: 9.618 A) 9.6 B) 9.62

102)

105)

106)

D) 6.74 × 10-8

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. 107) In 1960, in the town of Thornton the percentage of 50 year old women that had never been married 107) was 9.8%. Last year, the percentage of 50 year old women that had never been married was 27.3%. A) Absolute change: 17.5 percentage points B) Absolute change: 178.6 percentage points Percentage change: 178.6% Percentage change: 17.5% C) Absolute change: 17.5 percentage points D) Absolute change: -17.5 percentage points Percentage change: 64.1% Percentage change: -64.1%

Solve the problem. 108) Computer sales for a certain company have reached $41 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) $4.9 million B) $36.2 million C) $48.3 million D) $45.9 million Decide whether the statement is believable, given the precision with which it is stated. 109) A mountain's peak is 21,600 feet above sea level. A) Believable B) Not believable at that precision 110) Using a meter stick, I measured the length of the kitchen to within 0.0664 centimeters. A) Believable B) Not believable at that precision Write as a percent. 29 111) 250 A) 11.6%

109)

110)

111) B) 12

C) 116%

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 112) % of 125 cartons is 18.9 cartons. A) 0.2 B) 0.1 C) 15.1

D) 1.16%

D) 661.4

State the number of significant digits and the implied precision of the given number. 113) 302 people A) 2 significant digits, precise to the nearest 100 people B) 3 significant digits, precise to the nearest person C) 2 significant digits, precise to the nearest person D) 1 significant digit, precise to the nearest 100 people Write as a percent. 114) 9 A) 450%

108)

B) 900%

C) 0.9%

113)

D) 0.09%

Solve the problem. 115) The appliance store where the Scott family shops offers a 8% discount for paying cash. The Scott family received a discount of $45. What was their total bill before the discount? A) $4 B) $400 C) $563 D) $6 True or false? 116) If I earn 50% more than you, then you must earn 33.3% less than me. A) True B) False Solve the problem. 117) Suppose the current cost of gasoline is $3.07 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) 18.5 B) 5.4 C) 250.3 D) 541.4

112)

114)

115)

116)

117)

Determine ratio of A to B. Round as indicated. 118) A = 15 and B = 3 (Do not round.) 1 3 A) B) 5 5

5 C) 3

119) A = 2.9 million is the population of City A B = 1.7 million is the population of City B (Round to the nearest hundredth when necessary.) A) 0.17 B) 17.06

D) 5

119)

Write the number in ordinary notation. 120) 9 × 10-4 A) 0.009

118)

B) -90,000

Write the number in scientific notation. 121) 58.7 A) 5.87 × 101 B) 5.87 × 10-2

C) 1.71

D) 0.59

C) 0.0009

D) 0.00009

C) 5.87 × 10-1

D) 5.87 × 102

120)

121)

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. 122) In the last election, in a certain city the percentage of eligible voters who voted in the local election 122) was 62.5%. This year, the percentage fell to 52.8%. A) Absolute change: -9.7 percentage points B) Absolute change: -9.7 percentage points Percentage change: -18.4% Percentage change: -15.5% C) Absolute change: 9.7 percentage points D) Absolute change: 9.7 percentage points Percentage change: 18.4% Percentage change: -15.5%

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 123) (6 × 10-4 ) ÷ (12 × 102 ) A) -5.0 × 105 B) 5.0 × 10-7 C) -5.0 × 10-7 D) 5.0 × 105 Carry out the indicated operation and give your answer with the specified number of significant digits. 124) (9.1 × 109 ) ÷ (3.2 × 10-5 ); 2 significant digits A) 2.8 × 1014

B) 2.8 × 104

C) 3 × 1014

D) 2.84 × 1014

State the number of significant digits and the implied precision of the given number. 125) 50,000.010 A) 8 significant digits, precise to the nearest thousandth B) 2 significant digits, precise to the nearest hundredth C) 3 significant digits, precise to the nearest thousandth D) 7 significant digits, precise to the nearest hundredth Write the number in scientific notation. 126) 177 A) 1.77 × 102 B) 1.77 × 101 127) The population of a small country is 4,394,000 . A) 4.394 × 105 B) 4.394 × 104

123)

124)

125)

126)

C) 1.77 × 103

D) 1.77 × 10-2

C) 4.394 × 106

D) 4.394 × 10-5

127)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 128) 3 × 10-8, 3 × 10-32 128)

A) 1024

B) 1040

C) 10-24

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 129) % of 7 gross is 0.03 gross. A) 0.4 B) 4.3 C) 233.3

D) 101/4

D) 42.9

129)

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. 130) At a certain college, the percentage of male students decreased from 59% in 1970 to 45% this year. 130) A) Absolute change: 14 percentage points B) Absolute change: -14 percentage points Percentage change: 31.1% Percentage change: -31.1% C) Absolute change: -23.7 percentage points D) Absolute change: -14 percentage points Percentage change: -14% Percentage change: -23.7%

Write as a percent. 2 131) 7

131)

A) 28.6%

B) 285.7%

C) 2.9%

D) 20.0%

Answer the question. 132) 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 : 6160 D) 1 : 73,920 Determine ratio of A to B. Round as indicated. 133) A = $93,000 is the average cost of a home in Town A and B = $210,000 is the average cost of a home in Town B. (Round to the nearest hundredth when necessary.) A) 0.44 B) 0.04 C) 4.43 D) 2.26

132)

133)

Solve the problem. 134) The table below shows the result of a polygraph test conducted on 2000 college students. Students were134) asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds Test finds student lying student truthful Total Has cheated 78 14 92 Has not cheated 223 1685 1908 Total 301 1699 2000 What percentage of those that were found to be lying were actually telling the truth? A) 88.3% B) 15.2% C) 74.1% D) 84.8%

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 135) You have covered 62.3 miles of a 2600 mile journey. How much further do you have to go? 135) A) 2537.7 miles B) 2538 miles C) 2500 miles D) 2540 miles

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. 136) Last year the Mayor of the town of Little Heath had an approval rating of 73%. This year his 136) approval rating had fallen to 25%. A) Absolute change: -48 percentage points B) Absolute change: -48 percentage points Percentage change: -65.8% Percentage change: -6.6% C) Absolute change: 48 percentage points D) Absolute change: -48 percentage points Percentage change: 192% Percentage change: -192%

True or false? 137) 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 Determine whether the source of error represents random or systematic error. 138) 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) Random error B) Systematic error

137)

138)

Use scientific notation to solve the problem.

139) 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) 5.0 × 1031 bacteria C) 2.0 × 1030 bacteria

139)

B) 2.0 × 10-30 bacteria D) 5.0 × 10-31 bacteria

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. 140) In the next hour, roughly 109 people will die worldwide. 140)

A) No

B) Yes

Round to the indicated place value. 141) Round to the nearest ten thousandth: 16.98479 A) 16.985 B) 16.9848

C) 16.9847

D) 16.98

True or false? 142) If you score 60% on the midterm math exam and 70% on the final exam, your overall score will be greater than 65%. Assume that the final counts for 60% of the grade and that the midterm counts for 40% of the grade. A) True B) False Write the number in scientific notation. 143) The hard drive of the computer has a capacity of 30 gigabytes. (The prefix giga means 1 billion). A) 3 × 109 bytes B) 30 × 109 bytes C) 3 × 1013 bytes

142)

143) D) 3 × 1010 bytes

Carry out the indicated operation and give your answer with the specified number of significant digits. 144) 26.8 × 0.117; 3 significant digits A) 3 B) 3.14 C) 3.1 D) 3.136

141)

144)

Use scientific notation to solve the problem.

145) 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 × 10-10 m B) 5.7 × 1010 m C) 1.50 × 1010 m D) 1.50 × 1011 m

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 146) 960 employees is % of 731 employees. A) 76.1 B) 1.3 C) 0.1

D) 131.3

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 147) The weight of the child is 5 kilos while the weight of her father is 96.2 kilos. 96.2 kilos is what percent of 5 kilos? A) 19,240.0 B) 5.2 C) 0.5 D) 1924.0

145)

146)

147)

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. 148) It would take me about 1 × 106 seconds to walk across the United States (from New York to 148) California). A) No

B) Yes

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. 149) In a certain country, the life expectancy for men is 70.6 years while the life expectancy for women is 149) 75.7 years. A) Absolute difference: -5.1 years B) Absolute difference: -5.1 years Relative difference: -7.2% Relative difference: -0.7% C) Absolute difference: 5.1 years D) Absolute difference: -5.1 years Relative difference: 7.2% Relative difference: -6.7%

Carry out the indicated operation and give your answer with the specified number of significant digits. 150) 533 ÷ 0.0201; 1 significant digit A) 26,517.4 B) 26,517 C) 27,000 D) 30,000

150)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 151) 1048, 1016 151)

A) 1032

B) 1048 - 1016

C) 103

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 152) $957 is % of $1745. A) 0.5 B) 182.3 C) 54.8

D) 32

D) 0.1

Determine ratio of A to B. Round as indicated. 153) A = 66.7 is the average number of points scored in a college basketball game. B = 53.5 is the average number of points scored in a high school basketball game. (Round to the nearest hundredth when necessary.) A) 0.8 B) 12.47 C) 1.25 D) 0.12

152)

153)

Solve the problem. 154) The table below shows the result of a polygraph test conducted on 2000 college students. Students were154) asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds Test finds student lying student truthful Total Has cheated 85 13 98 Has not cheated 209 1693 1902 Total 294 1706 2000 What percentage of those that were lying were found to be truthful? A) 13.3% B) 11% C) 28.9%

D) 0.8%

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. 155) Last year the total amount spent by Americans on food was about 1011 dollars. 155)

A) No

B) Yes

Solve the problem. 156) Suppose it cost $2.84 to fill a gas tank in 1965. How much would it cost to fill the same tank in 1975? 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) $5.16 B) $6.45

C) $5.73

D) $7.37

Round to the indicated place value. 157) Round to the nearest hundredth: 0.351 A) 0.34 B) 0.36

C) 0.35

D) 0.4

True or false? 158) 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

156)

157)

158)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 159) 1 trillion, 1 hundred 159) 14 6 10 12 2 A) 10 B) 10 C) 10 D) 10 - 10

Use the Consumer Price Index below to answer the question.

160) Suppose you needed $48,000 to maintain a particular standard of living in 1986. How much would you have needed in 1994 to maintain the same standard of living? If necessary, round values to the nearest thousandth. A) $35,000 B) $68,000 C) $60,000 D) $65,000 Solve the problem. 161) Brand X copier advertises that its copiers run 19% longer between service calls than its competitor. If Brand X copiers run 49,900 copies between services, how many copies would the competitor run? A) 59,381 copies B) 40,419 copies C) 41,933 copies D) 27,569 copies

160)

161)

Restate the fact as indicated.

162) In a given year, the U.S.annual energy consumption is roughly 1 × 1020 Joules. Express this as energy consumption per person per second. Assume that the U.S. population during this year is roughly 280 million. . A) 680,000 Joules per person per second C) 3.6 × 1011 Joules per person per second

B) 190.3 Joules per person per second D) 11,324.9 Joules per person per second

Write the number in ordinary notation. 163) 7.8 × 106 A) 468

162)

B) 780,000

C) 7,800,000

D) 78,000,000

Determine whether the source of error represents random or systematic error. 164) 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) Systematic error B) Random error Use scientific notation to solve the problem. 165) 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) 7.61 × 106 years

B) 1 × 1014 years D) 3.17 × 106 years

C) 3.17 × 101.3 years

163)

164)

165)

Determine ratio of A to B. Round as indicated. 166) A = 6 and B = 48 (Do not round.) 3 A) 8 B) 4

1 C) 8

166) D) 6

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 167) Thompson's Hardware spent $40,570 this year on business insurance alone. If total sales were $707,800, what percent of total sales was spent on business insurance? Round to the nearest tenth of a percent. A) 174.0% B) 17.4% C) 5.7% D) 0.6% Solve the problem. 168) A store manager paid $64 for an item and set the selling price at $86.40. What was the percent markup? A) 36% B) 33% C) 35% D) 25% 169) Find the gasoline price index for 1975 using the 1955 price as the reference value. Use the table below.

167)

168)

169)

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) 175.3

B) 19.5

C) 51.3

D) 194.8

Restate the fact as indicated. 170) Worldwide there are approximately 132 million births per year. Express this quantity in births per second. A) 101 births per second B) 63,300 births per second C) 4.2 births per second D) 251 births per second Write the percentage as a fraction or decimal, as indicated. 171) Write as a fraction. 32% 8 4 A) B) 25 25

170)

171) C)

Determine ratio of A to B. Round as indicated. 172) A = 22.8% is the divorce rate in City A B = 31.6% is the divorce rate in City B (Round to the nearest hundredth when necessary.) A) 0.07 B) 7.22

16 5

16 25

172)

C) 1.39

D) 0.72

Answer the question. 173) 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) 0.143 m B) 0.00143 m C) 0.000143m D) 0.0143 m True or false? 174) It is possible for one person's weight to be 400% more than another person's weight. A) True B) False

173)

174)

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. 175) In the college there are 1310 male students and 1150 female students. 175) A) Absolute difference: 160 B) Absolute difference: -160 Relative difference: 13.9% Relative difference: -12.2% C) Absolute difference: 160 D) Absolute difference: 160 Relative difference: 12.2% Relative difference: 1.4%

Write the number in ordinary notation. 176) 1.229 × 10-6 A) 0.0000001229

B) -1,229,000

Write the number in scientific notation. 177) 0.05 × 107 A) 0.5 × 106

B) 5 × 10<6

Round to the indicated place value. 178) Round to the nearest tenth: 0.3361 A) 0.2 B) 0.34 179) Round to the nearest whole number: 39.3 A) 38 B) 39

C) 0.000001229

D) 0.00001229

C) 5 × 105

D) 5 × 109

C) 0.3

D) 0.4

C) 40

Determine whether the source of error represents random or systematic error. 180) 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 Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 181) Brett has saved $768 at the bank. He wants to save $3120 for a trip to Alaska. What percent of his goal has been reached? A) 2.5% B) 4.1% C) 24.6% D) 41% True or false? 182) If 19% of the students in Mr. Harris's class speak Spanish and 7% speak French, then 26% must speak either Spanish or French A) True B) False

176)

177)

178)

179)

180)

181)

182)

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. 183) Last year the total revenue for Clearline phone company was $13.6 million while the revenue for 183) its competitor, the Speakmore was $8.6 million. A) Absolute difference: $-5 million B) Absolute difference: $5 million Relative difference: -36.8% Relative difference: 36.8% C) Absolute difference: $5 million D) Absolute difference: $5 million Relative difference: 5.8% Relative difference: 58.1%

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 184) 1012, 1036 184)

A) 10-24

1 3

C) 101/3

D) 1012 - 1036

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 185) (4 × 104 ) × (2 × 102 ) A) 8.0 × 107 B) 8.0 × 108 C) 8.0 × 105 D) 8.0 × 106

185)

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. 186) Two years ago I earned $87,000. Last year I earned $60,000. 186) A) Absolute change: $-27,000 B) Absolute change: $27,000 Percentage change: -45% Percentage change: 31% C) Absolute change: $-27,000 D) Absolute change: $27,000 Percentage change: -31% Percentage change: 45%

Round to the indicated place value. 187) Round to the nearest hundredth: 13.9263 A) 13.925 B) 13.94

C) 13.93

D) 13.926

Carry out the indicated operation and give your answer with the specified number of significant digits. 188) 2518 × 33.73; 2 significant digits A) 84,932.14 B) 84,900 C) 80,000 D) 85,000 Write as a percent. 1 189) 3 A) 333.333333%

187)

188)

189) B) 33.3333333%

C) 3.33333333%

D) 30%

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 190) You drive from your house to the store, a distance of 1.94 miles, then you drive another 36 miles to 190) work. What is the total distance that you drive? A) 38 miles B) 37.9 miles C) 37.94 miles D) 40 miles

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 191) (5 × 10-5 ) ÷ (10 × 10-3 ) A) 2.0 × 10-2 B) 2.0 × 108 C) 5.0 × 107 D) 5.0 × 10-3 192) (3 × 106 ) × (7 × 10-3 ) A) 2.1 × 102

B) 2.1 × 103

C) 2.1 × 10-2

D) 2.1 × 104

191)

192)

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. 193) The book contains 106 letters. 193)

A) Yes

B) No

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 194) $788.06 is % of $53.19. A) 1481.6 B) 14,816.0 C) 0.7

D) 6.7

194)

Solve the problem. 195) Find the gasoline price index for 1985 using the 2000 price as the reference value. Use the table below. 195) 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) 84.9

B) 7.7

C) 77.2

Write the number in ordinary notation. 196) 4.053 × 106 A) 243.18

B) 405,300

C) 40,530,000

D) 129.6

D) 4,053,000

196)

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. 197) In his lifetime my grandfather spent 5 × 104 hours watching television. 197)

A) No

B) Yes

Find the absolute and relative errors. 198) The true distance from your home to your office is 34.8 miles but your odometer reads 35.9 miles. A) absolute error: 1.1 miles B) absolute error: 1.1 miles relative error: 0.3% relative error: 3.1% C) absolute error: -1.1 miles D) absolute error: 1.1 miles relative error: -3.2% relative error: 3.2%

198)

Solve the problem. 199) The table below shows a housing index that can be used to compare housing prices in different cities. 199) 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 $860,000 in Palo Alto. Find the price of a comparable house in Manhattan. A) $1,166,301 B) $634,141 C) $933,041 D) $1,049,671

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. 200) The population density in country A is 76 people per square mile while in country B, it is 630 200) people per square mile. A) Absolute difference: -554 people per square mile Relative difference: -87.9% B) Absolute difference: -554 people per square mile Relative difference: -8.8% C) Absolute difference: 554 people per square mile Relative difference: 728.9% D) Absolute difference: -554 people per square mile Relative difference: -728.9%

Write as a percent. 201) 0.538 A) 0.0538%

B) 53.8%

C) 0.538%

D) 538%

201)

Use the Consumer Price Index below to answer the question.

202) Suppose you needed $54,000 to maintain a particular standard of living in 2000. How much would you have needed in 1986 to maintain the same standard of living? If necessary, round values to the nearest thousandth. A) $36,000 B) $33,000 C) $34,000 D) $85,000 True or false? 203) In Fremont in 1990, the mayor's approval rating was 80%. In 1998, his approval rating was only 60%. True or false? in absolute terms his approval rating decreased by 20 percentage points whereas in relative terms, it decreased by 25%. A) True B) False Use scientific notation to perform the following operations. Leave your answer in scientific notation. 204) (4.8 × 1024) ÷ (1.2 × 106 ) A) 4 × 104

B) 4.8 × 1018

C) 4 × 1030

D) 4 × 1018

Answer the question. 205) 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) 0.04497 m B) 0.4497 m C) 44.97 m D) 4.497 m State the number of significant digits and the implied precision of the given number. 206) 26,000 A) 5 significant digits, precise to the nearest unit B) 2 significant digits, precise to the nearest 1000 C) 5 significant digits, precise to the nearest 1000 D) 2 significant digits, precise to the nearest 10,000

202)

203)

204)

205)

206)

Solve the problem. 207) The table below shows the number of people testing positive for a certain disease amongst those who do 207) have the disease and amongst those who don't. Use the table to answer the question. Test Test positive negative Total Disease 119 14 133 No disease 1047 8820 9867 Total 1166 8834 10,000 What percentage of those that don't have the disease tested negative? A) 88.2% B) 89.4% C) 98.7%

Round to the indicated place value. 208) Round to the nearest thousandth: 3.6877 A) 3.688 B) 3.69

C) 3.687

D) 99.8%

D) 3.689

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 209) Joe's Discount claims that of its 5975 items in inventory, 5373 items are clothes, while the rest are non-clothes. What percent of total inventory is non-clothes? Round to the nearest tenth of a percent. A) 9.9% B) 10.1% C) 0.9% D) 89.9% Carry out the indicated operation and give your answer with the specified number of significant digits. 210) 781 ÷ 0.00716; 3 significant digits A) 109,000 B) 109,078 C) 109,100 D) 109,078.212

208)

209)

210)

Use scientific notation to solve the problem. 211) 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 × 10-7 sec

Write the number in scientific notation. 212) 4100 million A) 4.1 × 109 B) 4.1 × 1010

C) 1.4 × 105 sec

D) 1.4 × 1012 sec

C) 41 × 108

D) 4.1 × 103

Find the absolute and relative errors. 213) The length of the piece of fabric is 25 inches but you measure it as 23.8 inches. A) absolute error: -1.2 inches B) absolute error: 1.2 inches relative error: -5% relative error: 4.8% C) absolute error: -1.2 inches D) absolute error: -1.2 inches relative error: -12% relative error: -4.8% Determine whether the source of error represents random or systematic error. 214) 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

211)

212)

213)

214)

Answer the question. 215) Find the scale ratio for a map if 1 centimeter on the map represents 100 kilometers on the ground. A) 1 : 10,000,000 B) 1 : 100,000 C) 1 : 10,000 D) 1 : 1,000,000 Write the number in ordinary notation. 216) 7.14 × 103 A) 7140

B) 714

C) 214.2

D) 71,400

215)

216)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 217) Find your speed by dividing the distance you traveled, 267 kilometers, by the time, 2.1 hours. 217) A) 130 kilometers per hour B) 100 kilometers per hour C) 127 kilometers per hour D) 127.1 kilometers per hour

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 218) Students at East Central High School earned $286 selling subscriptions. They want to make $3120 for a club trip. What percent of their goal has been reached? A) 0.9% B) 109% C) 10.9% D) 9.2%

218)

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. 219) The value of Anna's house increased from $250,000 when she bought it 20 years ago to $1.31 219) million today. A) Absolute change: $1,060,000 B) Absolute change: $1,060,000 Percentage change: 80.9% Percentage change: 42.4% C) Absolute change: $-1,060,000 D) Absolute change: $1,060,000 Percentage change: 424% Percentage change: 424%

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 220) Maria's company has 979 employees, Ruth's company has 702 employees. 979 is what percent of 702 ? A) 0.1 B) 1.4 C) 71.7 D) 139.5 Write the percentage as a fraction or decimal, as indicated. 221) Write as a fraction. 1 37 % 2 A)

15 4

220)

221)

3 8

3 16

3 4

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. 222) In Jose's hometown, there are 218,000 people whose first language is English and 50,000 whose first 222) language is Spanish . A) Absolute difference: 168,000 B) Absolute difference: -168,000 Relative difference: 336% Relative difference: -77.1% C) Absolute difference: 168,000 D) Absolute difference: 168,000 Relative difference: 33.6% Relative difference: 77.1%

State the number of significant digits and the implied precision of the given number. 223) 0.00000046 meter A) 8 significant digits, precise to the nearest 0.00000001 meter B) 2 significant digits, precise to the nearest 0.0000001 meter C) 8 significant digits, precise to the nearest 0.0000001 meter D) 2 significant digits, precise to the nearest 0.00000001 meter

223)

224) 6.700 × 108 A) 4 significant digits, precise to the nearest thousandth B) 2 significant digits, precise to the nearest 100,000 C) 4 significant digits, precise to the nearest 100,000 D) 9 significant digits, precise to the nearest unit

224)

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 225) (3 × 102 ) + (2 × 101 ) A) 5 × 101

B) 3.2 × 103

C) 3.2 × 102

D) 5 × 102

Use scientific notation to solve the problem. 226) 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 × 103 hr

C) 3.2 × 104 hr

B) 3.2 hr

225)

226)

D) 3.2 × 102 hr

Decide whether the statement is believable, given the precision with which it is stated. 227) A business projects next year's profits to be $5,950,000. A) Believable B) Not believable at that precision

227)

Write as a percent. 228) 0.00841 A) 0.4205%

228)

B) 0.000841%

C) 0.0841%

D) 0.841%

Decide whether the statement is believable, given the precision with which it is stated. 229) There are 485,324,152 flowers in the botanical gardens. A) Believable B) Not believable at that precision

229)

Answer the question.

230) The distance from the Earth to the Sun is about 1.5 × 108 km, while the distance from the Earth to the moon is about 3.8 × 105 km. If a scale model of the solar system is constructed so that the

230)

distance from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon? A) 39.5 m B) 6.36 m C) 0.25 m D) 39, 474 m

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 231) If you buy 207 items which weigh 0.025 lb each, what is the total weight of your purchase? 231) A) 5.2 lb B) 5.18 lb C) 5.175 lb D) 5 lb

Write the percentage as a fraction or decimal, as indicated. 232) Write as a decimal. 99.1% A) 9.91 B) 0.991

232) C) 0.0991

D) 0.881

Solve the problem. 233) The table below shows the result of a polygraph test conducted on 2000 college students. Students were233) asked whether they had ever cheated on a test. All of them denied having cheated. Use the table to answer the question. Test finds Test finds student lying student truthful Total Has cheated 84 13 97 Has not cheated 210 1693 1903 Total 294 1706 2000 What percentage of those that were telling the truth were found to be lying? A) 13.4% B) 71.4% C) 89%

Write as a percent. 234) 22.392 A) 2.2392%

B) 0.22392%

C) 2239.2%

D) 11%

D) 22.392%

234)

Solve the problem. 235) The table below shows the number of people testing positive for a certain disease amongst those who do 235) have the disease and amongst those who don't. Use the table to answer the question. Test Test positive negative Total Disease 112 10 122 No disease 1006 8872 9878 Total 1118 8882 10,000 What percentage of those that tested negative actually have the disease? A) 0.1% B) 99.9% C) 11.2%

Write the number in ordinary notation. 236) 3.93 × 10-4 A) 0.0000393

B) 0.000393

C) -393,000

D) 8.2%

D) 0.00393

Answer the question. 237) Find the scale ratio for a map if 4 centimeters on the map represents 10 kilometers on the ground. A) 1 : 25,000 B) 1 : 250,000 C) 1 : 1,000,000 D) 1 : 2500

236)

237)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 238) Subtract the weight 2.6 lb from 207 lb. 238) A) -204.4 lb B) 200 lb C) 204 lb D) 204.4 lb

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. 239) Brett and Helina went on a 52-mile canoe trip with their class. On the first day they traveled 13 miles. What percent of the total distance was that? A) 400% B) 25% C) 4% D) 0.25% Restate the fact as indicated. 240) 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 $24,642.86 per person B) About $246.43 per person C) About $2464.29 per person D) About $246,428.57 per person True or false? 241) 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

239)

240)

241)

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. 242) The unemployment rate in Midtown a decade ago was 20%. This year it was 24%. 242) A) Absolute change: 4 percentage points B) Absolute change: 4 percentage points Percentage change: 16.7 % Percentage change: 20% C) Absolute change: 20 percentage points D) Absolute change: -4 percentage points Percentage change: 4% Percentage change: 16.7 %

Write as a percent. 9 243) 1 14 A) 82.1428571%

243) B) 164.285714%

C) 1.64285714%

D) 16.4285714%

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 244) At the beginning of last year, the population of your city was 372,000. By the end of the year it had 244) increased by 3522 people. What was the population at the end of the year? A) 380,000 B) 375,500 C) 375,522 D) 376,000 Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 245) 5.6 × 108 , 1.4 × 10-4 245)

A) 4 × 104

B) 4 × 1012

C) 4 × 102

D) 4.2 × 1012

Use scientific notation to solve the problem. 246) How many liters of oil are needed to supply the electrical energy needs of an average U.S. home for 10 weeks? Assume that the energy released by burning one liter of oil is 1.2 × 107 joules and that 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) 2.4 liters B) 16.8 liters C) 291.7 liters D) 41.7 liters

246)

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 247) % of 61 clients is 682 clients. A) 111.8 B) 0.9 C) 1118.0

D) 0.1

247)

Solve the problem. 248) The table below shows a housing index that can be used to compare housing prices in different cities. 248) 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 $210,000 in Spokane. Find the price of a comparable house in Juneau. A) $163,800 B) $242,308 C) $296,154 D) $269,231 Use the Consumer Price Index below to answer the question.

249) Find the inflation rate from 1986 to 1987. If necessary, round values to the nearest tenth. A) 4% B) 3.6% C) 3.5% D) 1.0% Determine whether the source of error represents random or systematic error. 250) A survey is conducted on smoking amongst teenagers. When questioned by adults, teenagers tend to underreport how much they smoke. A) Systematic error B) Random error Solve the problem. 251) An outlet store had monthly sales of $62,000 and spent 18% of it on legal fees. How much was spent on legal fees? A) $111,600 B) $344,444 C) $34,444 D) $11,160 Round to the indicated place value. 252) Round to the nearest hundred: 159.716 A) 200 B) 160

C) 100 38

249)

250)

251)

252)

State the number of significant digits and the implied precision of the given number. 253) 9100.0 A) 3 significant digits, precise to the nearest tenth B) 5 significant digits, precise to the nearest 100 C) 2 significant digits, precise to the nearest 100 D) 5 significant digits, precise to the nearest tenth

253)

Use scientific notation to solve the problem. 254) 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 × 107 miles

B) 6.0 × 1012 miles

C) 6.0 × 1014 miles

254)

D) 6.0 × 105 miles

Solve the problem. 255) Suppose the current cost of gasoline is $3.23 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) 202.5 B) 37.3 C) 268 D) 2.7

255)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significant digits. 256) A city has a deficit of $40.9 million. How much is this per person if the population of the city is 256) 279,600? A) $150 per person B) $146.3 per person C) $100 per person D) $146 per person

Round to the indicated place value. 257) Round to the nearest thousandth: 4.42576 A) 4.426 B) 4.427

C) 4.4258

D) 4.425

257)

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. 258) My age in seconds is about 5 × 109 . 258)

A) Yes

B) No

Answer the question. 259) Find the scale ratio for a map if 1 inch on the map represents 10 miles on the ground. A) 1 : 633,600 B) 1 : 63,360 C) 1 : 52,800 D) 1 : 10 Write the percentage as a fraction or decimal, as indicated. 260) Write as a decimal. 0.16% A) 0.016 B) 0.16

259)

260) C) 0.0026

D) 0.0016

Solve the problem. 261) The table below shows the number of people testing positive for a certain disease amongst those who do 261) have the disease and amongst those who don't. Use the table to answer the question. Test Test positive negative Total Disease 112 15 127 No disease 1201 8672 9873 Total 1313 8687 10,000 What percentage of those that tested positive actually have the disease? A) 1.3% B) 1.1% C) 88.2%

D) 8.5%

Solve for the percentage in the problem. Round to the nearest tenth of a percent. 262) $18.33 is % of $275.74. A) 6.6 B) 66.0 C) 1504.3

D) 150.4

262)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 263) One million, one millionth 263) 12 11 6 -1 -6 A) 10 B) 10 C) 10 D) 10 - 10

Write the percentage as a fraction or decimal, as indicated. 264) Write as a decimal. 950% A) 9.5 B) 9.51

264) C) 95

D) 0.95

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. 265) The total rainfall in Laketown last year was 7.4 inches. This year it was 0.8 inches. 265) A) Absolute change: -6.6 in. B) Absolute change: -6.6 in. Percentage change: -8.9% Percentage change: -825% C) Absolute change: -6.6 in. D) Absolute change: 6.6 in. Percentage change: -89.2% Percentage change: 825%

Determine whether the source of error represents random or systematic error. 266) A government census fails to include homeless people. A) Random error B) Systematic error

266)

Solve the problem. 267) Midtown Antiques collects 3% sales tax on all sales. If total sales including tax are $1813.61, find the portion that is the tax amount. A) $1760.79 B) $42.82 C) $52.82 D) $54.41 Solve for the percentage in the problem. Round to the nearest tenth of a percent. 268) 96.0 yards is % of 7 yards. A) 0.7 B) 7.3 C) 13,714.0

D) 1371.4

267)

268)

Round to the indicated place value. 269) Round to the nearest ten: 86.1 A) 90

B) 89

269)

C) 91

True or false? 270) If the value of my home has quadrupled since I bought it, that means its value has increased by 400%. A) True B) False Find the absolute and relative errors. 271) Your credit card applies a finance charge of $24.69. The finance charge should have been $22.28. A) absolute error: $2.41 B) absolute error: -$2.41 relative error: 9.8% relative error: -10.8% C) absolute error: $2.41 D) absolute error: $2.41 relative error: 24.1% relative error: 10.8% Write the percentage as a fraction or decimal, as indicated. 272) Write as a fraction. 0.075% 3 3 A) B) 2000 8000

270)

271)

272) C)

3 400

3 4000

Use the Consumer Price Index below to answer the question.

273) A meal in a restaurant cost $34 in 2000. What was its price in 1997 dollars? If necessary, round values to the nearest dollar. A) $36 B) $31 C) $30 D) $32 State the number of significant digits and the implied precision of the given number. 274) 212.2 A) 1 significant digit, precise to the nearest tenth B) 1 significant digit, precise to the nearest unit C) 4 significant digits, precise to the nearest unit D) 4 significant digits, precise to the nearest tenth

273)

274)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 275) 1.2 × 10-5 , 4.8 × 10-15 275)

A) 2.5 × 109

B) 2.5 × 101/3

Determine ratio of A to B. Round as indicated. 276) A = 280 and B = 430 (Do not round.) 1 1 A) B) 43 28

C) 2.5 × 1020

D) 2.5 × 1010

43 C) 28

28 D) 43

Use scientific notation to solve the problem. 277) 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 sec B) 7.6 × 102 min

C) 76 sec

Write the number in scientific notation. 278) 520,000 A) 5.2 × 105 B) 5.2 × 10-4

C) 5.2 × 10-5

276)

277)

D) 7.6 × 103 sec

D) 5.2 × 104

278)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 279) 400 million, 8 trillion 279) A) 5 × 10-4 B) 0.5 × 102/3 C) 5 × 10-7 D) 5 × 10-5

Solve the problem. 280) The table below shows the number of people testing positive for a certain disease amongst those who do 280) have the disease and amongst those who don't. Use the table to answer the question. Test Test positive negative Total Disease 112 11 123 No disease 1086 8791 9877 Total 1198 8802 10,000 What percentage of those that have the disease tested positive? A) 91.1% B) 9.3% C) 12%

D) 89%

Use scientific notation to solve the problem. 281) The national debt of a small country is $6,440,000,000 and the population is 2,794,000. What is the amount of debt per person? A) $2.30 B) $2.30 × 103 C) $23.00 D) $2.30 × 106 Solve the problem. 282) In a local election, 27,700 people voted. This was an increase of 5% over the last election. How many people voted in the last election? A) 26,315 people B) 26,381 people C) 29,158 people D) 29,085 people

281)

282)

Round to the indicated place value. 283) Round to the nearest tenth: 1.59 A) 2 B) 1.6

C) 1.7

D) 1.5

Use scientific notation to perform the following operations. Leave your answer in scientific notation. 284) (5 × 109 ) - (3 × 108 ) A) 2 × 109

B) 4.7 × 109

C) 4.7 × 108

D) 2 × 101

283)

284)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is than the second. 285) 1 billion, 1 thousand 285) A) 1012 B) 109 - 103 C) 103 D) 106

Write the number in scientific notation. 286) A beam of light can travel from my house to yours in 600 nanoseconds. (the prefix nano means one billionth). A) 6 × 10-6 B) 6 × 10-7 C) 6 × 10-9 D) -6 × 107 Solve the problem. 287) In a local election, 25,100 people voted. This was a decrease of 8% over the last election. How many people voted in the last election? A) 23,092 people B) 23,241 people C) 27,108 people D) 27,283 people 288) Find the gasoline price index for a year in which the cost of gasoline was $1.87 per gallon. Use the 1965 price as the reference value. In 1965, the cost of gasoline was 31.2 cents per gallon. A) 599.4 B) 155.8 C) 6 D) 16.7

286)

287)

288)

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. 289) Yesterday the total number of gallons of gasoline used by people driving cars in the United States 289) was 7 × 1010.

A) No

B) Yes

Solve the problem. 290) The regular selling price of an item is $253. For a special year-end sale the price is at a markdown of 20%. Find the discount sale price. A) $202.40 B) $210.83 C) $303.60 D) $50.60

290)

Answer Key Testname: CHAPTER 3 1) A 2) D 3) C 4) A 5) D 6) D 7) D 8) D 9) A 10) D 11) C 12) A 13) B 14) A 15) C 16) A 17) C 18) A 19) B 20) A 21) A 22) D 23) D 24) D 25) B 26) A 27) D 28) C 29) A 30) B 31) A 32) C 33) B 34) A 35) C 36) A 37) B 38) C 39) C 40) B 41) 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.

Answer Key Testname: CHAPTER 3 42) 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. 43) 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. 44) 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. 45) Relative change in cost = 48.1% 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. City A City B 46) Death Rates Health Insurance. No health insurance Total

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. 47) 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. 48) 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. 49) 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. 50) The 1992 price in 2000 dollars is $921. So a price of $921 per month in 2000 would be equivalent to a price of $750 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.

51) 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

52)

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. 53) 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. 54) No regular Regular exercise exercise UNDER 40 1.1% 1% OVER 40 4% 3% AGE GROUPS COMBINED 1.8% 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. 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. 56) Home schooled Traditional 10th grade 26.0% 25.0% 12th grade 98.0% 95.7% AGE GROUPS COMBINED 44.0%% 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. 57) 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

Answer Key Testname: CHAPTER 3 58) D 59) D 60) D 61) A 62) B 63) B 64) B 65) A 66) D 67) B 68) C 69) D 70) D 71) A 72) D 73) B 74) B 75) C 76) C 77) D 78) B 79) D 80) B 81) D 82) B 83) D 84) B 85) D 86) C 87) C 88) C 89) B 90) B 91) C 92) B 93) C 94) B 95) A 96) B 97) D 98) C 99) C 100) D 101) D 102) D 103) B 104) A 105) A 106) D 107) A 47

Answer Key Testname: CHAPTER 3 108) D 109) A 110) B 111) A 112) C 113) B 114) B 115) C 116) A 117) D 118) D 119) C 120) C 121) A 122) B 123) B 124) A 125) A 126) A 127) C 128) A 129) A 130) D 131) A 132) D 133) A 134) C 135) C 136) A 137) B 138) A 139) C 140) A 141) B 142) A 143) D 144) B 145) D 146) D 147) D 148) A 149) D 150) D 151) A 152) C 153) C 154) A 155) A 156) A 157) C 48

Answer Key Testname: CHAPTER 3 158) B 159) C 160) D 161) C 162) D 163) C 164) A 165) D 166) C 167) C 168) C 169) D 170) C 171) A 172) D 173) D 174) A 175) A 176) C 177) C 178) C 179) B 180) B 181) C 182) B 183) D 184) A 185) D 186) C 187) C 188) D 189) B 190) A 191) D 192) D 193) A 194) A 195) C 196) D 197) B 198) D 199) A 200) A 201) B 202) C 203) A 204) D 205) C 206) B 207) B 49

Answer Key Testname: CHAPTER 3 208) A 209) B 210) A 211) C 212) A 213) D 214) A 215) A 216) A 217) A 218) D 219) D 220) D 221) B 222) A 223) D 224) C 225) C 226) C 227) A 228) D 229) B 230) C 231) A 232) B 233) D 234) C 235) A 236) B 237) B 238) C 239) B 240) A 241) B 242) B 243) B 244) D 245) B 246) C 247) C 248) D 249) B 250) A 251) D 252) A 253) D 254) B 255) C 256) D 257) A 50

Answer Key Testname: CHAPTER 3 258) B 259) A 260) D 261) D 262) A 263) A 264) A 265) C 266) B 267) C 268) D 269) A 270) B 271) D 272) D 273) D 274) D 275) A 276) D 277) A 278) A 279) D 280) A 281) B 282) B 283) B 284) B 285) D 286) B 287) D 288) A 289) A 290) A

Chapter 4 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) What type of spending is easiest for the government to control? A) Interest payments on the debt B) Discretionary spending C) Entitlement spending D) Medicare

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

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

Solve the problem. 4) Suppose that you need a loan of $80,000. Find the total cost of all the monthly payments for each of the 4) 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 8% Option 2: a 15-year loan at an APR of 7% A) Option 1: $211,324 B) Option 1: $245,608 Option 2: $129,431 Option 2: $186,056 C) Option 1: $220,326 D) Option 1: $204,326 Option 2: $134,438 Option 2: $122,416 Provide an appropriate response. 5) Which of the following will allow the federal debt to be retired? A) Zero gross debt B) Zero gross deficit C) Zero net surplus D) Zero net deficit

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

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

Solve the problem. 8) Assume you have a balance of $1400 on a credit card with an APR of 18%, or 1.5% per 8) month. You start making monthly payments of $600, but at the same time you charge an additional $280 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 $600 $280 2 $600 $280 3 $600 $280

Interest 1.5% × $1400 = $21.00

New Balance $1400 $1400 - $600 + $280 + $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. 9) The bank paid an annual interest rate (APR) of 6% but at the end of the year my account balance had grown by only 5.9%

10) My annual income after tax is only $25,000. I need to cut back on my nonessential 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 $16 and I have a mango smoothie every day at my favorite cafe. It costs $4.50 plus tax.

10)

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

11)

12) I have a fixed-rate 30-year mortgage of $120,000 at 6%. 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.

12)

13) Bill is in the 15% tax bracket so the tax he owes will be 15% of his taxable income.

13)

14) Sandi has a credit card balance of $4000. The credit card company charges interest of 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 $180 at the end of the three months. That's because 18% APR is equivalent to 1.5% monthly and 1.5% of $4000 is $60, and 3 times $60 is $180.

14)

15) 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.

15)

16) Maria saved $750 in taxes after donating $3000 to charity. So Maria's sister also donated $ 3000 to charity thinking that she would save $750 but she only saved $450.

16)

17) I was offered a 30-year mortgage at a fixed rate of 5% or an adjustable rate mortgage that starts at 4% 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.

17)

18) Steve is planning to open a savings account either at Quarterly Bank or at Daily Bank. Quarterly Bank is offering an APR of 6% compounded quarterly, which is clearly the better deal since Daily Bank is offering an APR of 6% but with daily compounding.

18)

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

19)

20) Paul has about $1800 available for all his personal expenses combined. He figures that he can easily afford to pay $900 in rent.

20)

21) I have a 30-year mortgage and have been paying it off for 10 years now so I should have paid off about one third of the principal by now.

21)

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

22)

23) Raul is planning to invest his money for one year only. He chose an account paying simple interest at 5% per year which was clearly a better deal than an account paying a 4.6% APR with interest compounded annually.

23)

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

24)

25) The two accounts were offering the same APR, and both accounts had the same annual percentage yield, but one account compounded interest continuously while the other compounded interest daily.

25)

26) If I pay off my mortgage in 12 years instead of 24, I will have to pay about twice as much per month since I will be paying the mortgage off in half the time.

26)

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 student loan of $41,996 with a fixed APR of 8.0% for 10 years.

Decide whether the statement makes sense. Explain your reasoning. 28) In 2005, the federal deficit was about 9 trillion dollars.

28)

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

29)

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

30)

31)

32) Jeremy hasn't paid off his credit card debt but he knows that it's important to start saving. 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 22.5% per month.

32)

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

33)

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. 34) Calculate the monthly payment and the portions of the payments that go to the principal 34) and to interest during the first 3 months for a home mortgage of $132,171 with a fixed APR of 7.0% for 20 years.

Decide whether the statement makes sense. Explain your reasoning. 35) I am young and I am looking for high-return investments even if that means higher risk. That's why I am putting most of my money into stocks.

35)

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

36)

Solve the problem. 37) The table below shows the expenses and payments for 4 months on a credit card account 37) 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. 38) Sheila is in the 28% tax bracket, so a $500 charitable contribution will reduce her total tax bill by 0.28 × $500 = $140.

38)

39) Before the government borrows money from its own trust funds such as the Social Security trust fund to finance a deficit, it first tries to cover the deficit by borrowing from the public .

39)

40) We will never be able to send our daughter to college. In order to have $100,000 in 20 years we would have to save at least $500 each month, That's more than we can afford.

40)

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

41)

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

42)

43) If two accounts offer the same APR, the account which compounds interest weekly will be a better deal than the account which compounds interest monthly.

43)

44) Sam is in the 35% tax bracket, so a $500 tax credit will reduce his total tax bill by 0.35 × $500 = $175.

44)

45) Paul figures that at today's prices he can live on $25,000 per year. Currently, banks are offering an APR of 5%. 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 5% for ever, and if I lived for ever, I could live on the interest alone for ever. That's because 5% of $500,000 is $25,000."

45)

46) My mortgage payment is $1500 per month so I will have a tax deduction of 12 × $1500 = $18,000.

46)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 47) Assume that you have a health insurance plan with the following provisions: · Office visits require a copayment of $25 · Emergency room visits have a $200 deductible (you pay the first $200) · Surgical operations have a $1200 deductible (you pay the first $1200) · You pay a monthly premium of $700

47)

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 $2350,without policy $10,280 B) With policy $10,050,without policy $10,280 C) With policy $17,030,without policy $10,820 D) With policy $9330,without policy $10,980

Provide an appropriate response. 48) The relative change in the investment value is the ______. A) annual return B) complete return C) total return D) None of the above 49) A savings plan in which payments are made at the end of each month is called a(n)_____? A) future annuity B) ordinary annuity C) annuity due D) None of the above

48)

49)

Solve the problem. Refer to the table if necessary.

50) You are married filing jointly and have a taxable income of $257,431. You make monthly contributions of $926 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 $3667 more per year with tax-deferred plan B) Take-home pay will be $3667 less per year with tax-deferred plan C) Take-home pay will be $3111 more per year with tax-deferred plan D) Take-home pay will be $3111 less per year with tax-deferred plan Evaluate or simplify the following the expression. 51) 2 -4 A) - 16

50)

51)

B) 16

1 8

1 16

Solve the problem. Refer to the table if necessary.

52) Ken is head of household with a dependent child and a taxable income of $84,493. He also is entitled to a $1000 tax credit. Calculate the amount of tax owed. A) $14,376 B) $20,123 C) $14,713 D) $15,376 Solve the equation for the unknown quantity. 53) 7n - 10 = 25 A) 28 B) 5

C) 13

D) 32

Solve the problem. 54) 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 -146 -320 -566 -773 Debt (accumulated) Assume that for 2018, total receipts are $1,036,214, operating expenses are $618,312, employee benefits are $209,299, security costs are$123,570, and interest on debt is $63,000. Calculate the year-end surplus or deficit. A) $690,201.00 B) $148,033.00 C) $813,771.00 D) $22,033.00

52)

53)

54)

55) Kerry invests $739 in a savings account that earns 3.7% compounded annually. Andy invests $739 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: $1142.85; $1142.85 B) Kerry: $1062.75; $1528.34 Andy: $1487.01; $1487.01 Andy: $1323.44; $2370.07 C) Kerry: $1024.83; $1473.81 D) Kerry: $988.27; $1321.61 Andy: $1248.52; $2235.92 Andy: $1177.85; $1877.32

55)

56) 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 -146 -320 -566 -773 Debt (accumulated)

56)

Assume that for 2018, total receipts are $1,052,701, operating expenses are $578,542, employee benefits are $195,175, security costs are $133,588, and interest on debt is $63,000. Calculate the year-end accumulated debt. A) -$690,604.00 B) $92,922.00 C) -$564,604.00 D) -$40,666.00

57) You have money in an account at an APR of 5% compounded monthly. To the nearest year, how long will it take for your money to double? A) 14 years B) 11 years C) 8 years D) 19 years Evaluate or simplify the following the expression. 58) 2 2 × 2 3 A) 12

B) 24

C) 32

D) 64

57)

58)

Solve the problem. Refer to the table if necessary.

59) Bill earned wages of $54,515, received $1873 in interest from a savings account, and contributed $3063 to a tax deferred retirement plan. He was entitled to a personal exemption of $4050 and had deductions totaling $7139. Find his adjusted gross income. A) $66,590 B) $59,451 C) $53,325 D) $42,136 Solve the equation for the unknown. 60) (x - 2)3 = 8 A) x = 3

B) x = 4

Evaluate or simplify the following the expression. 61) 2 3 A) 6

B) 5

C) x = -3

D) x = -4

C) 4

D) 8

Provide an appropriate response. 62) True or False? With tax-exempt investments, you never have to pay tax on the earnings. A) True B) False

59)

60)

61)

62)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 63) $3000 deposit at an APR of 3% with monthly compounding for 6 years 63) A) $3045.28 B) $2872.68 C) $11,444.09 D) $3590.85

Answer the question. 64) You put $192 per month in an investment plan that pays an APR of 5% compounded monthly. How much money will you have after 19 years? Compare this amount to the total amount of deposits made over the time period. A) $72,881.41; this is $18,161.41 more than the total amount of the deposits. B) $61,909.38; this is $29,058.57 more than the total amount of the deposits. C) $72,787.79; this is $36,307.79 more than the total amount of the deposits. D) $72,834.57; this is $29,058.57 more than the total amount of the deposits. Provide an appropriate response. 65) 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) future value C) present value D) None of the above Solve the problem. 66) You want to have a $100,000 college fund in 20 years. How much will you have to deposit now in an account with an APR of 5% and daily compounding? A) $36,790.46 B) $38,940.29 C) $36.794.39 D) $35,950.49 Provide an appropriate response. 67) True or False? A progressive income tax means that people with a higher income pay at a higher tax rate. A) True B) False 68) True or False? If net income is positive, the budget has a surplus. A) False B) True Calculate the balance under the given assumptions. 69) Find the savings plan balance after 32 months with an APR of 2% and monthly payments of $393. A) $4022.41 B) $12,906.36 C) $10,970.41 D) $4732.25 Solve the problem. 70) 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 5.6%. 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 $104.82 more than Anna. C) Anna has $88.14 more than Dave. D) Dave has $74.43 more than Anna. Solve.

71) Jim is in the 35% tax bracket and itemizes his deductions. How much will his tax bill be reduced if he makes a $4639 contribution to charity? A) -$3015.35 B) $6262.65 C) $4639 D) $1623.65

64)

65)

66)

67)

68)

69)

70)

71)

Answer the question. 72) Stephen sets up an IRA with an APR of 4% compounded monthly at age 26. At the end of each month, he deposits $37 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) $41,586.06; this is $24,270.06 more than the total amount of the deposits. B) $30,424.44; this is $19,772.46 more than the total amount of the deposits. C) $1003.17; this is $41.17 more than the total amount of the deposits. D) $30,916.45; this is $16,116.45 more than the total amount of the deposits. Provide an appropriate response. 73) What is the compound interest formula for interest paid more than once a year? A) A = P 1 +

APR Y Y

B) A = P 1 +

C) A = P x (1 + APR)Y

72)

73)

APR nY n

D) A = P x (1 + APR)nY

Calculate the balance under the given assumptions. 74) Find the savings plan balance after 9 months with an APR of 4% and monthly payments of $255. A) $3135.92 B) $2665.53 C) $2325.84 D) $1976.96

74)

Calculate the amount of interest you'll have at the end of the indicated period. 75) You invest $49,400 in an account that pays simple interest of 4% for 5 year(s). A) $988.00 B) $39,520.00 C) $2470.00

75)

D) $9880.00

Answer the question. 76) You currently drive 240 miles per week in a car that gets 16 miles per gallon of gas. You are considering buying a new fuel-efficient car for $13,000 (after trade-in on your current car) that gets 40 miles per gallon. Insurance premiums for the new and old car are $800 and $600 per year, respectively. You anticipate spending $1400 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 old car is $1020 less expensive B) the new car is $1020 less expensive C) the old car is $1190 less expensive D) the new car is $1190 less expensive Solve the problem. 77) Suppose you have a student loan of $90,000 with an APR of 7% for 30 years. If you decide you would like to pay off the loan in 15 years instead of 30, how much more will you have to pay each month? A) $227.18 B) $220.18 C) $235.22 D) $210.18

76)

77)

Solve the problem. Refer to the table if necessary.

78) Kelsey earned $58,750 in wages. Conner earned $58,750, all in dividends and long-term capital 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% for income in the 10% and 15% tax brackets and at 15% for income in all higher tax brackets except the highest 39.6% bracket. If necessary, round values to the nearest dollar. A) Kelsey: 0.0% B) Kelsey: 21.0% C) Kelsey: 13.3% D) Kelsey: 19.7% Conner: 4.4% Conner: 2.7% Conner: 2.7% Conner: 11.6% Evaluate or simplify the following the expression. 79) 161/2 ÷ 16-1/2 A) 8

B) -1

C) 4

Solve the equation for the unknown quantity. 80) 5x + 5 = 4x + 14 19 A) 11 B) 9

D) 16

78)

79)

80) C) 9

D) 1

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

81) A couple under the age of 30 has a combined household income of $4200 per month and spends $ 210 per month on entertainment. A) at average B) above average C) below average

81)

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 83) Elena spends $4 per day on a coffee at the neighborhood cafe and $360 per month on food. A) 34% B) 8% C) 5% D) 406% Solve the problem. 84) 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 20 years. Assume an annual interest rate of 4%. A) $1251 billion B) $1274 billion C) $1287 billion D) $1243 billion 85)

Mutual Fund Listing (MFABC) 1-Day Net Change1-Day Return NAV $24.68 ^$0.00 ^0.00% YTD 1-YR 5-Yr 10-Yr Fund 2.80% 5.56% -3.21% -1.67% TOTAL RETURNS (%) 5 and 10 year returns are annualized Suppose you had invested $3000 in this fund 5 years ago. How much would your investment be worth now? A) $3444.19 B) $2757.73 C) $2602.87 D) $3259.01

83)

84)

85)

Solve the problem. Refer to the table if necessary.

86) Matt is single and earned wages of $32,315. He received $445 in interest from a savings account. He contributed $485 to a tax-deferred retirement plan. He had $595 in itemized deductions from charitable contributions. Calculate his taxable income. A) $37,295 B) $21,875 C) $27,630 D) $25,330

86)

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

87) A single 42-year old woman with a monthly salary of $3700 spends $1200 on rent. A) at average B) below average C) above average

87)

Provide an appropriate response. 88) True or False? A mortgage lender will typically require a down payment of 30% to 40% of the purchase price. A) False B) True 89) True or False? If you deposit $1,000 in an in investment account today, it can double in value to $2,000 in just a couple decades even at a relatively low interest rate (4%). A) False B) True Solve the problem. 90) You need a $193,854 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: $1303.33 B) Option 1: $1344.65 Option 2: $1668.87 Option 2: $1779.41 C) Option 1: $1322.43 D) Option 1: $1350.77 Option 2: $1720.81 Option 2: $1798.47

88)

89)

90)

Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period. 91) A $44,956 deposit in an account with an APR of 3.6% compounded continuously for 10 years. 91) A) $62,790.94 B) $64,333.07 C) $64,436.76 D) $64,030.25

Solve the problem. 92) You just put $1909 in a CD that is expected to earn 7% compounded monthly, and $7713 in a savings account that is expected to earn 4% compounded annually. Determine when, to the nearest year, the values of your two investments will be the same. A) 59 years B) 18 years C) 46 years D) 32 years Solve the equation for the unknown quantity. 93) 9x = 27 A) 18

1 C) 3

B) 243

93) D) 3

Solve the problem. 94) Calculate the current yield for a $1000 Treasury bond with a coupon rate of 7.1% that has a market value of $750. A) 9.47% B) 7.10% C) 8.52% D) 10.41% Solve the equation for the unknown. 95) v3 = 27 A) v = 81

B) v = 9

C) v = 3

Evaluate or simplify the following the expression. 96) 64-1/3 1 A) 4

1 B) 256

1 C) 12

92)

D) v = 19,683

94)

95)

96) D) -4

97) 9 1/2 A) 12

B) 3

C) 6

9 D) 2

Solve the problem. 98) $249 is deposited into a savings account at 7% interest, compounded monthly. To the nearest year, how long will it take for the account balance to reach $452? A) 8 years B) 6 years C) 9 years D) 12 years Find the annual percentage yield (APY). 99) A bank offers an APR of 1.5% compounded quarterly. A) 1.51% B) 1.5% C) 3.02%

D) 0.75%

97)

98)

99)

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

100) A couple over the age of 65 with a fixed monthly salary of $4200 spends $290 per month on entertainment. A) above average B) at average C) below average

100)

Solve the problem. 101) 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.

101)

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) $479 billion C) $388 billion

D) $470 billion

Solve the problem. Refer to the table if necessary.

102) Andy earned $71,520 from wages as an engineer. Determine his overall tax rate on his gross 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) 23.1% B) 22.0% C) 23.0% D) 29.2%

102)

Answer the question. 103) You must decide whether to buy a new car for $26,000 or lease the same car over a three-year period. Under the terms of the lease, you make a down payment of $1600 and have monthly payments of $320. 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 $15,000. 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 $12,000, lease $13,120 B) Buy $11,000, lease $12,820 C) Buy $11,000, lease $13,120 D) Buy $11,000, lease $13,420

103)

Solve the problem. Refer to the table if necessary.

104) Caitlin is single and earned wages of $34,108. She received $300 in interest from a savings account. She contributed $511 to a tax-deferred retirement plan. She had $446 in itemized deductions from charitable contributions. Calculate her gross income. A) $34,408 B) $33,897 C) $34,919 D) $33,451 Solve the problem. 105) 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 148 million people, how much would each worker be charged? A) About $18,500,000 per worker. B) About $5000 per worker. C) About $54,000 per worker. D) About $1,850,000 per worker. Compute the total and annual returns on the described investment. 106) Four years after buying 400 shares of XYZ stock for $50 per share, you sell the stock for $2000. A) Total Return: -94.50% B) Total Return: -76.50% Annual Return: -45.95% Annual Return: -37.20% C) Total Return: -90.00% D) Total Return: -81.00% Annual Return: -43.77% Annual Return: -39.39% 19

104)

105)

106)

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 107) George spends $15 per week at the movies and $650 per month on rent. A) 120% B) 10% C) 1% D) 13% Solve. 108) Determine the total payment over the term of a student loan of $155,807 at a fixed APR of 8.5% for 30 years. A) $431,452.62 B) $431,240.43 C) $431,353.58 D) $431,287.57

107)

108)

Solve the problem. Refer to the table if necessary.

109) Jeff earned wages of $52,380, received $1598 in interest from a savings account, and contributed $3762 to a tax deferred retirement plan. He was entitled to a personal exemption of $4050 and had deductions totaling $7678. Find his taxable income. A) $38,488 B) $46,588 C) $57,740 D) $65,418

109)

110) Carla earned wages of $46,774, received $1572 in interest from a savings account, and contributed $3575 to a tax deferred retirement plan. She was entitled to a personal exemption of $4050 and had deductions totaling $7166. Find her gross income. A) $33,555 B) $51,921 C) $48,346 D) $44,771

110)

Solve. 111) Calculate the monthly payment for a student loan of $74,876 at a fixed APR of 6% for 14 years. A) $565.44 B) $659.83 C) $990.54 D) $792.05

111)

Calculate the balance under the given assumptions. 112) Find the savings plan balance after 17 months with an APR of 2% and monthly payments of $551. A) $8069.00 B) $9492.94 C) $5656.71 D) $6654.95

112)

Answer the question. 113) 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) $2910 B) $754 C) $1954 D) $4110

113)

Solve the problem. Refer to the table if necessary.

114) Carl is single and has a taxable income of $38,367. Calculate the amount of tax owed. A) $5304 B) $5331 C) $9592 D) $4203 Provide an appropriate response. 115) A _______ represents a promise of future cash. A) stock C) bond

B) return D) None of the above

114)

115)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 116) $7000 deposit at an APR of 4% with daily compounding for 5 years 116) A) $7056.22 B) $6698.05 C) $8549.82 D) $1400.00

Solve the problem. Refer to the table if necessary.

117) Jim earned wages of $98,793, received $5403 in interest from a savings account, and contributed $6417 to a tax deferred retirement plan. He was entitled to a personal exemption of $4050 and had deductions totaling $9168. Find his adjusted gross income. A) $97,779 B) $93,729 C) $110,613 D) $84,561 Provide an appropriate response. 118) ________ is interest paid only on the original principal, and not on any interest added at later dates. A) Compound Interest B) Basic interest C) Simple interest D) None of the above

117)

118)

Solve the problem. Refer to the table if necessary.

119) Tom and Toni are married and file jointly. Their combined wages were $84,102. They earned a net of $2370 from a rental property they own, and they received $1678 in interest. They claimed four exemptions for themselves and two children. They contributed $3967 to their tax-deferred retirement plans, and their itemized deductions total $10,409. Find their taxable income. A) $58,174 B) $55,283 C) $63,217 D) $68,583 Solve the problem. 120) Suppose your after-tax income is $36,266. Your annual expenses are $32,299 for rent, $6006 for food and household expenses, $1239 for interest on credit cards, and $8108 for entertainment, travel, and other. Do you have a surplus or deficit? A) Deficit B) Surplus Find the annual percentage yield (APY). 121) A bank offers an APR of 1.75% compounded semiannually. A) 1.76% B) 1.75% C) 3.52%

D) 0.88%

Provide an appropriate response. 122) A plan in which payments are made at the beginning of each period is called a(n) ________. A) future annuity B) ordinary annuity C) annuity due D) None of the above Prorate the given expenses to find the monthly cost. 123) Linda enrolls for 10 credit-hours for each of two semesters at a cost of $650 per credit-hour (tuition and fees). In addition, textbooks cost $300 per semester. Round your answer to the nearest dollar. A) $1700 B) $158 C) $567 D) $1133

119)

120)

121)

122)

123)

Provide an appropriate response. 124) For any loan, the ______ is the amount of money owed at any particular time. A) interest B) installment C) principal D) None of the above

124)

Solve the problem. Refer to the table if necessary.

125) Jenny earned wages of $86,618, received $5452 in interest from a savings account, and contributed $6460 to a tax deferred retirement plan. She was entitled to a personal exemption of $4050 and had deductions totaling $9123. Find her taxable income. A) $85,610 B) $98,530 C) $72,437 D) $80,537

125)

Find the monthly interest payments in the situation described. Assume that monthly interest rates are 1/12 of annual interest rates. 126) Derek bought a new car for $34,000. He made a down payment of $18,000 and financed the balance 126) through the car dealer. He was unable to make the first monthly payments. Until he makes a payment he is paying 2% interest per month on the balance. A) $320 B) $3840 C) $680 D) $8160

Provide an appropriate response. 127) ______, or income, represent money that has been collected. A) Net income B) Receipts C) Outlays D) None of the above

127)

Solve the problem. 128) 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 -146 -320 -566 -773 Debt (accumulated)

128)

Assume that for 2018, total receipts are $1,044,561, operating expenses are $541,042, employee benefits are $170,187, security costs are$126,783, and interest on debt is $63,000. Calculate the outlays for 2018. A) $1,945,573.00 B) $901,795.00 C) $901,012.00 D) $1,818,790.00

Provide an appropriate response. 129) _______ is interest paid both on the original principal and on all interest that has been added to the original principal. A) Simple interest B) Basic interest C) Compound interest D) None of the above Find the annual percentage yield (APY). 130) A bank offers an APR of 2.9% compounded monthly. A) 2.94% B) 5.88% C) 0.48%

D) 0.24%

Provide an appropriate response. 131) The average annual percentage yield (APY) that would give the same overall growth is the ______. A) total return B) annual return C) complete return D) None of the above

129)

130)

131)

Find the monthly interest payments in the situation described. Assume that monthly interest rates are 1/12 of annual interest rates. 132) Ashton maintains an average balance of $1000 on his credit card which carries an annual interest 132) rate of 15%. A) $12.50 B) $125 C) $1500 D) $150

Provide an appropriate response. 133) _________ loans differ from installment loans in that you are not required to pay off your balance in any set period of time. A) Mortgage B) Credit card C) Auto D) None of the above Calculate the amount of interest you'll have at the end of the indicated period. 134) You invest $8000 in an account that pays simple interest of 3% for 3 years. A) $1205.81 B) $1021.01 C) $240.00

D) $720.00

133)

134)

Solve the problem. 135) Calculate the annual interest for a $1000 Treasury bond with a current yield of 3.5% that is quoted at 115.8 points. A) $28.00 B) $31.50 C) $48.64 D) $40.53 Solve. 136) Determine the total payment over the term of a student loan of $35,604 at a fixed APR of 7% for 16 years. A) $59,328.80 B) $59,268.70 C) $59,282.06 D) $59,300.76 Solve the problem. 137) You need a $120,690 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: $829.12 B) Option 1: $832.96 Option 2: $1104.52 Option 2: $1116.40 C) Option 1: $803.13 D) Option 1: $815.15 Option 2: $1035.62 Option 2: $1068.00 Use the given stock table to answer the question. 138) 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? 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s High ABC 0.63 2.5 21 4156 25.68 XYZ 0.21 1.2 13 9175 18.17

A) cheap

B) about right

Low Close 24.87 25.35 17.26 17.75

135)

136)

137)

138)

Net Chg +0.22 +0.09

C) expensive

Solve. 140) Genevieve is in the 35% tax bracket. George is in the 25% tax bracket. They each itemize their deductions and they each donate $4446 to charity. Compute their true costs for charitable donations. A) Genevieve: $2889.9 B) Genevieve: $3334.5 George: $3334.5 George: $2889.9 C) Genevieve: $1111.5 D) Genevieve: $1556.1 George: $1556.1 George: $1111.5 Calculate the amount of interest you'll have at the end of the indicated period. 141) You invest $500 in an account that pays simple interest of 3% for 2 year(s). A) $30.00 B) $3.00 C) $83.33

D) $750.00

140)

141)

Solve the problem. 142) Suppose your after-tax income is $36,920. Your annual expenses are $30,787 for rent, $6851 for food and household expenses, $1305 for interest on credit cards, and $7997 for entertainment, travel, and other. You expect to get a 25% raise next year. Will this affect the outcome? A) No, a raise would still create a deficit. B) Yes, a raise would create a surplus. Solve the equation for the unknown quantity. 143) 2r + 5 = 21 A) 5 B) 14

C) 8

D) 18

Provide an appropriate response. 144) A ______ gives you a share of ownership in a company. A) cash B) bond C) stock D) None of the above

142)

143)

144)

145) What is the general form of the compound interest formula for interest paid once a year? A) A = P × APR B) A = P × APRY

145)

D) A = P × (1 + APR)Y

C) A = P - APR × Y

Use the given stock table to answer the question. 146) How does the share price for company XYZ compare to the profit per share that it earned in the past year? 146) 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s High ABC 0.63 2.5 24 4156 25.68 XYZ 0.21 1.2 14 9175 18.17

Low Close 24.87 25.22 17.26 17.51

A) price = 1.2 × earnings C) earnings = 14 × price

Net Chg +0.16 +0.09

B) price = 14 × earnings D) price = 17.51 × earnings

Calculate the amount of interest you'll have at the end of the indicated period. 147) You invest $14,000 in an account that pays simple interest of 2% for 1 year. A) $420 B) $28 C) $14,280

D) $280

Solve. 148) Determine the total payment over the term of a home mortgage of $120,000 with a fixed APR of 4% for 25 years. A) $187,843.64 B) $141,509.43 C) $190,021.26 D) $192,845.81 Provide an appropriate response. 149) True or False? There is high risk for investing money in U.S. Treasury bills. A) False B) True Solve the problem. 150) 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 7% while receipts turn out to be lower by 7%, what would the 2013 surplus or deficit be? A) $215 billion deficit B) $571 billion deficit C) $601 billion deficit D) $155 billion deficit

147)

148)

149)

150)

Solve the problem. Refer to the table if necessary.

151) Kyle is single and earned wages of $31,284. He received $323 in interest from a savings account. He contributed $468 to a tax-deferred retirement plan. He had $516 in itemized deductions from charitable contributions. Calculate his adjusted gross income. A) $30,623 B) $32,075 C) $31,139 D) $31,559

151)

152) Stephen earned $53,158 from wages as an accountant and made $1820 in interest. Find how much 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) $15,311 B) $10,950 C) $10,924 D) $10,224

152)

Solve the problem. 153) The average cost of a 4-year college education is projected to be $140,000 in 15 years. How much money should be invested now at 7%, compounded quarterly, to provide $140,000 in 15 years? A) $17,458.14 B) $140,000.00 C) $49,438.24 D) $107,922.44 Solve. 154) Mike and Carrie are in the 28% marginal tax bracket and claim the standard deduction. How much will their tax bill be reduced if they qualify for a $900 tax credit? A) $430.00 B) $252.00 C) $900 D) $1152.00 155) You are in the 25% tax bracket. An apartment rents for $1000 per month. Your monthly mortgage payments would be $1200, of which an average of $900 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) Buying is cheaper; $975 per month for buying versus $1000 per month for renting B) Renting is cheaper; $1000 per month for renting versus $1200 per month for buying C) Renting is cheaper; $1000 per month for renting versus $1150 per month for buying D) Buying is cheaper; $900 per month for buying versus $1000 per month for renting 28

153)

154)

155)

Solve the problem. 156) Suppose that the federal debt increases at an annual rate of 3% per year. Use the compound interest formula to determine the size of the debt in 20 years. Assume that the current size of the debt is $17 trillion. A) $36.4 trillion B) $32.3 trillion C) $28.8 trillion D) $30.7 trillion

156)

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 157) $20,000 is invested at an APR of 2% for 2 years. 157) A) $800.00 B) $401.50 C) $20,400.00 D) $20,808.00

Solve the problem. 158) Calculate the annual interest for a $1000 Treasury bond with a current yield of 2.5% that is quoted at 109 points. A) $27.25 B) $32.70 C) $20.00 D) $22.50 159) Consider an account with an APR of 6%. Find the APY with quarterly compounding, monthly compounding, and daily compounding. A) 21.14%, 21.17%, 21.18% B) 15.14%, 16.17%, 16.18% C) 6.14%, 6.17%, 6.18% D) 1.50%, 0.50%, 6.31% Provide an appropriate response. 160) The ______ is the actual percentage by which a balance increases in 1 year. A) APY B) AARP C) APR D) None of the above

C) -2

D) -1

Use the given stock table to answer the question. 163) 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 High ABC 0.63 2.5 26 4156 25.68 XYZ 0.21 1.2 13 9175 18.17

Low Close 24.87 25.13 17.26 17.75

A) $1.45

B) $1.37

C) $1.16

159)

160)

Solve the problem. 161) You need a loan of $120,000 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) $290 B) $270 C) $280 D) $300 Solve the equation for the unknown quantity. 162) 4x + 2 = 2x - 2 A) 1 B) 2

158)

161)

162)

163)

Net Chg -0.19 +0.09

D) $1.21

Solve the equation for the unknown quantity. 164) y/4 + 1 = 9 A) -32 B) 32 165) 9x - 9 = 15 - 3x A) 2

B) 1

C) 34

D) -34

C) 4

D) -2

Calculate the amount of interest you'll have at the end of the indicated period. 166) You invest $9000 in an account that pays simple interest of 3% for 20 years. A) $5400.00 B) $1003.30 C) $3737.19

D) $270.00

164)

165)

166)

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. 167) 167) Income Expenses Part-time job: $1100 /month Rent: $640/month Student loan: $6000/year Groceries: $80/week Scholarship: $5800/year Tuition and fees: $4200 twice a year Entertainment: $190/month A) $233 B) $583 C) $203 D) $473

Compute the total and annual returns on the described investment. 168) Seven years after paying $5603 for shares in a new company, you sell the shares for $18,621. A) Total Return: 232.34% B) Total Return: 220.72% Annual Return: 18.72% Annual Return: 17.78% C) Total Return: 243.96% D) Total Return: 185.87% Annual Return: 19.65% Annual Return: 14.97% Solve the equation for the unknown. 169) p1/3 = 9 1 A) p = 27

B) p = 729

1 D) p = 729

C) p = 27

Use the given stock table to answer the question. 170) 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 High ABC 0.63 2.5 21 4156 25.68 XYZ 0.21 1.2 12 9175 18.17

A) cheap

B) about right

Low Close 24.87 25.35 17.26 17.94

168)

169)

170)

Net Chg +0.22 +0.09

C) expensive

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 171) $10,000 is invested at an APR of 2.4% for 18 years. 171) A) $14,965.78 B) $14,080.00 C) $14,320.00 D) $15,324.96

Solve the problem. 172) Suppose you start saving today for a $8000 down payment that you plan to make on a condo in 4 years. Assume that you make no deposits into the account after your initial deposit. The account has quarterly compounding and an APR of 6%. How much would you need to deposit now to reach your $8000 goal in 4 years? A) $5893.39 B) $6893.39 C) $5969.40 D) $6304.25 Solve the equation for the unknown. 173) x2 = 121 121 A) x = 2

172)

173)

121 B) x = ± 2

C) x = ±11

D) x = 11

You need a loan of $100,000 to buy a condo. Calculate your monthly payments and total closing costs for each choice. 174) Choice 1: 30-year fixed rate at 4% with closing costs of $1194 and no points 174) Choice 2: 20-year fixed rate at 3.5% with closing costs of $1194 and 2 points A) Choice 1: $477.42; $1194 B) Choice 1: $543.49; $1194 Choice 2: $579.96; $3194 Choice 2: $474.36; $2994 C) Choice 1: $421.10; $1194 D) Choice 1: $605.98; $1194 Choice 2: $586.19; $2388 Choice 2: $449.04; $2944 Compute the total and annual returns on the described investment. 175) Five years after buying 200 shares of XYZ stock for $45 per share, you sell the stock for $20,000. A) Total Return: 128.33% B) Total Return: 103.89% Annual Return: 18.18% Annual Return: 14.72% C) Total Return: 122.22% D) Total Return: 110.00% Annual Return: 17.32% Annual Return: 15.58% Solve the problem. 176) 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% decrease in total outlays? A) $306 billion B) $329 billion C) $302 billion D) $296 billion Solve the equation for the unknown. 177) (t/2)2 = 25 A) t = 1250

B) t = 25

Solve the equation for the unknown quantity. 178) t - 3 = 18 A) -15 B) 21

C) t = 10

D) t = ±10

C) -21

D) 15

175)

176)

177)

178)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 179) $8430 deposit at an APR of 4% with semiannual compounding for 8 years 179) A) $11,127.60 B) $11,537.04 C) $11,572.58 D) $9877.09

Solve the problem. Refer to the table if necessary.

180) Mark earned $72,978 from wages as a mechanic and made $3389 in interest. Calculate his FICA tax. If necessary, round values to the nearest cent. A) $5548.93 B) $5582.82 C) $5842.08 D) $5631.96 Evaluate or simplify the following the expression. 181) 5 5 ÷ 5 2 1 A) 125

181)

B) 125

C) 625

D) 15

Solve the problem. 182) Suppose that you want to have a $95,706 retirement fund after 40 years. How much will you need to deposit now if you can obtain an APR of 5%, compounded daily? Assume that no additional deposits are to be made to the account. A) $23,926.50 B) $91,038.37 C) $8598.09 D) $12,954.17 Solve the equation for the unknown quantity. 183) x + 14 = 19 A) -5

180)

14 C) 19

B) 5

183) D) 33

Solve. 184) Calculate the monthly payment for a home mortgage of $523,000 with a fixed APR of 3.0% for 15 years. A) $3611.74 B) $35,568.06 C) $1313.92 D) $4378.47

182)

184)

185) Determine how much of the total loan payment applies toward principal and how much applies toward interest for a home mortgage of $136,538 with a fixed APR of 4.4% for 15 years. A) $136,538 pays off the principal and $50,340.10 represents interest payments. B) $136,538 pays off the principal and $50,267.78 represents interest payments. C) $136,538 pays off the principal and $50,219.55 represents interest payments. D) $136,538 pays off the principal and $50,185.10 represents interest payments. Solve the problem. 186) Mutual Fund Listing (MFABC) 1-Day Net Change1-Day Return NAV $7.61 ^$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

185)

186)

Suppose you invest $4000 in this fund today. How many shares will you buy? Round to three decimal places. A) 1902.500 shares B) 3044.000 shares C) 52.562 shares D) 525.624 shares

187) You have a choice between a 30-year fixed rate loan at 4.5% 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 $ 180,000 loan. A) $320 B) $300 C) $350 D) $280

187)

Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period. 188) A $7000 deposit in an account with an APR of 4.4% compounded continuously for 9 years. 188) A) $10,401.09 B) $10,313.42 C) $3210.99 D) $7314.88 Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 189) $1200 deposit at an APR of 4% with quarterly compounding for 2 years 189) A) $1297.92 B) $1296.00 C) $1224.12 D) $1299.43

Provide an appropriate response. 190) A ______ represents money that is borrowed (or taken from savings) during a single year. A) debt B) deduction C) deficit D) None of the above Find the annual percentage yield (APY). 191) A bank offers an APR of 2.1% compounded daily. A) 2.18% B) 102.12%

C) 4.20%

D) 2.12%

190)

191)

Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period. 192) A $6958 deposit in an account with an APR of 6.5% compounded continuously for 4 years. 192) A) $9362.68 B) $9024.04 C) $8951.23 D) $9005.20

Answer the question. 193) 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 $2350, without policy $1850 C) With policy $1900, without policy $1850 D) With policy $1950, without policy $2000 Solve the equation for the unknown. 194) v3 + 4 = 129 A) v = 1,953,125

B) v = 41.7

C) v = 375

D) v = 5

Solve. 195) Calculate the monthly payment for a home mortgage of $99,000 with a fixed APR of 3.6% for 15 years. A) $712.61 B) $297.51 C) $6759.51 D) $858.77 Provide an appropriate response. 196) True or False? A home appraisal is one example of a closing cost when taking out a mortgage loan. A) True B) False

193)

194)

195)

196)

Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 197) $310 is invested at an APR of 3.3% for 12 years. 197) A) $432.76 B) $443.06 C) $457.68 D) $422.53

Solve. 198) 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 $154 tax credit? A) $53.90 B) $1508.50 C) $154 D) $207.90 Answer the question. 199) 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 $173,282 after 18 years, how much should you deposit monthly? A) $496.22 B) $421.79 C) $545.84 D) $9290.32

198)

199)

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. 200) The credit card APR is 21% and you want to pay off the balance in 2 years. 200) A) $247.51; $5940.18 B) $164.43; $3946.42 C) $140.80; $3051.17 D) $197.60; $4277.35 Use the compound interest formula to determine the accumulated balance after the stated period. Assume that interest is compounded annually. 201) $8000 is invested at an APR of 3.1% for 5 years. 201) A) $249.50 B) $9319.30 C) $1240.00 D) $9039.09

Provide an appropriate response. 202) If you sell a stock for more than you paid for it, you have a __________. A) return B) capital gain C) dividend D) None of the above

202)

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. 203) Principal: $6865 Rate: 2% Years: 17 203) A) $7278.56 B) $413.56 C) $4944.46 D) $362.37

Solve. 204) Calculate the monthly payment for a student loan of $130,257 at a fixed APR of 8.7% for 25 years. A) $913.99 B) $1066.48 C) $1280.03 D) $1600.53 Solve the problem. 205) Calculate the current yield for a $100 Treasury bond with a coupon rate of 4% that has a market value of $85. A) 5.18% B) 4.24% C) 4.00% D) 4.71% 206) Suppose the government has a unified net income of -$60 billion, but was supposed to deposit $190 billion in the Social Security trust fund. What was the on-budget surplus or deficit? A) $250 billion surplus B) $250 billion deficit C) $130 billion surplus D) $130 billion deficit Answer the question. 207) 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 $16,900 B) In-state $17,700, out-of-state $15,000 C) In-state $17,400, out-of-state $15,000 D) In-state $17,400, out-of-state $16,900 Provide an appropriate response. 208) The ________ in financial formulas is the balance upon which interest is paid. A) percentage B) principal C) power D) None of the above

204)

205)

206)

207)

208)

Solve the problem. Refer to the table if necessary.

209) Kelly and Kurt are married filing jointly with a taxable income of $83,634. Calculate the amount of tax owed. A) $9184 B) $20,909 C) $12,386 D) $12,809 Evaluate or simplify the following the expression. 210) 7 2 × 7 -2 A) 49

B) 7

C) 1

49 D) 2

Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 211) Wendy buys a $1 lottery ticket every day and takes 2 yoga classes per week which cost $14 each. A) 4% B) 25% C) 109% D) 15%

209)

210)

211)

Solve the problem. Refer to the table if necessary.

212) Your deductible expenditures are $9135 for interest on a home mortgage, $3722 for contributions to charity, and $579 for state income taxes. Your filing status entitles you to a standard deduction of $12,700. 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, -$422 C) Yes, $736 D) Yes, $26,136 Solve. 213) Determine how much of the total loan payment applies toward principal and how much applies toward interest for a student loan of $68,472 at a fixed APR of 8% for 19 years. A) $68,472 pays off the principal and $64,902.51 represents interest payments. B) $68,472 pays off the principal and $64,967.22 represents interest payments. C) $68,472 pays off the principal and $64,929.47 represents interest payments. D) $68,472 pays off the principal and $65,023.83 represents interest payments. Provide an appropriate response. 214) True or False? The bank that pays the highest annual percentage rate (APR) is always the best deal, no matter what. A) True B) False Solve the problem. 215) You want to have a $40,000 college fund in 6 years. How much will you have to deposit now in an account with an APR of 5% and annual compounding? A) $24,949.06 B) $28,949.30 C) $31,930.99 D) $29,848.62

212)

213)

214)

215)

Solve. 216) Denise is in the 28% tax bracket and claims the standard deduction. How much will her tax bill be reduced if she makes a $2422 contribution to charity? A) $2422 B) $0 C) $3100.16 D) $678.16

216)

You need a loan of $100,000 to buy a condo. Calculate your monthly payments and total closing costs for each choice. 217) Choice 1: 30-year fixed rate at 4.25% with closing costs of $1261 and 1 points 217) Choice 2: 20-year fixed rate at 3.75% with closing costs of $1261 and 3 points A) Choice 1: $497.36; $2261 B) Choice 1: $501.43; $3061 Choice 2: $602.49; $4261 Choice 2: $463.16; $5061 C) Choice 1: $481.74; $2261 D) Choice 1: $491.94; $2261 Choice 2: $542.26; $1261 Choice 2: $592.89; $4261 Provide an appropriate response. 218) True or False? Short-term capital gains are profits on items sold within 12 months of their purchase. A) False B) True Solve. 219) Calculate the monthly payment for a loan of $11,000 at a fixed APR of 7% over a period of 4 years. A) $64.17 B) $309.13 C) $263.41 D) $16.04 Solve the problem. 220) Suppose your after-tax income is $42,667. Your annual expenses are $25,996 for rent, $6979 for food and household expenses, $1234 for interest on credit cards, and $7977 for entertainment, travel, and other. You expect to get a 25% raise next year. Could you afford $4113 in tuition and fees without going into debt? A) Yes B) No 221) You have money in an account at an APR of 4% compounded quarterly. To the nearest year, how long will it take for your money to triple? A) 39 years B) 17 years C) 22 years D) 28 years

218)

219)

220)

221)

Solve the problem. Refer to the table if necessary.

222) Kevin is married, but he and his wife filed separately. His gross salary was $34,707, and he earned $466 in interest. He had $1848 in itemized deductions and claimed three exemptions for himself and two children. Find his taxable income. A) $14,825 B) $22,925 C) $24,773 D) $16,673 Prorate the given expenses to find the monthly cost. 223) Sarah takes courses on a quarter system. Three times a year, she takes 15 credits at a tuition rate of $300 per credit; her fees are $210 per quarter and her room in a shared house costs $150 per week. Round your answer to the nearest dollar. A) $1828 B) $1043 C) $1328 D) $2563 Solve the problem. 224) You need a $119,286 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: $887.98 B) Option 1: $891.49 Option 2: $1108.07 Option 2: $1119.74 C) Option 1: $875.28 D) Option 1: $864.45 Option 2: $1072.18 Option 2: $1040.38

222)

223)

224)

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

225) A single 31-year old woman with a monthly salary of $3100 spends $560 on food. A) at average B) above average C) below average

225)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 226) $5500 deposit at an APR of 4% with monthly compounding for 6 years 226) A) $30,902.61 B) $6989.08 C) $5610.92 D) $5591.26

Solve the problem. Refer to the table if necessary.

227) You are single and have a taxable income of $61,855. You make monthly contributions of $540 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 $2160 less per year with tax-deferred plan B) Take-home pay will be $1620 less per year with tax-deferred plan C) Take-home pay will be $2160 more per year with tax-deferred plan D) Take-home pay will be $1620 more per year with tax-deferred plan Solve the problem. 228) You need a $89,515 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: $648.70 B) Option 1: $669.00 Option 2: $806.28 Option 2: $865.08 C) Option 1: $656.83 D) Option 1: $666.36 Option 2: $829.82 Option 2: $856.42 Provide an appropriate response. 229) True or False? If you buy an item (such as property or stock) at one price and later sell it at a higher price, the profit is called a capital gain. A) True B) False Complete the sentence: On an annual basis the first set of expenses is ____ % of the second set of expenses. 230) Julio goes to a concert once every two weeks at an average ticket price $70; he spends $800 per year on car insurance. A) 19% B) 455% C) 105% D) 228%

227)

228)

229)

230)

Provide an appropriate response. 231) True or False? A loan that you pay off with equal regular payments is called an installment loan. A) True B) False Solve the problem. 232) Suppose you start saving today for a $20,000 down payment that you plan to make on a house in 10 years. Assume that you make no deposits into the account after your initial deposit. The account has quarterly compounding and an APR of 3%. How much would you need to deposit now to reach your $20,000 goal in 10 years? A) $15,490.39 B) $12,342.98 C) $9495.49 D) $14,832.96

231)

232)

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

233) 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 Solve the problem. 234) 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 2% decrease in total receipts? A) $361 billion B) $369 billion C) $365 billion D) $355 billion Provide an appropriate response. 235) All of your income for the year including wages, tips, profits from a business, interest or dividends from investments is called your _____ income. A) taxable B) adjusted gross C) gross D) None of the above

233)

234)

235)

Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period. 236) $19,000 deposit at an APR of 2% with semiannual compounding for 5 years 236) A) $20,900.00 B) $20,987.82 C) $19,969.19 D) $20,977.54

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

237) A single 51-year old woman with a monthly salary of $4800 spends $240 on health care. A) at average B) above average C) below average Answer the question. 238) You currently drive 360 miles per week in a car that gets 20 miles per gallon of gas. A new fuel-efficient car costs $12,000 (after trade-in on your current car) and gets 60 miles per gallon. Insurance premiums for the new and old car are $900 and $600 per year, respectively. You anticipate spending $1400 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) 4.7 years B) 4.1 years C) 5.2 years D) 3.7 years Provide an appropriate response. 239) ________ 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 240) True or False? Early in an installment loan term, the portion going toward interest is relatively high and the portion going toward principal is relatively low. As the term proceeds, the portion going toward interest gradually decreases and the portion going toward principal gradually increases. A) False B) True

237)

238)

239)

240)

Solve the problem. 241) 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.

241)

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) $847 billion B) $1.1 trillion C) $1 trillion

D) $965 billion

Provide an appropriate response. 242) A(n) ________ deduction is the addition of all individual deductions to which you are entitled. A) itemized B) complete C) standard D) None of the above

242)

Solve the problem. Refer to the table if necessary.

243) Carmen and James are married and filed jointly. Their combined wages were $88,560. They earned a net of $2146 from a rental property they own, and they received $1692 in interest. They claimed four exemptions for themselves and two children. They contributed $4113 to their tax-deferred retirement plans, and their itemized deductions total $10,460. Find their adjusted gross income. A) $84,901 B) $88,285 C) $106,971 D) $77,825

243)

244) John is married filing separately with taxable income of $172,163. Calculate the amount of tax owed. A) $39,983 B) $49,538 C) $44,422 D) $41,648 Solve the equation for the unknown. 245) x2 - 6 = 30 A) x = 5

B) x = ± 5

C) x = 6

D) x = ± 6

244)

245)

Solve the problem. Refer to the table if necessary.

246) Your deductible expenditures $5238 for contributions to charity and $646 for state income taxes. Your filing status entitles you to a standard deduction of $6350. Should you itemize your deductions rather than claiming the standard deduction? If so, what is the difference? A) Yes, $466 B) Yes, $5884 C) Yes, $1758 D) No, you are better off with the standard deduction. Prorate the given expenses to find the monthly cost. 247) Keiko pays $280 per month for food, a semiannual health insurance premium of $1200, and an annual car insurance premium of $500. Round your answer to the nearest dollar. A) $265 B) $422 C) $563 D) $522 Provide an appropriate response. 248) True or False? The publicly held debt represents money the government must repay to individuals and institutions that bought Treasury issues. A) True B) False

246)

247)

248)

Use the given stock table to answer the question. 249) How does the share price for company ABC compare to the profit per share that it earned in the past year? 249) 52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s High ABC 0.63 2.5 26 4156 25.68 XYZ 0.21 1.2 14 9175 18.17

Low Close 24.87 25.13 17.26 17.51

A) price = 26 × earnings C) price = 2.5 × earnings

Net Chg -0.19 +0.09

B) price = 25.13 × earnings D) earnings = 26 × price

Compute the total and annual returns on the described investment. 250) Five years after paying $14,077 for shares in a new company, you sell the shares for $8877. A) Total Return: -35.09% B) Total Return: -38.79% Annual Return: -8.37% Annual Return: -9.25% C) Total Return: -36.94% D) Total Return: -29.55% Annual Return: -8.81% Annual Return: -7.05% Calculate the balance under the given assumptions. 251) Find the savings plan balance after 8 years with an APR of 4% and monthly payments of $473. A) $53,410.47 B) $4959.51 C) $5834.72 D) $45,398.90

250)

251)

You need a loan of $100,000 to buy a condo. Calculate your monthly payments and total closing costs for each choice. 252) Choice 1: 30-year fixed rate at 4.5% with closing costs of $1341 and no points 252) Choice 2: 20-year fixed rate at 4% with closing costs of $1341 and 4 points A) Choice 1: $506.69; $1341 B) Choice 1: $510.04; $1341 Choice 2: $605.98; $5341 Choice 2: $609.07; $5091 C) Choice 1: $516.61; $1341 D) Choice 1: $496.67; $1341 Choice 2: $615.99; $2682 Choice 2: $595.94; $5141 Solve the problem. 253) $702 is deposited into a savings account at 6% interest, compounded monthly. To the nearest year, how long will it take for the account balance to reach $1,000,000? A) 121 years B) 85 years C) 109 years D) 170 years

253)

Solve the problem. Refer to the table if necessary.

254) Kelly earned wages of $98,276, received $4944 in interest from a savings account, and contributed $6169 to a tax deferred retirement plan. She was entitled to a personal exemption of $4050 and had deductions totaling $8773. Find her gross income. A) $97,051 B) $84,228 C) $103,220 D) $109,389 Use the given stock table to answer the question. 255) How much profit per share did company ABC earn in the past year?

255)

52-Week High Low 33.16 16.74 27.83 12.07

Yld Vol Stock Div % P/E 100s High ABC 0.63 2.5 21 4156 25.68 XYZ 0.21 1.2 13 9175 18.17

Low Close 24.87 25.35 17.26 17.39

A) $1.21

B) $1.15

C) $1.27

D) $1.02

C) -8

D) 8

Solve the equation for the unknown quantity. 256) 6z + 13 = 5z + 5 A) 18 B) -18

254)

Net Chg +0.22 +0.09

256)

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. 257) 257) Income Expenses Salary: $32,000/year House payments: $1700/month Jewelry sales: $350/month Groceries: $120/week Household expenses: $360/month Car insurance: $480 semiannually Donations: $500/year Miscellaneous: $800/month A) -$405 B) -$445 C) -$85 D) -$766

Provide an appropriate response. 258) True or False? A full-service broker offers advice based on in-depth research. A) True B) False

258)

Solve the problem. Refer to the table if necessary.

259) Abbey earned $67,862 in wages. Kathryn earned $67,862, all in dividends and long-term capital 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% for income in the 10% and 15% tax brackets and at 15% for income in all higher tax brackets except the highest 39.6% bracket. If necessary, round values to the nearest dollar. A) Abbey: $10,104 B) Abbey: $14,531 C) Abbey: $15,569 D) Abbey: $15,296 Kathryn: $2927 Kathryn: $8153 Kathryn: $4878 Kathryn: $2927

259)

Answer the question. 261) 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 $359,052 per year-forever! How can you do it? Assume a constant APR of 5% compounded monthly. A) Deposit $4705.73 per month. B) Deposit $5654.29 per month. C) Deposit $3605.86 per month. D) Deposit $4174.75 per month.

261)

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. 262) Principal: $810 Rate: 4% Years: 17 262) A) $188.71 B) $217.00 C) $1027.00 D) $476.20

Answer Key Testname: CHAPTER 4 1) B 2) A 3) A 4) A 5) A 6) B 7) 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. 8) Month Payment Expenses Interest New Balance 0 $1400 1 $600 $280 $21.00 $1101.00 2 $600 $280 $16.52 $797.52 3 $600 $280 $11.96 $489.48 4 $600 $280 $7.34 $176.82 A partial 5th payment will pay off the loan. 9) No, the statement does not makes sense. The annual percentage yield would be equal to 6% if the interest were compounded annually or more than 6% if the interest were compounded more frequently. The annual percentage yield cannot be less than the APR of 6%. 10) 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 $16 × 52 = $832 per year. 11) 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. 12) Yes, the statement makes sense. With a shorter-term loan, the total amount of interest paid will be less. 13) 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. 14) No, the statement does not make sense. The extra amount she will end up owing after three months will be more than $180. 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. 15) 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. 16) Yes, the statement makes sense. Maria and her sister must be in different tax brackets. Maria must be in the 25% tax bracket so the tax deduction of $3000 saves her 0.25 × $3000 = $750. Her sister must be in the 15% tax bracket so she saves only 0.15 × $3000 = $450. 17) 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. 18) 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. 19) 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. 20) The average person spends about 33% of their budget on housing. If Paul spends $900 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. 21) No, the statement does not make sense. After 10 years, less than one third 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. 50

Answer Key Testname: CHAPTER 4 22) 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. 23) 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. 24) 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. 25) No, the statement does not make sense. If both accounts are paying the same APR, the account which compounds interest continuously will have a higher annual percentage yield than the account which compounds daily. 26) 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 12 years instead of 24. Payment Toward End of... Interest Principal New Principal 27) Month 1 $279.97 $229.55 $41,766.45 Month 2 $278.44 $231.08 $41,535.36 Month 3 $276.90 $232.62 $41,302.74 28) 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. 29) 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. 30) 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. 31) 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 6% for 10 years would have given an accumulated amount of P(1 + 0.06)10 which comes to 1.79P, a total return of 79% not 60%. In fact, the annual return corresponding to a total return of 60% over 10 years would be 1.6 1/10 - 1 which comes to 4.8%. 32) 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 22.5% 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. 33) 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. Payment Toward End of... Interest Principal New Principal 34) Month 1 $771.00 $253.72 $131,917.28 Month 2 $769.52 $255.20 $131,662.07 Month 3 $768.03 $256.69 $131,405.38 35) 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. 36) Yes, this statement makes sense.

Answer Key Testname: CHAPTER 4 37)

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

38) Yes, the statement makes sense. 39) 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. 40) 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. 41) 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. 42) 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. 43) 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. 44) 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. 45) No, the statement does not make sense. Due to inflation, the buying power of $25,000 will decrease over time. As the years go by, the amount that Paul needs to live on per year will increase, and $25,000 per year will no longer be enough. 46) 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. 47) B 48) C 49) B 50) A 51) D 52) A 53) B 54) D 55) B 56) A 57) A 58) C 59) C 60) B 61) D 62) A 63) D 64) D 65) C 66) A 67) A 68) B 52

Answer Key Testname: CHAPTER 4 69) B 70) D 71) D 72) A 73) B 74) C 75) D 76) D 77) D 78) B 79) D 80) C 81) A 82) A 83) A 84) A 85) A 86) B 87) A 88) A 89) B 90) C 91) C 92) C 93) D 94) A 95) C 96) A 97) B 98) C 99) A 100) A 101) D 102) A 103) C 104) A 105) C 106) C 107) B 108) D 109) A 110) C 111) B 112) B 113) D 114) B 115) C 116) C 117) A 118) C 53

Answer Key Testname: CHAPTER 4 119) B 120) A 121) A 122) C 123) D 124) C 125) C 126) A 127) B 128) C 129) C 130) A 131) B 132) A 133) B 134) D 135) D 136) C 137) D 138) C 139) A 140) A 141) A 142) B 143) C 144) C 145) D 146) B 147) D 148) C 149) A 150) C 151) C 152) B 153) C 154) C 155) A 156) D 157) D 158) A 159) C 160) A 161) D 162) C 163) B 164) B 165) A 166) A 167) A 168) A 54

Answer Key Testname: CHAPTER 4 169) B 170) B 171) D 172) D 173) C 174) A 175) C 176) A 177) D 178) B 179) C 180) B 181) B 182) D 183) B 184) A 185) C 186) D 187) B 188) A 189) D 190) C 191) D 192) B 193) B 194) D 195) A 196) A 197) C 198) C 199) A 200) B 201) B 202) B 203) B 204) B 205) D 206) B 207) D 208) B 209) C 210) C 211) B 212) C 213) C 214) B 215) D 216) B 217) D 218) B 55

Answer Key Testname: CHAPTER 4 219) C 220) A 221) D 222) D 223) A 224) C 225) B 226) B 227) D 228) C 229) A 230) D 231) A 232) D 233) A 234) A 235) C 236) B 237) A 238) D 239) C 240) B 241) C 242) C 243) B 244) C 245) D 246) D 247) D 248) A 249) A 250) C 251) A 252) A 253) A 254) C 255) A 256) C 257) B 258) A 259) D 260) A 261) A 262) B

Chapter 5 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer as requested. 1) 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) Evidence that larger amounts of the suspected cause produce larger amounts of the effect. B) A physical model demonstrating how abortion can cause breast cancer C) Verification that breast cancer rates differ among groups that differ only in the presence or absence of the suspected cause (abortion). D) An experiment to establish causality between abortion and breast cancer. Answer the question. 2) Which of the following describes the bias that can occur when members of a study's sample are volunteers? A) Participation bias B) Single-blind bias C) Selection bias D) Sample bias Choose the best wording for the question in the study. 3) 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 do you think is the most popular car on the road? B) What kind of car do you drive? C) Do you agree that the Gemini is the most popular car on the road? D) What kind of car do you recall seeing most often on the highway?

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? 4) Are short women more likely to develop breast cancer than tall women? 4) A) Experiment with double blinding B) Experiment without blinding C) Case-control study D) Experiment with single blinding E) Observational study

5) Does caffeine cause birth defects? A) Experiment with single blinding B) Observational study C) Experiment without blinding D) Experiment with double blinding E) Case-control study

Answer as requested. 6) A researcher finds a positive correlation between the amount of wine people drink and the number of 6) 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) A and B C) B and C D) A

Answer the question. 7) Which of the following describes a study in which the researchers do not attempt to change the characteristics of those being studied? A) Case-control study B) Single-blind experiment C) Double-blind experiment D) Observational study

8) Which of the following quantities of interest would be the most difficult to define? A) The least expensive brand of paint B) The paint with the best looking finish C) How water resistant a brand of paint is D) The levels of lead in various brands of paint

9) Which of the following describes the process by which scientists examine each others' research? A) Interpretation B) Peer review C) Participation review 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. 10) Describe the trend in world population during the period 1960-1962 A) It remains constant B) It decreases at a steady rate C) It increases at a constant rate D) It increases at a faster and faster rate

10)

Answer as requested. 11) Which of the following pairs of variables is likely to have no correlation? A) The amount of time studying math and grade on a math test 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 unemployment rate and the number of home foreclosures

11)

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. 12) In which year during the period 1960-2010 is estimated world population the greatest? A) 1960 B) 1963 C) 1970 D) 2010

13) How does world population in 1978 compare to world population in 1977? A) It is the same B) It is 1.75% less C) It is 1.75 million greater D) It is 1.75% greater

12)

13)

Answer as requested. 14) Suppose that there is perfect positive correlation between the number of hours studied for a test and score 14) 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) A B) A and D C) All statements are true D) B and C

Answer the question. 15) Double blinding is used in an experiment to avoid which of the following problems? A) If an experimenter knows whether the patient has received the treatment or the placebo, this may influence how he or she questions the patient B) If the patient knows that he received the placebo and not the treatment he may be angry and fail to tell the truth C) If improvement is observed in a patient, it is difficult to know whether this is due to the treatment or the placebo effect D) If the researcher knows that the patient received the treatment, the researcher may also experience health changes

15)

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. 16) In which year(s) during the period 1960-2010 is world population growing at the fastest rate? A) 2010 B) 1963-1964 C) 1984 D) 1970

16)

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? 17) Can acupuncture relieve anxiety? [The level of anxiety at any given time will be determined by 17) interviewing the patient. The interviewer will be a person other than the acupuncturist.] A) Experiment with double blinding B) Case-control study C) Experiment without blinding D) Observational study E) Experiment with single blinding

Answer the question. 18) In a study to determine the average weight of a house cat, which of the following is the most representative sample? A) All of the cats that a veterinarian sees in one week B) All of the cats in your neighborhood C) All of the cats that a pet groomer sees in one week D) Some of the cats in each of several neighborhoods 4

18)

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? 19) Does an hour of meditation per day lower blood pressure? 19) A) Observational study B) Case-control study C) Experiment with single blinding D) Experiment without blinding E) Experiment with double blinding

Choose the best wording for the question in the study. 20) 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 know which proposition will raise state sales tax and fund music education? B) Will you vote for proposition EZ which will raise the amount of state sales tax that you pay every year? C) Are you planning to vote for Proposition EZ which will raise state sales taxes and support music education? D) Do you believe that music education is important?

20)

Answer as requested. 22) Which of the following is not a guideline for establishing causality? A) Find a physical model that explains how the cause produces the effect. B) Seek evidence that larger amounts of the cause produce larger amounts of the effect. C) If possible, test the suspected cause with an experiment. D) Consider only the suspected cause, ignoring other potential causes.

22)

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. 23) How does world population in the year 1000 AD compare with world population in the year 2000 BC?23)

A) The 1000 AD population is roughly one 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 ten million larger than the 2000 BC population. D) The 1000 AD population is roughly 14% larger than the 2000 BC population. Answer the question. 24) Which of the following describes a study in which neither the participants nor the experimenters know which participants are in the control group? A) Observational study B) Single-blind experiment C) Double-blind experiment D) Case-control study Choose the best wording for the question in the study. 25) In a survey to assess attitudes toward genetically modified foods, which of the following survey questions will give the most accurate results? A) Do you agree with increasing the production of genetically modified foods which could be harmful to the environment? B) How do you feel about allowing untested genetically modified foods to be sold in stores? 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?

24)

25)

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? 26) Does the new medication relieve depression? 26) A) Experiment with double blinding B) Experiment with single blinding C) Observational study D) Case-control study E) Experiment without 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. 27) Describe the trend in world population during the period 1976-1978 A) It increases at a faster and faster rate B) It remains constant C) It increases at a steady rate D) It decreases at a steady rate

Answer the question. 28) 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) Double-blind bias B) Availability bias C) Selection bias D) Participation bias 29) 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) 83% of the seniors who applied for admission to Valley State College were accepted. C) 53% of the senior class was accepted for admission to Valley State College in the fall. D) 25% of the senior class scored below average on the math portion of a national aptitude test.

27)

28)

29)

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. 30) Describe the trend in world population during the period 1990-2000 A) It decreases at a faster and faster rate B) It increases at a steady rate C) It decreases at a steady rate D) It increases at a slower and slower rate

Choose the best wording for the question in the study. 31) 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) Is our selection as good as the selection of our competitor? B) Is there anything you would have purchased if our stock was not without it? C) Do you agree that our selection is better than our competitor? D) Are you satisfied with the selection at this store? Answer as requested. 32) 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) Cause beyond reasonable doubt B) Probable cause C) Possible cause D) Absolute certainty

30)

31)

32)

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? 33) In which of these four soil types will the plants grow fastest? 33) A) Experiment without blinding B) Case-control study C) Experiment with double blinding D) Observational study E) Experiment with single blinding

Log World Population

Year Use the graph to answer the question. 34) During the period 4000 BC to 1000 BC, approximately what was the doubling time for world population? 34)

A) Approximately 23,000 years C) Approximately 1000 years

B) Approximately 5000 years D) Approximately 3000 years

Answer the question. 35) Which of the following quantities of interest would be the most difficult to measure? A) The team member with the highest salary B) The best looking team member C) The team member with the longest hair D) The average height of a volleyball team

35)

36) In a study to determine the most popular automobile on the road, which of the following is the 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 that drive by your house D) A random sample of the cars parked at an airport

36)

37) Which of the following quantities of interest would be the most difficult to measure? A) The largest crop of tomatoes B) The best tasting tomato crop C) The levels of pesticides in a tomato crop D) The crop with the largest tomatoes

37)

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? 38) Do Super-Slimmer Shakes increase weight loss? 38) A) Observational study B) Experiment with single blinding C) Experiment with double blinding D) Experiment without 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. 39) In which year(s), if any, during the period 1960-2010 is world population constant? A) None B) 1969-1971 C) 1962-1964 D) 1962-1964, 1969-1971, 1975-1980

Choose the best wording for the question in the study. 40) 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) Are you in favor of the new environmental law which will improve the quality of our air? B) Are you in favor of the new environmental law which will cost taxpayers ten million dollars? C) How do you feel about the new environmental law? D) How do you feel about this latest new environmental law? Answer the question. 41) 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) She is certain to win B) It is about 50-50 C) She has a 54% chance of winning D) She is very likely to win

39)

40)

41)

42) Which of the following describes a study in which the participants naturally form groups by choice? A) Double-blind experiment B) Case-control study C) Observational study D) Single-blind experiment

42)

43) Which of the following is not an argument against using blinding in an experiment? A) The participants in the experiment don't believe in the placebo effect B) The experiment is done on plants, not people C) The experiment involves animals, not people D) It would be impossible to conceal from the participants whether they are receiving the treatment or the placebo

43)

Answer as requested. 44) Which of the following is likely a coincidence? A) Higher incidence of skin cancer in regions with more sunshine B) Higher real estate prices in cities with more employment opportunities C) More crime in neighborhoods with fewer streetlights D) Higher annual rainfall in states with fewer homicides Answer the question. 45) Which of the following quantities of interest would be most difficult to determine? A) The percentage of children who brush their teeth at least twice a day B) The number of children not counted in the last census C) The percentage of second graders who read above grade level D) The number of children living below the poverty line 46) A researcher wishes to determine the percentage of voters in a town who favor stronger environmental laws. Which of the following would be the most representative sample? A) A random sample of college students B) A sample selected randomly from the phone book C) A sample consisting of every 10th person leaving an organic food store D) A sample of listeners who call in to a radio talk show

44)

45)

46)

Log World Population

Year Use the graph to answer the question. 47) How does world population in the year 2000 AD compare with world population in the year 4000 BC?47)

A) The 2000 AD population is roughly thirty times as large as the 4000 BC population. B) The 2000 AD population is roughly three billion larger than the 4000 BC population. C) The 2000 AD population is roughly 44% larger than the 4000 BC population. D) The 2000 AD population is roughly one thousand times as large as the 4000 BC population. 48) Describe the general trend in world population during the period 2000 BC to the year 1 AD.

48)

A) World population increases at a slower and slower rate. B) World population increases at a faster and faster rate. C) World population increases at a constant rate. D) World population is constant. Answer the question. 49) 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) Double-blind experiment B) Single-blind experiment C) Case-control study D) Observational study Choose the best wording for the question in the study. 50) 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) Which restaurant in the city do you visit most often? B) Which restaurant in the city do you think is the most crowded? C) Which restaurant do you think is the most popular in the city? D) Do you agree that Snazzy's is the most popular restaurant in the city? 12

49)

50)

51) A researcher wants to determine the level of support for the war. Which of the following questions would produce the most accurate results? A) Do you agree that it is important to defend our country against terrorism? B) Do you support the troops? C) How do you feel about the war? D) Do you agree that the troops should be brought home to safety now?

51)

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? 52) What percentage of the population reads a newspaper on a regular basis? 52) A) Case-control study B) Experiment without blinding C) Experiment with single blinding D) Experiment with double blinding E) Observational study

53) How do lawyers' salaries compare to doctors' salaries? A) Case-control study B) Observational study C) Experiment with single blinding D) Experiment without blinding E) Experiment with double blinding Answer as requested. 54) Which of the following is likely a cause-and-effect relationship? A) When the rooster crows, the morning glories open. B) When I see stars, I also see the moon. C) When the temperature drops, consumption of heating oil rises. D) When I drive to work, the sun rises.

53)

54)

55) Which of the following is likely the result of some common underlying cause rather than a direct cause? A) When the NASDAQ rises, the Dow Jones Industrial Average also tends to rise. B) The more items sold, the greater the revenue. C) The more cash I take out at the ATM, the more my account balance decreases. D) People who eat a lot of dessert tend to be heavier than those who don't.

55)

56) Which of the following pairs of variables is likely to have a negative correlation? A) Interest rates and the number of real estate transactions B) Height and weight. C) The unemployment rate and the number of homeless people D) The price of jet fuel and the price of airline tickets.

56)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 57) 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.

57)

Use the indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 58) The weekly incomes (in dollars) of 20 college students are shown below. 58) 120 178 90 74

180 215 144 136

240 268 336 85

330 165 0 305 116 0 165 62

Use 50-point bins (0-49, 50-99, etc)

Provide an appropriate response. 59) Shortly before a mayoral election, a market research firm took a poll to find out which candidate 59) 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.

60) Suppose that a histogram is constructed for the frequency table shown below: 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?

60)

Describe how you would apply the five basic steps of a statistical study to the given issue. 61) 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. 62) 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. Solve the problem. 63) 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. Describe how you would apply the five basic steps of a statistical study to the given issue. 64) You want to know the average amount paid in rent by tenants of the city of Hazelwood. Answer the question. 65) 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.

61)

62)

63)

64)

65)

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 66) A researcher from an environmental group wishes to gauge political sentiment regarding 66) 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. Describe how you would apply the five basic steps of a statistical study to the given issue. 67) 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. Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 68) 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.

67)

68)

Make a bar graph to represent the data. 69) The following table shows the number of male infants born at Hospital X on New Year's Day (Jan. 69) 1). Create a horizontal bar graph. No. of Male Year Infants Born on Jan 1 1980 15 1981 35 1982 25 1983 40 1984 25 1985 25

Provide an appropriate response. 70) 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?

70)

Use the graph to answer the question. 71) The bar graph below shows the relative frequencies of the different blood types. Write a sentence 71) describing what is revealed by the graph.

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. 72) The table below gives information about U.S. families with children under the age of 18. 72) 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%

Answer the question. 73) Andrew creates a bar graph to show the increase in his company's sales. He wants to show 73) 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?

Provide an appropriate response. 74) Construct a frequency table and the corresponding histogram in which the following conditions 74) 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 Describe how you would apply the five basic steps of a statistical study to the given issue. 75) You want to know the percentage of adults in the U.S. who have ever sought treatment from a practitioner of complementary medicine.

75)

Provide an appropriate response. 76) Shortly before an election, a market research firm took a poll to find out whether people were 76) planning to vote for or against a particular ballot measure. The results are shown below. 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 indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 77) On a math test, the scores of 24 students were as follows: 77) 97 78 74 65 74 74 97 81 74 63 87 78 78 87 74 78 87 74 78 81 78 87 81 65 Use ten-point bins (60-69, 70-79, etc)

Use the graph to answer the question. 78) The following time-series diagram tracks the performance of two stocks during the month of 78) October.

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?

79)

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.

Describe how you would apply the five basic steps of a statistical study to the given issue. 80) 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. Solve the problem. 81) A researcher finds a negative correlation between blood pressure and the number of 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. Provide an appropriate response. 82) Suppose that you want to construct a graph to represent the following data.

80)

81)

82)

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.

Construct the specified histogram. 83) In a survey, 20 voters were asked their age. The results are summarized in the frequency table 83) below. Construct a histogram . Age Number of voters 20-29 5 30-39 5 40-49 6 50-59 0 60-69 4

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. 84) The table below shows statistics for AIDS. The first column shows the estimated number of 84) 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

Make a bar graph to represent the data. 85) 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

2 1 9 1 6 1

Relative frequency 0.10 0.05 0.45 0.05 0.30 0.05

85)

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 86) A TV show announced that their survey had revealed that 87% of Americans would rather be free than rich.

86)

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)

Provide an appropriate response. 88) 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.

88)

Use the indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 89) The ages of 25 patients who suffered strokes are as follows. 89) 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)

Solve the problem. 90) 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.

90)

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

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 92) 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.

92)

93) A researcher is interested in why Americans have such a high divorce rate. She randomly selects 93) 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. Answer the question. 94) The bar graph below shows the number of car accidents occurring in one city in each of the years 94) 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?

Provide an appropriate response. 95) Suppose that you want to construct a pie chart to represent the following data. 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.

95)

96) Consider the frequency table below which has single values as classes: Value 10 11 12 13 14 15 16 17 18 19 20 21

96)

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?

Answer the question. 97) The graph below shows the approximate annual percentage growth rate in world population for 97) the years 1960 through 2010. Data is estimated by the UN Census Bureau. 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.

Construct the specified histogram. 98) 24 high school students were asked how many hours they had spent preparing for a test. The 98) 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.

Answer the question. 100) 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

100)

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?

Use the indicated bin size to construct a frequency table for the set of data. Include columns for relative frequency and cumulative frequency. 101) Kevin asked some of his friends how many hours they had studied for the test. The times are 101) shown below: 6 5

5 6 3 8 6 5

6 6 8 6

9 5

7 6 4 8 5 7 5 8 7 3

Use 2-point bins (3-4, 5-6, etc)

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 102) 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.

102)

103) 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. Use the graph to answer the question. 104)

103)

104)

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.

Construct the specified histogram. 105) 30 police detectives were asked how many days they had taken off in the previous year. The 105) results are summarized in the frequency table below . Days off Frequency 0- 1 10 2 -3 1 4-5 7 6-7 7 8-9 1 10 -11 4 Construct a histogram.

Use the guidelines to evaluate the study. Discuss flaws that you see in the study. 106) 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?" Solve the problem. 107) 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.

106)

107)

Make a bar graph to represent the data. 108) The following table shows the number of female infants born at Hospital X on New Year's Day108) (Jan. 1). Create a vertical bar graph. No. of Female Year Infants Born Jan 1 1980 21 1981 12 1982 18 1983 30 1984 27 1985 24

Female 237 225 282 270 216 192 189 236

Use the graph to answer the question. 110) The time series line chart below shows the price of a volatile stock from January to December of 110) the same year. Describe the overall trend in the price during that period.

Make a bar graph to represent the data. 111) The following table shows the number of inches of rainfall measured at City X during the following days. Create a horizontal bar graph.

111)

No. of Inches Day of Rainfall April 9 1.26 April 24 1.94 May 9 3.26 May 24 2.54 June 9 2.02 June 24 1.86

Answer the question. 112) A parcel delivery service lowered its prices and finds that it has delivered twice as many parcels 112) 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?

113) A television manufacturer sold three times as many televisions in 1995 as it did in 1985. To 113) 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?

Make a bar graph to represent the data. 114) 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

114)

Answer the question. 115) The bar graph below shows the average cost of renting a studio in a certain city in each of the 115) 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?

Use the graph to answer the question. 116) This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period.

116)

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 .

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 117) For the study described below, identify the sample statistic.

117)

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) 120, the number of light bulbs in the sample B) The average lifetime of all 75-watt light bulbs manufactured by the company C) The 120 randomly selected 75-watt light bulbs D) The average lifetime of the 120 randomly selected 75-watt light bulbs

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; common underlying cause B) Negative correlation; direct cause C) Positive correlation; direct cause D) Positive correlation; common underlying cause

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 119) A market researcher selects 500 people from each of 10 cities. A) Systematic B) Convenience C) Simple random D) Stratified Make a scatter diagram for the data.

119)

120) The table shows the unemployment rate and the median price of renting an apartment in nine cities. 120) 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.

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 121) A researcher interviews 19 work colleagues who work in his building. A) Stratified B) Simple random C) Convenience D) Systematic

121)

Identify the variable as either qualitative or quantitative. 122) The heights of individuals in meters A) Quantitative

122)

B) Qualitative

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 123) 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) Selection bias C) The source of the study D) Confounding variables E) Participation bias 124) "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) Selection bias B) Participation bias C) Confounding variables D) Setting may not encourage honest responses E) Wording of question

123)

124)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 125) Actual temperature on a given day and the temperature that had been forecast for that day 10 days 125) previously. A) Weak positive correlation B) Strong negative correlation C) Strong positive correlation D) Weak negative correlation E) No correlation 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. 126) In which year was the total value of Danny's investments the greatest? A) year 0 B) year 5 C) year 8

D) year 4

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 127) 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) Variables are difficult to define/measure D) The setting may not encourage honest responses E) The source of the study

126)

127)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 128) Number of siblings and number of pairs of shoes owned by children 128) A) Weak positive correlation B) No correlation C) Weak negative correlation D) Strong negative correlation E) Strong positive correlation

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 129) 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 B) Selection bias C) The source D) Confounding variables E) Participation bias

129)

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. 130) The CEO of a company claims that 90% of its employees have very high job satisfaction. A poll of 130) the company's employees revealed that 88 percent had very high job satisfaction with a margin of error of 2.4 percentage points. Can we conclude that the CEO was lying? A) 85.6% to 88%; yes B) 86.8% to 89.2%; yes C) 88% to 90.4%; no D) 85.6% to 90.4%; no

Construct a pie chart representing the given data set. 131) Intended major of high school students: Science: 32% Social Science: 8% Humanities: 20% Business: 16% Other: 24%

131)

Solve the problem. 132) For the study described below, identify the population parameter.

132)

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) The average wait time for the 300 customers polled. B) All customers of the bank C) The percentage of dissatisfied customers. D) The average wait time for all the bank's customers.

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 133) You are interested in the degree of satisfaction amongst customers at your video store. For one week, you 133) 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) Participation Bias and Selection Bias B) Selection Bias C) No Bias D) Participation Bias

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 134) 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 B) Selection bias C) Confounding variables D) The source E) Variables are hard to define/measure

134)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 135) Number of appliances sold and revenue of appliance store 135) A) Strong positive correlation B) Weak negative correlation C) Weak positive correlation D) Strong negative correlation E) No correlation

Identify the variable as either qualitative or quantitative. 136) The colors of the houses in a city A) Quantitative

B) Qualitative

136)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 137) Test score and height for adults 137) A) Weak positive correlation B) Strong positive correlation C) No correlation D) Strong negative correlation E) Weak negative correlation

Solve the problem. 138) For the study described below, identify the population.

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) All American women B) All American women working for large companies C) The 1500 women polled D) The percentage of American women working for large companies who feel that women are under represented in management positions in their company.

Identify the variable as either qualitative or quantitative. 139) 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

139)

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 140) 140)

A) Strong negative correlation B) Strong positive correlation C) Weak positive correlation D) No correlation E) Weak negative correlation Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 141) 49 students are selected at random from the Sophomore class, 39 from the Junior class, and 48 from the Senior classes. A) Systematic B) Convenience C) Simple random D) Stratified

141)

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 142) 142)

A) Strong negative correlation B) No correlation C) Weak positive correlation D) Strong positive correlation E) Weak negative correlation 38

Solve the problem. 143) For the study described below, identify the population.

143)

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) All 75-watt light bulbs manufactured by the company B) The 120 randomly selected 75-watt light bulbs C) All 75-watt light bulbs D) The average lifetime of all 75-watt light bulbs manufactured by the company

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. 144) Over the last 10 years in this town, as the amount of open space has decreased, consumer spending 144) has increased. A) Positive correlation; direct cause B) Positive correlation; common underlying cause C) Negative correlation; common underlying cause D) Negative correlation; direct cause

Solve the problem. 145) For the study described below, identify the sample statistic.

145)

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 300 people polled B) The average wait time for all of the bank's customers C) The average wait time for the 300 customers polled D) The percentage of dissatisfied customers among all of the bank's 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. 146) In a survey conducted in a certain city it was found that 5.3% of men and 6.1% of women were 146) unemployed. The margin of error for each report was 0.6 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: 5% to 5.6% B) men: 5.3% to 5.9% women: 5.8% to 6.4% women: 5.5% to 6.1% yes no C) men: 4.7% to 5.9% D) men: 4.7% to 5.3% women: 5.5% to 6.7% women: 6.1% to 6.7% no yes

Construct a pie chart representing the given data set. 147) Main form of exercise for employees of one company: None: 28% Walking: 19% Running: 6% Golf: 11% Weight Training: 25% Other: 11%

147)

Identify the variable as either qualitative or quantitative. 148) The speed of a car in miles per hour A) Qualitative

B) Quantitative

148)

Solve the problem. 149) For the study described below, identify the sample.

149)

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) All emergency-room nurses in the U.S. B) The average stress rating for the 275 emergency-room nurses interviewed C) The 275 emergency-room nurses interviewed D) The questionnaire given to the 275 emergency-room nurses interviewed

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 150) You are interested in the percentage of people in your city who favor tax cuts. You interview every 150) twentieth person as they leave the church in your neighborhood. A) Participation bias and selection bias B) Participation bias C) No bias D) Selection bias

Construct a pie chart representing the given data set. 151) Favorite Beverage Number of responses Cola 68 Juice 42 Milk 46 Tea 62 Water 30

151)

32%

28%

19%

16%

12%

27%

25%

19%

17%

30%

68%

62%

46%

42%

24%

28%

19%

21%

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. 152) People who eat a lot of junk food are heavier, on the whole, than those who do not. 152) A) Positive correlation; coincidence B) Positive correlation; direct cause C) Negative correlation; direct cause D) Positive correlation; common underlying cause

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 153) A tax auditor selects every 1000th income tax return that is received. A) Stratified B) Convenience C) Simple random D) Systematic Construct a line chart for the data.

153)

154)

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

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 155) 155)

A) Strong negative correlation B) Strong positive correlation C) No correlation D) Weak negative correlation E) Weak positive correlation Solve the problem. 156) For the study described below, identify the population parameter.

156)

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) All emergency-room nurses in the U.S. B) The average stress rating for all emergency-room nurses in the U.S. C) The average stress rating for the 275 emergency-room nurses interviewed D) The average stress rating for all emergency-room nurses in the world

Answer the question. 157) 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) Inflation has gone down B) The price of grain is decreasing C) The real cost of grain has gone down D) The rate at which the price is rising is decreasing Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 158) A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers. A) Simple random B) Stratified C) Systematic D) Convenience

157)

158)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 159) Time spent walking and distance walked 159) A) Strong negative correlation B) Weak positive correlation C) Strong positive correlation D) Weak negative correlation E) No correlation

Make a scatter diagram for the data. 160) 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

160)

Answer the question. 161) 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) Stack plot B) Multiple bar graph C) Contour map D) Pictograph

161)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 162) The unemployment rate and the number of homeless people. 162) 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. 163) In Angela's class, the taller students got lower scores on the test. 163) A) Positive correlation; coincidence B) Negative correlation; common underlying cause C) Negative correlation; coincidence D) Positive correlation; common underlying cause

Solve the problem. 164) For the study described below, identify the sample statistic.

164)

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 number of women polled. B) The 1500 women polled C) The percentage of women in the sample who feel that women are under represented in management positions in their company. D) The percentage of American women working for large companies who feel that women are under represented in management positions in their company.

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 university 165) showed that 52.8 percent favored Mario, the rest favoring Yin Ling. The margin of error was 3.6 percentage points. Should Yin Ling have conceded the election? A) 52.8% to 56.4%; yes B) 49.2% to 52.8%; no C) 49.2% to 56.4%; no D) 51% to 54.6%; yes

Answer the question. 166) What name is given to a statistical graph that plots three or more related quantities simultaneously? A) Three dimensional graph B) Contour map C) Pictograph D) Multiple bar graph

166)

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 167) 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 setting may discourage honest responses B) Selection bias C) The wording of the question D) Participation bias E) The source of the study

167)

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 168) 168)

A) Strong negative correlation B) Weak positive correlation C) No correlation D) Weak negative correlation E) Strong positive 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. 169) Towns with a lot of churches had a lot of homicides last year. Towns with fewer churches had 169) fewer homicides. A) Negative correlation; common underlying cause B) Positive correlation; direct cause C) Positive correlation; coincidence D) Positive correlation; common underlying cause

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. 170) In year 0, approximately what percentage of Danny's total investment was in the CD? A) 20% B) 15% C) 30% D) 25%

170)

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. 171) As the temperature has been rising over the past three months, the Dow Jones Industrial Average 171) has also been rising. A) Negative correlation; coincidence B) Positive correlation; common underlying cause C) Positive correlation; direct cause D) Positive correlation; coincidence State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 172) Age and remaining life expectancy. 172) A) No correlation B) Weak positive correlation C) Weak negative correlation D) Strong positive correlation E) Strong negative correlation

Construct a pie chart representing the given data set. 173) Main form of exercise for employees of one company: None: 30% Walking: 18% Running: 4% Golf: 11% Weight Training: 26% Other: 11%

173)

Use the graph to answer the question. 174) In which year was the value of Danny's investment in individual stocks the least? A) year 8 B) year 0 C) year 1 D) year 7

174)

Construct a line chart for the data. 175) 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:

175)

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)

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. 176) People who drive faster, cover the distance in a shorter time. 176) A) Positive correlation; direct cause B) Negative correlation; direct cause C) Positive correlation; common underlying cause D) Negative correlation; common underlying cause Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 177) A researcher published this survey result: "74% of people would be willing to spend 10 percent 177) 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) Participation bias only B) Participation bias and selection bias C) Selection bias only D) No bias

Answer the question. 178) 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) An exponential scale B) A three dimensional graph C) A color coded map D) A stack plot

178)

Make a scatter diagram for the data. 179) The table shows the life expectancy at birth for females and per capita GDP for nine countries. (Data for179) 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.

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. 180) Hours of exercise per week and blood pressure. 180) A) Strong negative correlation B) No correlation C) Strong positive correlation D) Weak negative correlation E) Weak positive correlation

Use the graph to answer the question. 181)

181)

In what quarter was the revenue the least for 2000? A) second quarter B) third quarter

C) fourth quarter

D) first quarter

Answer the question. 182) 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) Pictograph B) Contour map C) Multiple bar graph D) Stack plot

182)

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) Following the Republican National Convention, a poll of voters in a Central Illinois community 183) showed that 57.0% 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) 52.2% to 61.8%; yes B) 54.6% to 59.4%; yes C) 57.0% to 61.8%; yes D) 47.4% to 57.0%; no

Construct a line chart for the data. 184) 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

184)

Age (years)

Age (years) D) None of the above

Age (years)

State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 185) Height and body temperature of adults. 185) A) Weak positive correlation B) No correlation C) Strong positive correlation D) Strong negative correlation E) Weak negative correlation

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 186) 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 B) Wording of the questions C) Participation Bias D) Setting may not encourage honest responses E) Selection Bias Identify the variable as either qualitative or quantitative. 187) Waiting time at a bus stop (in minutes) A) Quantitative

B) Qualitative

Solve the problem. 188) For the study described below, identify the population parameter.

186)

187)

188)

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

Use the graph to answer the question. 189) In year 8, approximately what percentage of Danny's total investment was in mutual funds? A) 70% B) 50% C) 80% D) 60%

Use the graph to answer the question. 190) The following chart shows the percentage of cigarette smokers in Gotham City.

In which year does the percentage of men who smoke exceed the percentage of women who smoke by roughly 9 percentage points. A) None of the above B) 1985 C) 1975 D) 1995

Construct a pie chart representing the given data set.

189)

190)

191)

Computers Number of per household households 0 54 1 96 2 57 3 27

14%

20%

21%

45%

12%

23%

24%

41%

10%

25%

26%

39%

27%

54%

57%

96%

Use the graph to answer the question. 192) In which year was the value of Danny's investment in individual stocks the highest? A) year 4 B) year 5 C) year 0 D) year 8

192)

Use the graph to answer the question. 193)

193)

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. Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 194) A medical researcher randomly selects 500 Japanese people and 500 Americans. She questions the 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) Participation bias B) Confounding variables C) Variables are hard to define/measure D) Selection bias E) The source

194)

State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 195) 195)

A) Weak negative correlation B) Strong positive correlation C) Weak positive correlation D) No correlation E) Strong negative correlation Use the graph to answer the question. 196) This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period.

196)

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 increased steadily over the four-year period. The number of female athletes increased in 1987 then decreased again in 1988 and 1989. B) 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. C) The number of male athletes and the number of female athletes increased steadily over the four-year period. D) 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.

Construct a line chart for the data. 197) The table shows the end-of-the-month checking account balance of a statistics teacher for the months 197) 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

500

Construct a time series line chart for the data.

D) None of the above Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 198) 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 B) Participation bias C) The setting may discourage honest responses D) The wording of the question E) Selection bias Construct a pie chart representing the given data set. 199) Favorite Food Number of Responses Chinese 115 Indian 75 Mexican 120 Thai 90

198)

199)

22.5%

28.8%

30%

18.7%

90%

120%

115%

75%

23%

30%

29%

19%

21%

31%

32%

20%

Identify the variable as either qualitative or quantitative. 200) The political affiliations of residents of a city A) Qualitative

B) Quantitative

Use the guidelines to evaluate the study. From the information given, what is the biggest flaw in the study? 201) 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) Setting may not encourage honest responses B) Selection bias C) Confounding variables D) Participation bias E) Wording of the question Answer the question. 202) What name is given to a statistical graph that is embellished with additional art work? A) Multiple bar graph B) Pictograph C) Contour map D) Stack plot Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 203) To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day. A) Simple random B) Systematic C) Convenience D) Stratified

200)

201)

202)

203)

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. 204) Ten years ago, according to government records, 17% of the population of Elmwood had no health 204) insurance. This year a poll revealed that 21.0% were without insurance. The margin of error was 3.2 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) 14.6% to 21.0%; no B) 17.8% to 24.2%; yes C) 21.0% to 24.2%; yes D) 19.4% to 22.6%; yes

Construct a line chart for the data. 205) The table shows the price of a volatile stock from the months January through December of the same year 205) 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

D) None of the above 66

Use the graph to answer the question. 206)

206)

In what quarter was the revenue the greatest for 1999? A) first quarter B) fourth quarter C) second quarter

D) third quarter

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 207) 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) Stratified D) Simple random

207)

Use the graph to answer the question. 208)

208)

Identify the utility that makes up about 25% of the total bill in May. A) Water B) Gas C) Electric D) None of the utilities makes up 25% of the total bill in May

Identify the variable as either qualitative or quantitative. 209) The area of apartments in a city A) Qualitative

B) Quantitative

Solve the problem. 210) For the study described below, identify the sample.

209)

210)

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) The 27 people who were dissatisfied. B) All customers of the bank C) The customers who were waiting in line at the bank the day of the poll D) The 300 customers polled

Answer the question. 211) Which type of graphs can be difficult to interpret because of visual distortion on a flat page? A) Contour map B) Stack plot C) Multiple bar graph D) Three dimensional graph

211)

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 213) As voters left various polls across the city, every tenth voter at each polling place was asked who they had 213) chosen to be the next mayor. A) No Bias B) Participation Bias C) Selection Bias D) Participation Bias and Selection Bias State whether the scatter diagram shows strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 214) 214)

A) Weak negative correlation B) No correlation C) Strong negative correlation D) Strong positive correlation E) Weak positive correlation

Use the graph to answer the question. 215) In year 8, what was the approximate value of Danny's investment in mutual funds? A) $6000 B) $4000 C) $2500 D) $1900

215)

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 216) A sample consists of every 20th student who leaves the library. A) Simple random B) Stratified C) Systematic D) Convenience

216)

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. 217) People with higher incomes tend to live longer than those with lower incomes. 217) A) Negative correlation; common underlying cause B) Positive correlation; direct cause C) Positive correlation; coincidence D) Positive correlation; common underlying cause

Identify which of these types of sampling is used: simple random, stratified, systematic, or convenience. 218) A market researcher randomly selects 500 drivers under 30 years of age and 500 drivers over 30 years of age. A) Systematic B) Stratified C) Simple random D) Convenience Identify the variable as either qualitative or quantitative. 219) The professions of adults A) Quantitative

B) Qualitative

220) The marital status of individuals A) Quantitative

B) Qualitative

218)

219)

220)

Use the graph to answer the question. 221)

221)

What was the revenue for the fourth quarter of 1999? A) $11 million B) $12 million C) $60 million

222)

D) $55 million 222)

Identify the utility that accounts for over half the total bill in two months. A) Electric B) Gas C) Water D) No single utility accounts for more than half the total bill in two months.

Construct a pie chart representing the given data set.

223)

Favorite Pizza Topping Black olives Mushrooms Onions Pepperoni

223)

Number of Responses 144 120 56 312

144%

312%

120% 56%

23%

47%

21% 9%

23%

49%

19% 9%

19%

57%

17% 7%

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. 224) People who take more vacations score higher on standardized tests. 224) A) Positive correlation; coincidence B) Positive correlation; direct cause C) Positive correlation; common underlying cause D) Negative correlation; common underlying cause State whether you think that the variables have strong positive correlation, weak positive correlation, strong negative correlation, weak negative correlation, or no correlation. 225) The age of a computer and its value. 225) A) No correlation B) Strong negative correlation C) Strong positive correlation D) Weak negative correlation E) Weak positive correlation

Use the graph to answer the question. 226) In which year was the total value of Danny's investments the least? A) year 1 B) year 0 C) year 8

D) year 3

226)

Determine whether the study involves selection bias, participation bias, both selection bias and participation bias, or neither. 227) "38% of adults in the United States regularly visit a doctor". This conclusion was reached by a 227) college student after she had questioned 520 randomly selected members of her college. A) Selection bias B) No bias C) Participation bias and selection bias D) Participation bias

Construct a line chart for the data. 228) Weight of Cat (lb) Frequency 5-7 2 8-10 9 11-13 18 14-16 13 17-19 4 20-22 1

228)

D) None of the above

Construct a pie chart representing the given data set. 229) Main form of exercise for employees of one company: None: 27% Walking: 16% Running: 7% Golf: 12% Weight Training: 23% Other: 15%

229)

Identify the variable as either qualitative or quantitative. 230) The population of a town A) Qualitative

B) Quantitative

230)

Answer Key Testname: CHAPTER 5 1) B 2) A 3) B 4) E 5) E 6) D 7) D 8) B 9) B 10) D 11) C 12) D 13) D 14) A 15) A 16) B 17) A 18) D 19) D 20) C 21) D 22) D 23) B 24) C 25) D 26) A 27) C 28) C 29) D 30) D 31) D 32) C 33) A 34) C 35) B 36) A 37) B 38) B 39) A 40) C 41) D 42) B 43) A 44) D 45) B 46) B 47) D 48) B 49) B 50) A 77

Answer Key Testname: CHAPTER 5

51) C 52) E 53) B 54) C 55) A 56) A 57) 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. Bin Freq. Relative Freq. Cumulative Freq. 0-49 2 0.1 2 50-99 4 0.2 6 100-149 4 0.2 10 58) 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 59) 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. 60) 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. 61) 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 62) 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. 63) 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.

Answer Key Testname: CHAPTER 5 64) 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 65) Answers will vary. Possible answer: Yes, when a bar graph is truncated, differences between the bars appear exaggerated. 66) 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. 67) 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 68) 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. 69) Answers may vary. A possible answer follows.

1985 1984 1983 1982 1981 1980 0

20 30

70) 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. 79

Answer Key Testname: CHAPTER 5 71) 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. 72) 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. 73) 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. 74) Answers will vary. The class width of the second class should be twice the class width of the first class. 75) 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 76) 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. 77) 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

Answer Key Testname: CHAPTER 5 78) 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 wi some fluctuations. On day 30 its value fell. Overall, the value of stock 2 increased by 100% during the month of October.

79) 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. 80) 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 81) 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. 82) 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. 83)

Answer Key Testname: CHAPTER 5 84) Answers will vary. One possible answer:

85)

The multiple bar graph shows an increase in people living with HIV/AIDS, but a decrease in new cases of HIV.

86) 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? 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 88) 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

89)

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

90) 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. 91) 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 92) 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 93) 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. 94) 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%.

Answer Key Testname: CHAPTER 5 95) 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°. 96) 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. 97) 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).

98)

Answer Key Testname: CHAPTER 5 99) Answers will vary. One possible answer:

Two separate bar graphs work to show the individual distributions more clearly. 100) 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.

101)

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 24 102) 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.

103) 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. 104) 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 85

Answer Key Testname: CHAPTER 5 105)

106) 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 107) 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.

Answer Key Testname: CHAPTER 5 108) Answers may vary. A possible answer follows.

30 24 18 12 6

1980

1981

1982

1983

1984

1985

109) 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. 110) 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.

Answer Key Testname: CHAPTER 5 111) Answers may vary. The following is a possible answer.

June 24 June 9 May 24 May 9 April 24 April 9 1.2

1.6

2.4

2.8

3.2

3.6

112) 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. 113) 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. 114)

115) 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. 116) 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. 117) D 118) B 119) D 120) D 121) C 122) A 123) A 124) A 88

Answer Key Testname: CHAPTER 5 125) A 126) B 127) E 128) C 129) D 130) D 131) D 132) D 133) D 134) E 135) A 136) B 137) C 138) B 139) A 140) A 141) D 142) E 143) A 144) C 145) C 146) C 147) B 148) B 149) C 150) D 151) B 152) B 153) D 154) B 155) B 156) B 157) D 158) A 159) C 160) C 161) A 162) A 163) C 164) C 165) C 166) A 167) A 168) B 169) D 170) A 171) D 172) E 173) B 174) A 89

Answer Key Testname: CHAPTER 5 175) B 176) B 177) B 178) A 179) C 180) D 181) A 182) B 183) A 184) B 185) B 186) C 187) A 188) C 189) D 190) C 191) B 192) C 193) C 194) B 195) B 196) B 197) A 198) D 199) C 200) A 201) B 202) B 203) C 204) B 205) A 206) B 207) D 208) B 209) B 210) D 211) D 212) B 213) A 214) B 215) B 216) C 217) D 218) B 219) B 220) B 221) D 222) A 223) C 224) C 90

Answer Key Testname: CHAPTER 5 225) B 226) A 227) A 228) C 229) B 230) B

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select the requested distribution. 1) Which of the distributions is multimodal and approximately symmetric? A)

Provide an appropriate response. 2) 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 defendant is guilty. C) The treatment has no effect. D) The teaching method raises SAT scores.

3) A data set consists of 9 values which are not all the same. Which of the following is possible? A) The median is equal to the largest value. B) The mode is equal to the largest value. C) The mean is equal to the largest value. D) None of the above is possible.

4) A hypothesis test is conducted with the following hypotheses: 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 big as 118 or bigger is less than 0.01. C) 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. 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.

Answer the question. 5) Tell which of the following distributions would have the least variation. A) Weights of all children who have a pet cat B) Weights of all pet cats C) Weights of all pets D) Weights of all pet dogs 6) Tell which of the following distributions would have the most variation. A) Temperature over a one-year period in San Diego. B) Temperature over a one-month period in Boston. C) Temperature over a one-year period in Boston. D) Temperature over a one-month period in San Diego. Provide an appropriate response. 7) A data set consists of 9 values which are all different. Which of the following is possible? A) The median is equal to the second smallest value. B) The mode is equal to the second smallest value. C) The mean is equal to the second smallest value. D) None of the above is possible.

Select the requested distribution. 8) Which of the distributions is multimodal? A)

Provide an appropriate response. 9) 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) B and C B) D only C) A and B D) C and D E) C only 10) Of the mean, median, and mode, which take(s) into account the numerical size of all the data values? A) All of them B) The median and mode C) The mean only D) The mean and median Select the requested distribution.

10)

11) Which of the distributions is symmetric? A)

11)

Provide an appropriate response. 12) Heights of gymnasts at a certain college are normally distributed. Which of the following are the most plausible values for the mean and standard deviation? A) Mean = 61 in., standard deviation = 2.1 in. B) Mean = 61 in., standard deviation = 6.2 in. C) Mean = 60 in., standard deviation = 0.5 in. D) Mean = 60 in., standard deviation = -1 in.

12)

13) Rank the mean, median, and mode in order of ascending size for a right-skewed distribution. A) Mean, Median, Mode B) Median, Mode, Mean C) Mode, Mean, Median D) Mode, Median, Mean Answer the question. 14) Tell which of the following distributions would have the most variation. A) Salaries of high-school teachers B) Salaries of waitresses C) Salaries of bank clerks D) Salaries of CEOs of U.S. corporations Provide an appropriate response. 15) Of the mean, median, and mode, which is (are) affected by outliers? A) The mean and median B) The mean only C) The mean and mode D) The median and mode

13)

14)

15)

16) A criminal trial can be compared to a hypothesis test. The hypotheses are as follows: 16) 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. 17) A variable is normally distributed with a mean of 100. Which of the following is the largest? A) The percentage of observations between 100 and 110 B) The percentage of observations between 95 and 105 C) The percentage of observations between 80 and 90 D) The percentage of observations between 90 and 100

17)

18) 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 = 16 sec B) Mean = 77 sec, standard deviation = 9.1 sec C) Mean = 77 sec, standard deviation = 2.1 sec D) Mean = 77 sec, standard deviation = 20 sec

18)

Answer the question. 19) 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 B) The number of hours of light per day over a one-year period in New York 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 at the equator Provide an appropriate response. 20) 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 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.

19)

20)

21) 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 = 160 lb, standard deviation = 25 lb C) Mean = 155 lb, standard deviation = 12 lb D) Mean = 155 lb, standard deviation = -20 lb Answer the question. 22) Tell which of the following distributions would have the least variation. A) Number of children for women in India B) Number of children for women in Kenya C) Number of children for women in Haiti D) Number of children for women in Portland, Oregon

21)

22)

23) Tell which of the following distributions would have the least variation. A) Weights of adult men B) Weights of 20-year olds C) Weights of 20-year old women D) Weights of all adults

23)

24) Tell which of the following distributions would have the most variation. A) Scores on a test in which half the students got an A and half got a B B) Scores on a test in which all students got a perfect score 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 a C and half failed

24)

Provide an appropriate response. 25) 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. 26) 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) A and D D) B and C E) A and B

25)

26)

27) Toni is conducting a hypothesis test concerning a population proportion. The hypotheses are as follows. 27) 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. 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. 28) Which quantity describes how widely data values are spread about the center of a distribution? A) Number of peaks B) Mean C) Variation D) Skewness Select the requested distribution. 29) Which of the distributions has the greatest variation? A)

28)

29)

Provide an appropriate response. 30) Which of the following statements is not true for a left-skewed distribution? A) The mode is greater than the mean B) The median is smaller than the mode C) The mode is at the peak D) The mean is greater than the median Answer the question. 31) Tell which of the following distributions would have the least variation. A) 100-meter times for adults B) 100-meter times for male college seniors C) 100-meter times for male Olympic sprinters D) 100-meter times for college seniors Provide an appropriate response. 32) Which of the following statements is true? A) The median is always one of the data points in a set of data B) The mean 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 Select the requested distribution. 33) Which of the distributions is skewed to the right? A)

30)

31)

32)

33)

Provide an appropriate response. 34) Which of the following is not possible? A) A distribution is right-skewed and the mean is greater than the median B) A distribution is not symmetric and the median is equal to the mean C) A distribution has a single peak and the mean and median are different D) A distribution is left-skewed and the mean is equal to the median

34)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 35) An engineer has designed an elevator and wishes to determine the maximum number of 35) 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. 36) The range and standard deviation of the data set below are 35 and 12.47 respectively.

36)

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.

37) Draw one boxplot to illustrate bell-shaped data, another for uniform data, and a third for 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

37)

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. 38) Dave is a college student contemplating a possible career option. One factor that will 38) 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. 39) In essence, the standard deviation indicates how far, on average, the observations are from the39) 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? 2, 3, 4, 4, 5, 5, 6, 6, 100 What drawback of the standard deviation is illustrated by this example?

40) Do you think it is possible to find two data sets such that the first data set has a smaller 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.

40)

41) Four different distributions are represented by the four boxplots below.

41)

Which distribution has the smallest median? Which has the greatest variation? Which is skewed to the left?

42) Discuss the differences between the distributions represented by the two boxplots below. Explain 42) your reasoning.

43) 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.

43)

44) You are the coach of a basketball team. Player A's mean score per game over the last 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?

44)

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. 45) A company claims that it pays women the same as men for comparable work. The union decides 45) 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. 46) A state governor is planning a tax cut. The governor is to announce the average amount 46) 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?

Provide an appropriate response. 47) 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.

47)

48) A company advertises an average of 42,000 miles for one of its new tires. In the 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.

48)

49) How does Q3 - Q2 compare to Q2 - Q1 for a distribution which is skewed to the right? for

49)

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).

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 50) A shoe manufacturer wants to know in which size they should make the most shoes. 50) Which type of average would be the most useful?

Provide an appropriate response. 51) Describe any similarities or differences in the two distributions represented by the boxplots below. Assume the two boxplots have the same scale.

51)

52) An environmental group is investigating global warming and is conducting a hypothesis test. The 52) 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. 53) Suppose that a state introduces a state income tax which will be at a flat rate of 3%. The 53) 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?

Provide an appropriate response. 54) Can the sample variance ever be a negative number? If so, for what types of data? If not, why not? Can the sample variance ever be zero? If so, for what types of data? If not, why not? Explain your reasoning.

54)

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. 55) The mayor of a city claims that racial profiling is not a problem in his city. A civil rights 55) 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.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 56) A state governor is planning a tax cut. A researcher calculates the average amount that 56) 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. 57) 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.

57)

58) You wish to test the hypotheses shown below. 58) 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. 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. 59) The mean resting heart rate for students at Northridge College is 72 beats per minute. An 59) 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.

Provide an appropriate response. 60) You are late for work. You have two options for getting to work. You may take the bus which 60) 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. 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. 61) In the city of Heathville, the proportion of births that are by Caesarean section is 0.23 (23%). A 61) 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.

62) A company claims that the proportion of defectives among its new DVD players is only 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.

62)

Provide an appropriate response. 63) Jenny is conducting a hypothesis test concerning a population mean. The hypotheses are as 63) 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. 64) A consumer group believes that the mean volume of juice in a company's 24 ounce juice bottles 64)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.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 65) The table below provides a frequency distribution for the winner of the Davis Cup during 65) 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?

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. 66) A public bus company official claims that the mean waiting time for bus number 14 during 66) 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. 67) We want to compare two different groups of students, students taking Composition 1 in a 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?

67)

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explain your thinking. 68) You are considering moving to a new city and would like to know the average price of a 68) new home in that city. Which type of average would be the most useful to you?

69) Before a mayoral election, a pollster tries to predict which candidate will win the most votes. Which average does the pollster need to know?

69)

70) A parcel service wants to estimate how many vans it will need. It knows how many parcels are delivered each day, but it also needs to know the average volume of the parcels. Which average would be the most useful?

70)

Provide an appropriate response. 71) 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.

71)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the distribution as symmetric, left-skewed, or right-skewed. 72) Exam scores for an exam in which most students did very well but a few students failed A) Right-skewed B) Symmetric C) Left-skewed

72)

Solve the problem. 73) The weights, in pounds, of twelve apples are given below. Find the mean weight. Round your answer to 73) the nearest thousandth of a pound. 0.27 0.36 0.31 0.29 0.30 0.31 0.34 0.28 0.29 0.34 0.32 0.30 A) 0.305 lb B) 0.336 lb

C) 0.309 lb

D) 0.285 lb

State whether the distribution appears to be (roughly) normal. 74)

A) Normal

74)

B) Not normal

A hypothesis test is to be performed. State the null and alternative hypotheses. 75) 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 76) 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 B) Null hypothesis: mean fee = $1200 Alternative hypothesis: mean fee = $1200 Alternative hypothesis: mean fee $1200 C) Null hypothesis: mean fee < $1200 D) Null hypothesis: mean fee = $1200 Alternative hypothesis: mean fee > $1200 Alternative hypothesis: mean fee > $1200

75)

76)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 77) 55 12 32 20 18 51 80 77) A) 10,260.6 B) 24.7 C) 13,918 D) 32

Find the mode(s) for the given sample data. 78) The table shows the country represented by the winner of the 10,000 meter run in the Summer Olympic78) Games in various years. Year 1912 1920 1924 1928 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992

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) Morocco B) 7

C) 1912

D) Finland

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 79) In nine out of the last ten years, the stock market has gone up. 79) A) Statistically significant B) Not statistically significant

Identify the distribution as symmetric, left-skewed, or right-skewed. 80) Age at death for residents of the U.S. A) Right-skewed B) Symmetric

C) Left-skewed

Solve the problem. 81) 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) 1.50% B) 6.68% C) 93.32% D) 55.96%

80)

81)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 82) At Linden High School there are math tests at the end of each three-month session. On all of the 82) 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) Statistically significant B) Not statistically significant

Use the 68-95-99.7 rule to solve the problem. 83) The annual precipitation for one city is normally distributed with a mean of 25.8 inches and a standard deviation of 2.9 inches. Fill in the blanks.

83)

In 99.7% of the years, the precipitation in this city is between ___ and ___ inches. A) 20, 31.6 B) 20, 25.8 C) 17.1, 34.5 D) 25.8, 34.5

Use the range rule of thumb to approximate the standard deviation. 84) 2, 6, 15, 9, 11, 22, 1, 4, 8, 19 A) 6.3 B) 6.8 C) 5.25

D) 2

Find a 95% confidence interval for the true population proportion. 85) In a survey of 264 female employees of a large company, 29% said that they had experienced some form of sexual harassment while working for the company. A) 22.8% to 35.2% B) 16.7% to 41.3% C) 28.6% to 29.4% D) 28.9% to 29.1% Solve the problem. 86) Weights of adult females in a certain country are normally distributed with a mean of 136 lb and a standard deviation of 15 lb. A weight of 115 lb represents what percentile? Round the percentile to the nearest tenth. A) 8.1 B) 2.2 C) -1.4 D) 9.7 Use the 68-95-99.7 rule to solve the problem. 87) Assume that a distribution has a mean of 28 and a standard deviation of 4. What percentage of the values in the distribution do we expect to fall between 24 and 28? A) 68% B) 25% C) 34% D) 17% Use the range rule of thumb to approximate the standard deviation. 88) A distribution of data has a maximum value of 81, a median value of 49, and a minimum of 17. Round results to the nearest tenth. A) 8.5 B) 12.8 C) 16.0 D) 32.0 Solve the problem. 89) 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) 77 B) 65 C) 68 D) 63 Use the range rule of thumb to approximate the standard deviation. 90) The maximum value of a distribution is 12.6 and the minimum value is 4.3. Round results to the nearest tenth. A) 10.7 B) -0.9 C) 2.1 D) 7.1 Identify the distribution as symmetric, left-skewed, or right-skewed. 91) The diameters of the apples growing on a particular tree A) Left-skewed B) Right-skewed

C) Symmetric

84)

85)

86)

87)

88)

89)

90)

91)

Find a 95% confidence interval for the true population proportion. 92) In a poll of 1618 adults, 35% said that they exercised regularly. A) 34.9% to 35.1% B) 30.0% to 40.0% C) 32.5% to 37.5%

D) 33.8% to 36.2%

Find the median for the given sample data. 93) 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. 23 25 23 26 23 28 33 29 29 22 29 23 13 25 25 A) 24.85

26 25 27 18 25

B) 25

C) 29

93)

D) 26

Solve the problem. 94) 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) 11.51% C) 53.98% D) 88.49% Use the range rule of thumb to approximate the standard deviation. 95) 496, 598, 503, 528, 565, 601, 576, 543 A) 18.75 B) 60.6 C) 170.2

92)

D) 26.25

A hypothesis test is to be performed. State the null and alternative hypotheses. 96) Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon, which is the gas mileage of its competitor. A) Null hypothesis: mean gas mileage = 23 mpg Alternative hypothesis: mean gas mileage > 23 mpg B) Null hypothesis: mean gas mileage = 23 mpg Alternative hypothesis: mean gas mileage 23 mpg C) Null hypothesis: mean gas mileage > 23 mpg Alternative hypothesis: mean gas mileage = 23 mpg D) Null hypothesis: mean gas mileage < 23 mpg Alternative hypothesis: mean gas mileage > 23 mpg For the given data value, find the standard score and the percentile. 97) A data value 0.9 standard deviations below the mean. A) z = -0.9; percentile = 81.59 B) z = -0.09; percentile = 46.02 C) z = -0.9; percentile = 18.41 D) z = 0.9; percentile = 81.59 State how many peaks you would expect for the distribution described. 98) Speeds of everyone traveling on a country road, including cyclists and motorists A) One B) Three C) Two D) None

94)

95)

96)

97)

98)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 99) The numbers below represent the test scores of nine students. 99) 28, 68, 27, 84, 35, 26, 83, 55, 27 Find the standard deviation. A) 6.0 B) 24.8 C) 26.5 D) 23.3 19

Identify the distribution as symmetric, left-skewed, or right-skewed. 100) Number of siblings of adults in the U.S. A) Symmetric B) Left-skewed

C) Right-skewed

100)

Obtain the five-number summary for the given data. 101) The National Education Association collects data on the number of years of teaching experience of 101) 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 19 31 9 3 11 2 22 25 1 33 26 6 17 23 21 31 A) 1, 6, 18.0, 26, 33 C) 1, 5.25, 18.0, 25.25, 33

B) 1, 5.25, 19, 25.25, 33 D) 1, 6, 19, 26, 33

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 102) In a clinical study of an arthritis medication, 28% of those taking the placebo reported improvement. The 102) 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 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% B) 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% 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 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%

For the given data value, find the standard score and the percentile. 103) A data value 2.5 standard deviations above the mean. A) z = 2.5; percentile = 1.95 B) z = 0.25; percentile = 59.87 C) z = -2.5; percentile = 0.62 D) z = 2.5; percentile = 99.38 State whether you would expect the data set to be normally distributed. 104) Resting heart rates for adults A) Normal B) Not normal

103)

104)

Obtain the five-number summary for the given data. 105) The normal annual precipitation (in inches) is given below for 21 different U.S. cities. 39.1 31.7 18.5 32.4 27.1 27.8 8.6 23.4 42.6 31.9 20.6 12.0 5.1 13.1 22.4 10.9 16.1 25.4 17.2 15.3 51.7 A) 5.1, 14.20, 22.4, 31.80, 51.7 C) 5.1, 13.650, 21.50, 30.725, 51.7

B) 5.1, 13.650, 22.4, 30.725, 51.7 D) 5.1, 14.20, 21.50, 31.80, 51.7

Solve the problem. 106) 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%, 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) 62 B) 65 C) 56 D) 58 107) 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) 66 B) 74 C) 76 D) 71 Construct a boxplot as requested. 108) The test scores of 40 students are listed below. Construct a boxplot for the data set. 25 35 59 62 72 73 81 82 A)

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

105)

57 72 81 98

106)

107)

108)

Find the median for the given sample data. 109) 2, 12, 16, 21, 30, 30, 49 Find the median for the data. A) 16 B) 30

C) 25.5

D) 21

Find the mode(s) for the given sample data. 110) -20, -28, -46, -28, -49, -28, -49 A) -46 B) -28

C) -35.4

D) -49

109)

110)

Find the median for the given sample data. 111) The weights (in ounces) of 21 cookies are shown. Find the median weight. 0.62 1.00 0.69 1.62 0.82 0.77 1.35 1.00 1.53 0.93 0.62 1.18 1.12 0.89 0.47 1.18 0.77 1.12 1.72 0.82 0.56 A) 1.00 ounces B) 0.89 ounces

C) 0.91 ounces

111)

D) 0.93 ounces

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 112) In 50 rolls of a die, you got 40 sixes. 112) A) Statistically significant B) Not statistically significant

Obtain the five-number summary for the given data. 113) The weights (in pounds) of 18 randomly selected adults are given below. 120 144 187 153 119 135 127 143 179 165 182 202 114 173 132 150 167 173 A) 114, 129.50, 150, 170.0, 202 C) 114, 129.50, 151.5, 170.0, 202

113)

B) 114, 132, 151.5, 173, 202 D) 114, 130.75, 151.5, 174.50, 202

Solve the problem. 114) 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) 2.28% D) 37.45%

114)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 115) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The 115) diameters of the rolls (in m) are listed below. Compute the standard deviation. 0.589 0.53 0.473 0.628 0.411 0.151 0.202 A) 1.2720 m B) 0.1855 m C) 1.4785 m D) 0.628 m Find the standard score for the given data value. 116) A data value in the 58th percentile. A) z = -1.6 B) z = 72.57

C) z = 0.2

D) z = -2.5

Find the range for the given data. 117) The amount that Jeremy has saved in each of the last six months is shown below. $113 $483 $227 $570 $381 $336 A) $457 B) $483

C) $109

117)

D) $113

State how many peaks you would expect for the distribution described. 118) Heights of a group of college athletes consisting of the gymnastics team and the basketball team A) One B) Three C) None D) Two

116)

118)

Use the range rule of thumb to approximate the standard deviation. 119) 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) 1.09 B) 1.4 C) 0.8

119) D) 12.03

Find a 95% confidence interval for the true population proportion. 120) During the questioning of 90 potential jury members, 36% said that they had already formed an opinion as to the guilt of the defendant. A) 34.9% to 37.1% B) 35.9% to 36.1% C) 30.7% to 41.3% D) 25.5% to 46.5%

120)

Find the mode(s) for the given sample data. 121) The speeds (in mi/h) of the cars passing a certain checkpoint are measured by radar. The results are shown 121) below. 42.6 43.5 43.2 43.5 42.6 40.0 41.3 41.3 A) 43.5

43.0 40.0 44.1 43.0

44.1 40.0 41.5 44.9

43.2 44.1 43.5 42.6

B) 42.6, 44.1, 43.5

C) 43.40

D) 42.6

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 122) The numbers listed below represent the amount of precipitation (in inches) last year in six different U.S.122) cities. 19.9 18.8 35.4 33.4 11.0 11.3 Compute the standard deviation s. A) 10.57 in. B) 2808.0 in. C) 34.4 in. D) 3366.9 in. State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 123) There are two candidates for mayor, Maria Hernandez, and Eric Wong. Of 100 people polled, 53 123) say they will vote for Maria Hernandez. A) Not statistically significant B) Statistically significant

Find a 95% confidence interval for the true population proportion. 124) In a survey of 227 adults, 28% said that they had tried acupuncture at some point in their lives. A) 27.9% to 28.1% B) 24.7% to 31.3% C) 27.6% to 28.4% D) 21.4% to 34.6% Find the median for the given sample data. 125) A new business had the following monthly net gains:

124)

125)

$6815 $1630 $3093 $7663 $6757 $3945 $1818 $8166 $4215 $4875 Find the median net gain. A) $4215.00

B) $5441.89

C) $4545.00

D) $4897.70

Find a 95% confidence interval for the true population proportion. 126) In a survey of 352 adults, 55% said that they favored the proposed environmental laws. A) 54.7% to 55.3% B) 49.7% to 60.3% C) 52.3% to 57.7% D) 55% to 60.3%

126)

Solve the problem. Round your answer to two decimal places. 127) Scores on a test are normally distributed with a mean of 78 and a standard deviation of 6. What is the standard score for an exam score of 73 ? A) 0.86 B) -0.86 C) -1.2 D) -0.83

127)

Use the range rule of thumb to approximate the standard deviation. 128) The following is a set of data showing the water temperature in a heated tub at different time intervals.128) Round results to the nearest tenth. 113.7 115.6 116.3 115.6 115.6 115.5 112.5 113.9 A) 1.3 B) 0.8 C) -55.7 D) 1.0 Find the margin of error for the survey results described. 129) In a poll of 1757 adults, 30% said that they exercised regularly. Give your answer as a percentage to one decimal place. A) 1.2% B) 2.4% C) 0.1% Identify the distribution as symmetric, left-skewed, or right-skewed. 130) Weights of new-born babies A) Left-skewed B) Right-skewed

129) D) 4.8%

C) Symmetric

A hypothesis test is to be performed. State the null and alternative hypotheses. 131) 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 Solve the problem. Round your answer to two decimal places. 132) Scores on a test are normally distributed with a mean of 118 and a standard deviation of 15. What is the exam score corresponding to a standard score of 1.92? A) 89.2 B) 146.8 C) 118.13 D) None of the above

130)

131)

132)

Solve the problem. 133) The heights of nine different mountains are shown in the table below. Find the mean height. Round your 133) 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) 20,716 ft

B) 20,309 ft

C) 19,850 ft

D) 20,837 ft

A hypothesis test is to be performed. State the null and alternative hypotheses. 134) In a clinical study of an arthritis medication, 28% of those taking the placebo reported 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%

134)

Find the median for the given sample data. 135) The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find the median 135) of the data. 3.5 1.6 2.4 3.9 1.0 3.6 3.7 2.2 1.5 2.7 0.4 3.7 A) 2.94 in.

3.7 4.2 4.2 2.0

4.1 3.4 3.4 3.6

B) 3.50 in.

C) 3.45 in.

D) 3.40 in.

Construct a boxplot as requested. 136) The test scores of 32 students are listed below. Construct a boxplot for the data set. 32 37 57 57 70 71 81 82 A)

41 59 74 83

44 63 74 86

46 65 75 89

48 66 77 92

53 68 78 95

136)

55 69 79 99

Solve the problem. 137) 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) 43rd B) 93rd C) 91st D) 41st A hypothesis test is to be performed. State the null and alternative hypotheses. 138) 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%

137)

138)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 139) 223, 225, 300, 291, 289, 267, 171, 166, 141 139) A) 64.4 B) 56.8 C) 28.8 D) 60.3

State whether you would expect the data set to be normally distributed. 140) Age at death for residents of the U.S. A) Not normal B) Normal

140)

Find the mode(s) for the given sample data. 141) The weights (in ounces) of 14 different apples are shown below. 6.9 4.6 4.9 6.6 4.4 6.9 4.6 6.5 4.5 6.6 6.9 6.5 6.6 6.1 A) 6.75 B) 6.9, 6.6

141)

C) None

D) 6.9

Use the 68-95-99.7 rule to solve the problem. 142) The time it take Claudia to drive to work is normally distributed with a mean of 47 minutes and a standard deviation of 7 minutes. What percentage of the time will it take her less than 68 minutes to drive to work? A) 99.85% B) 0.15% C) 0.3% D) 99.7% 143) For adults in the town of Bridgeport, systolic blood pressure is normally distributed with a mean of 137 mmHg and a standard deviation of 9 mmHg. What percentage of adults in the town have a systolic blood pressure less than 128 mmHg? A) 32% B) 16% C) 68% D) 84% Identify the distribution as symmetric, left-skewed, or right-skewed. 144) The amounts of tax paid by U.S. residents A) Left-skewed B) Symmetric

C) Right-skewed

Find the median for the given sample data. 145) The distances traveled (in miles) to 7 different swim meets are given below:

142)

143)

144)

145)

15, 29, 39, 47, 70, 75, 85 Find the median distance traveled. A) 47 miles B) 70 miles

C) 39 miles

D) 51 miles

146) The salaries of ten randomly selected doctors are shown below.

146)

$114,000 $137,000 $170,000 $233,000 $206,000 $123,000 $140,000 $875,000 $235,000 $184,000 Find the median salary. A) $177,000

B) $242,000

C) $170,000

D) $269,000

Solve the problem. 147) Bill kept track of the number of hours he spent exercising each week. The results for four months are 147) shown below. Find the mean number of hours Bill spent exercising per week. Round your answer to the nearest tenth of an hour. 7.4 7.9 8.8 7.9 8.5 7.4 8.4 8.8 6.9 7.4 7.9 8.9 9.0 7.9 7.9 6.8 8.5 8.4 A) 8.5 hours

B) 7.6 hours

C) 8.3 hours

D) 8.0 hours

Find the range for the given data. 148) 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) $12.05

B) $10.95

C) $14.05

148)

D) $8.20

Find the margin of error for the survey results described. 149) During the questioning of 73 potential jury members, 36% 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) 5.9% B) 11.7% C) 23.4% D) 1.4%

149)

Use the range rule of thumb to approximate the standard deviation. 150) The heights in feet of people who work in an office are as follows. Round results to the nearest tenth. 150) 5.9 5.7 5.5 5.4 5.6 5.9 5.8 6.2 6.0 5.9 A) 0.1 B) 0.2 C) 0.5 D) 1.2 Find the range for the given data. 151) 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. 13.2 22.5 8.1 28.3 25.8 15.4 A) 15.9 hours

25.6 15.9 12.8 23.0 B) 8.1 hours

C) 9.3 hours

Use the range rule of thumb to approximate the standard deviation. 152) 15, 42, 53, 7, 9, 12, 14, 28, 47 A) 15.8 B) 11.5 C) 29.1

D) 20.2 hours

D) 16.6

Solve the problem. 153) 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) 66.7 B) 70.1 C) 68.8 D) 72.6

151)

152)

153)

Provide an appropriate response. 154) The area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular 154) 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) d

C) b

D) b, c

E) a, b

Find the mode(s) for the given sample data. 155) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find 155) the mode(s). 56 60 64 51 52 68 67 58 54 A) No mode C) 58.9

B) 58 D) 56, 60, 64, 51, 52, 68, 67, 58, 54

Solve the problem. 156) 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) 90 B) 80 C) 79 D) 82 157) 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) 44.04% C) 8.08% D) 1.40% State how many peaks you would expect for the distribution described. 158) Numbers of people with birthdays in a particular month (January through December) A) Two B) One C) Three D) None

156)

157)

158)

Construct a boxplot as requested. 159) The highest temperatures ever recorded (in °F) in 32 different U.S. states are shown below. Construct a 159) boxplot for the data set. 100 100 105 109 110 110 114 115 116 118 119 120 A)

105 112 117 121

106 112 118 122

106 112 118 125

107 114 118 128

107 114 118 134

Identify the distribution as symmetric, left-skewed, or right-skewed. 160) Lengths of human pregnancies A) Symmetric B) Right-skewed

C) Left-skewed

Solve the problem. 161) Find the mean for the given sample data. Round your answer to the nearest tenth if necessary. 19, 11, 18, 19, 17 A) 16.8 B) 19 C) 21 D) 16 State whether you would expect the data set to be normally distributed. 162) Times for able bodied female college students to run 400 meters. A) Not normal B) Normal

160)

161)

162)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 163) The governor of a state claims that since his tax cuts have taken effect, the unemployment rate has 163) 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%.

164) A health insurer has determined that the "reasonable and customary" fee for a certain medical 164) 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 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. C) 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. 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. For the given data value, find the standard score and the percentile. 165) A data value 1.3 standard deviations above the mean. A) z = -1.3; percentile = 9.68 B) z = 1.3; percentile = 2.2 C) z = 0.13; percentile = 55.96 D) z = 1.3; percentile = 90.32

165)

Solve the problem. 166) The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown 166) below. Find the mean score. Round your answer to the nearest tenth. 563 524 357 347 637 358 351 528 470 482 A) 461.7

B) 471.1

C) 476.0

D) 452.6

Find the margin of error for the survey results described. 167) In a survey of 257 adults, 35% said that they had tried acupuncture at some point in their lives. Give your answer as a decimal to three decimal places. A) 0.125 B) 0.004 C) 0.031 D) 0.062 A hypothesis test is to be performed. State the null and alternative hypotheses. 168) 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 Find the standard score for the given data value. 169) A data value in the 8th percentile. A) z = -1.4 B) z = -2.4

C) z = 78.81

D) z = 0.85

167)

168)

169)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 170) 3, 3, 15, 12, 17, 9, 5, 14, 9 170) A) 4.9 B) 1.2 C) 5.6 D) 5.2 Find the mode(s) for the given sample data. 171) 7.06, 7.41, 7.56, 7.06, 7.88, 7.99, 7.62 A) 7.41 B) 7.06

C) 7.511

D) 7.56

A hypothesis test is to be performed. State the null and alternative hypotheses. 172) 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%

171)

172)

Solve the problem. 173) Scores on a test are normally distributed with a mean of 71 and a standard deviation of 5. What is the percentile for an exam score of 67? Round the percentile to the nearest tenth. A) 21.2 B) 2.4 C) 19.9 D) -0.8

173)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 174) Of the people taking the medication, 38 out of 100 noticed improvement in their arthritis. Of the 174) people taking the placebo, 35 out of 100 noticed improvement in their arthritis. A) Not statistically significant B) Statistically significant

Construct a boxplot as requested. 175) Here are the heights of the male and female employees at First City Bank. Draw a double box plot for each 175) 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 A)

Find the standard score for the given data value. 176) A data value in the 31st percentile. A) z = -1.9 B) z = -0.5

C) z = 0.5

D) z = 61.79

176)

Solve the problem. 177) The local Tupperware dealers earned these commissions last month:

177)

$4364.42 $1552.79 $2099.95 $2494.30 $3788.65 $1581.98 $1748.47 $2559.19 $3899.29 $3412.17 What was the mean commission earned? Round your answer to the nearest cent. A) $3437.65 B) $2750.12 C) $2744.12 D) $3055.69

State whether you would expect the data set to be normally distributed. 178) The amount of coffee which a filling machine puts into "4 ounce jars" A) Normal B) Not normal

178)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 179) You draw a card at random from a deck of cards and replace it. You repeat this 60 times and get a 179) heart 13 times. A) Statistically significant B) Not statistically significant

Find the standard score for the given data value. 180) A data value in the 97th percentile. A) z = -2.3 B) z = 1.9

C) z = 82.89

D) z = -1.3

For the given data value, find the standard score and the percentile. 181) A data value 2.3 standard deviations below the mean. A) z = -0.23; percentile = 40.13 B) z = -2.3; percentile = 98.93 C) z = 2.3; percentile = 98.93 D) z = -2.3; percentile = 1.07 Find the mode(s) for the given sample data. 182) The blood types for 30 people who agreed to participate in a medical study were as follows. 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) O, A B) A

C) O

D) 13

180)

181)

182)

State whether the distribution appears to be (roughly) normal. 183)

A) Not normal

183)

B) Normal

Find the mode(s) for the given sample data. 184) 97, 25, 97, 13, 25, 29, 56, 97 A) 42.5 B) 25

C) 97

Find the standard score for the given data value. 185) A data value in the 46th percentile. A) z = 0.1 B) z = -2.6

C) z = -1.7

D) 54.9

D) z = -0.1

184)

185)

Use the range rule of thumb to approximate the standard deviation. 186) The race speeds for the top eight cars in a 200-mile race are listed below. Round results to the nearest 186) tenth. 188.5 188.6 189.2 187.2 175.6 178.5 176.8 185.4 A) 1.1 B) 3.4 C) 7.5 D) 6.8 Use the 68-95-99.7 rule to solve the problem. 187) The amount of Jen's monthly phone bill is normally distributed with a mean of $80 and a standard deviation of $10. Fill in the blanks. 68% of her phone bills are between $___ and $___. A) 60, 100 B) 70, 90

C) 60, 80

187)

D) 80, 90

Find the range for the given data. six 188) The owner of a small manufacturing plant employs six people. The commute distances, in miles, for the 188) employees are listed below. 2.3 5.7 1.5 4.7 6.6 3.6 A) 1.5 mi

B) 5.1 mi

C) 5.7 mi

D) 1.3 mi

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 189) 10.8, 15.3, 48.6, 45.1, 21.3, 19.9 189) A) 4320.2 B) 46.9 C) 15.98 D) 5596.4 State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 190) 34 of the 220 suicide cases occurred on a Monday. 190) A) Not statistically significant B) Statistically significant

Use the 68-95-99.7 rule to solve the problem. 191) 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 71 seconds? A) 5% B) 95% C) 97.5% D) 2.5% Identify the distribution as symmetric, left-skewed, or right-skewed. 192) Shoe sizes of adult women A) Left-skewed B) Right-skewed

C) Symmetric

Provide an appropriate response. 193) 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) Each sample proportion will be equal to 0.1. 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 1/10. D) The sample proportions are approximately normally distributed with a mean of 0.1 and a standard deviation of approximately 1/20. State how many peaks you would expect for the distribution described. 194) Sales of birthday cards over a one-year period A) None B) Three C) Two

D) One

191)

192)

193)

194)

Solve the problem. 195) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find 195) the mean retirement age. Round your answer to the nearest tenth. 53 67 63 50 67 58 60 50 52 A) 57.8

B) 57.1

C) 58.0

D) 56.5

Find the range for the given data. 196) Jeanne is currently taking college economics. On the past five quizzes, Jeanne got the following scores. 196) 7 18 3 15 11 A) 15

B) 4

C) 18

D) 3

Use the 68-95-99.7 rule to solve the problem. 197) Scores on a test are normally distributed with a mean of 106 and a standard deviation of 20. What percentage of scores are greater than 126? A) 16% B) 68% C) 32% D) 84%

197)

Find the range for the given data. 198) Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got198) the following scores. 26 32 12 44 59 A) 47

B) 6

C) 59

D) 12

State whether you would expect the data set to be normally distributed. 199) Amount of credit card debt of families in the U.S. A) Not normal B) Normal

199)

Construct a boxplot as requested. 200) The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. Construct a boxplot for the data set.

200)

310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700 A)

A hypothesis test is to be performed. State the null and alternative hypotheses. 201) 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% Find the margin of error for the survey results described. 202) In a survey of 659 employees of a large company, 34% said that they had high job satisfaction. Give your answer as a decimal to three decimal places. A) 0.039 B) 0.019 C) 0.078 D) 0.002

201)

202)

Find the range for the given data. 203) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The 203) diameters of the rolls (in m) are listed below. 0.546 0.573 0.225 0.384 0.272 0.113 A) 0.546 m

B) 0.113 m

C) 0.46 m

D) 0.047 m

Use the 68-95-99.7 rule to solve the problem. 204) At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.6 and 3.4? A) 95% B) 99.7% C) 68% D) 84%

204)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 205) Last month the average waiting time at a bank was 8.4 minutes. The manager has installed a new computer 205) 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 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. B) 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. C) 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. 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.

Obtain the five-number summary for the given data. 206) The test scores of 15 students are listed below.

206)

40 44 49 55 57 63 64 71 74 77 85 87 90 94 95 A) 40, 53.50, 71, 85.5, 95 C) 40, 53.50, 72.5, 85.5, 95

B) 40, 55, 72.5, 87, 95 D) 40, 55, 71, 87, 95

207) The weekly salaries (in dollars) of sixteen government workers are listed below. 690 612 813 645 728 582 476 620 530 660 685 463 549 787 507 826 A) 463, 534.75, 620, 718.5, 826 C) 463, 539.5, 632.5, 709, 826

207)

B) 463, 534.75, 632.5, 718.5, 826 D) 463, 530, 620, 690, 826

State whether you would expect the data set to be normally distributed. 208) Scores on a test in which most students have near perfect scores and a few fail. A) Not normal B) Normal

208)

Find the median for the given sample data. 209) A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.

209)

28, 15, 204, 194, 288, 246, 237 Find the median number of newspapers sold. A) 194 B) 204

C) 173

D) 237

For the given data value, find the standard score and the percentile. 210) A data value 1.8 standard deviations below the mean. A) z = -1.8; percentile = 3.59 B) z = -1.8; percentile = 96.41 C) z = -0.18; percentile = 42.07 D) z = 1.8; percentile = 96.41 Provide an appropriate response. 211) Which of the following statements concerning the standard normal curve is/are true (if any)?

210)

211)

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 B) a, b C) b, d D) a, c

State how many peaks you would expect for the distribution described. 212) Number showing when a single die is rolled 100 times A) Two B) One C) Three

D) None

212)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 213) The numbers listed below represent the amount of money that Tom has saved in each of the last 8 months. 213) $282 $310 $156 $138 $310 $418 $115 $254 Compute the standard deviation. A) $104.2 B) $282.0 C) $491,536.1 D) $567,569.0 State whether you would expect the data set to be normally distributed. 214) The diameters of the redwood trees in a forest. A) Not normal B) Normal

214)

Provide an appropriate response. 215) 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) a, b C) b, c D) a, c

215)

E) b

Construct a boxplot as requested. 216) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set.

216)

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 A)

Solve the problem. 217) The grocery expenses for six families were $84.62, $67.98, $88.25, $71.60, $40.14, and $58.07. Compute the mean grocery bill. Round your answer to the nearest cent. A) $102.67 B) $70.13 C) $68.44 D) $82.13

217)

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 218) 19, 16, 12, 13, 18, 16, 18, 7, 11 218) A) 3.7 B) 1.8 C) 4.2 D) 4.0 Use the 68-95-99.7 rule to solve the problem. 219) Assume that a distribution has a mean of 26 and a standard deviation of 4. What percentage of the values in the distribution do we expect to fall between 26 and 34? A) 25% B) 5% C) 95% D) 47.5%

219)

Find the mode(s) for the given sample data. 220) 90, 45, 32, 45, 29, 90 A) 45 B) 55.2

C) 90

D) 90, 45

220)

Find a 95% confidence interval for the true population proportion. 221) In a poll of 1096 college students, 15% said that they had cheated at least once on an exam. A) 13.5% to 16.5% B) 12.0% to 18.0% C) 14.9% to 15.1% D) 9.0% to 21.0%

221)

State how many peaks you would expect for the distribution described. 222) Sales of gloves in Boston over a one-year period A) Two B) Three C) One

222)

D) None

For the given data value, find the standard score and the percentile. 223) A data value 0.6 standard deviations above the mean. A) z = 0.6; percentile = 72.57 B) z = 0.6; percentile = 2.5 C) z = 0.06; percentile = 51.99 D) z = -0.6; percentile = 27.43 Find the margin of error for the survey results described. 224) In a poll of 1143 college students, 17% said that they had cheated at least once on an exam. Give your answer as a percentage to one decimal place. A) 1.5% B) 5.9% C) 0.1% D) 3.0% Provide an appropriate response. 225) 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 by chance 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 if the alternative hypothesis is true is 1 in 100 or more. D) The probability of the observed difference occurring by chance is 1 in 100 or less. Find the standard score for the given data value. 226) A data value in the 88th percentile. A) z = 1.2 B) z = 81.59

C) z = -2.4

D) z = -1.4

Solve the problem. 227) 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. 0.128 0.105 0.139 0.094 0.071 0.108 0.151 0.072 0.148 0.127 0.105 A) 0.108 in. B) 0.1248 in.

C) 0.1040 in.

224)

225)

226)

227)

D) 0.1135 in.

Find the margin of error for the survey results described. 228) In a poll of 358 adults, 44% said that they favored the proposed environmental laws. Give your answer as a decimal to three decimal places. A) 0.026 B) 0.053 C) 0.003 D) 0.106

223)

228)

Solve the problem. 229) 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

D A A F A

2 1 1 2 2

A) 8 C) 2.6

229)

B) 1.6 D) 2.3

Find a 95% confidence interval for the true population proportion. 230) In a survey of 693 employees of a large company, 34% said that they had high job satisfaction. A) 33.9% to 34.1% B) 30.2% to 37.8% C) 32.1% to 35.9% D) 34% to 37.8% A hypothesis test is to be performed. State the null and alternative hypotheses. 231) 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%

230)

231)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 232) You draw a card at random from a deck of cards and replace it. You repeat this 100 times and get 232) an ace 40 times. A) Not statistically significant B) Statistically significant

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. The 233) During one flu epidemic the proportion of adults nationwide who have come down with the flu is 8%. 233) 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 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%. 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 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%.

Find a 95% confidence interval for the true population proportion. 234) In a random sample of 186 births at one hospital, 33% were by Caesarean section. A) 32.5% to 33.5% B) 32.9% to 33.1% C) 25.7% to 40.3% D) 29.3% to 36.7%

234)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 235) A consumer advocacy group believes that the mean volume of juice in a company's 16-ounce juice 235) 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 less than 16 ounces. B) 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. C) 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. 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. 236) 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) 27.43% B) 51.99% C) 0.60% D) 72.57% State whether you would expect the data set to be normally distributed. 237) The number of siblings of the students at Bloomington High School A) Not normal B) Normal State whether the distribution appears to be (roughly) normal. 238)

A) Not normal

236)

237)

238)

B) Normal

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 239) 3, 5, 6, 6, 9, 1 239) A) 2.5 B) 7.6 C) 5.4 D) 2.8 A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 240) An environmental group believes that the health of the residents of Castletown is adversely affected by240) 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 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% B) 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% 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. 241) The amount of Jen's monthly phone bill is normally distributed with a mean of $58 and a standard deviation of $12. What percentage of her phone bills are between $22 and $94? A) 99.9% B) 68% C) 99.7% D) 95% Use the range rule of thumb to approximate the standard deviation. 242) 22, 29, 21, 24, 27, 28, 25, 36 A) 3.75 B) 4.2 C) 2.8

D) 1.65

Solve the problem. 243) Frank's Furniture employees earned the following amounts last week:

241)

242)

243)

$228.08 $310.82 $253.20 $250.97 $372.09 $312.32 $440.78 $497.95 $443.89 What was the mean amount earned by an employee last week? Round your answer to the nearest cent. A) $338.90 B) $345.57 C) $388.76 D) $444.30

State whether you would expect the data set to be normally distributed. 244) Sales of birthday cards over a one-year period A) Not normal B) Normal

244)

State how many peaks you would expect for the distribution described. 245) Voice pitch for the people in the school auditorium consisting of 6 year olds giving a concert, their mothers, and their fathers A) One B) None C) Two D) Three

245)

Identify the distribution as symmetric, left-skewed, or right-skewed. 246) Number of days worked last year by adult males in a U.S. city which has a low unemployment rate A) Right-skewed B) Symmetric C) Left-skewed

246)

Find the mode(s) for the given sample data. 247) 20, 24, 46, 24, 49, 24, 49 A) 49 B) 33.7

C) 46

D) 24

247)

Find the standard score for the given data value. 248) A data value in the 16th percentile. A) z = 1.0 B) z = 55.96

C) z = -1.0

D) z = -2.1

State whether you would expect the data set to be normally distributed. 249) The amount of property taxes paid by homeowners A) Normal B) Not normal

248)

249)

State whether you think the difference between what occurred and what you would expect by chance is statistically significant. 250) In eighteen of the last twenty years the annual precipitation in a certain region has been less than 250) in the previous year. A) Not statistically significant B) Statistically significant

Construct a boxplot as requested. 251) The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Construct a251) boxplot for the data set. 4.0 1.0 2.2 2.4 3.5 3.6 3.9 4.1 A)

1.5 2.7 3.6 4.2

1.6 3.4 3.7 4.2

2.0 3.4 3.7 7.0

Identify the distribution as symmetric, left-skewed, or right-skewed. 252) Amount of credit card debt of families in the U.S. A) Symmetric B) Right-skewed

C) Left-skewed

252)

Construct a boxplot as requested. 253) Here are the ages of the male and female employees at First River Bank. Draw a box plot for each of the253) two data sets. 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 A)

Solve the problem. 254) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles contain less than 32 oz of soda? A) 0.25% B) 40.13% C) 38.21% D) 59.87%

254)

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. 255) Carter Motor Company claims that its new sedan, the Libra, will average better than 22 miles per 255) 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 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. B) 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. 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 equal to 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. 256) Weights of the first graders at a school A) None B) Three C) One State whether the distribution appears to be (roughly) normal. 257)

A) Not normal

256)

257)

B) Normal

D) Two

258)

A) Not normal

B) Normal

Answer Key Testname: CHAPTER 6 1) D 2) C 3) B 4) B 5) B 6) C 7) C 8) C 9) E 10) C 11) C 12) A 13) D 14) D 15) B 16) B 17) B 18) B 19) C 20) A 21) B 22) D 23) C 24) C 25) D 26) C 27) C 28) C 29) C 30) D 31) C 32) C 33) B 34) D 35) 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. 36) 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. 37) 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. 38) 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. 39) 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. 40) It is possible to find two such data sets. Examples will vary. 41) Distribution C has the smallest median. Distribution D has the greatest variation. Distribution C is skewed to the left. 50

Answer Key Testname: CHAPTER 6 42) 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. 43) 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). 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) 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. 46) 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. 47) Answers will vary. 48) 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. 49) 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 .

50) The mode. The manufacturer needs to know the most common shoe size. 51) 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. 52) 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. 53) 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. 54) 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. 55) 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. 56) 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. 57) 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.

Answer Key Testname: CHAPTER 6 58) 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. 59) 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. 60) 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. 61) 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. 62) 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. 63) 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 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) 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). 66) 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. 67) 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. 68) 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. 69) 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. 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: 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. 72) C 73) C 74) B 75) D

Answer Key Testname: CHAPTER 6 76) D 77) B 78) D 79) A 80) C 81) C 82) A 83) C 84) C 85) A 86) A 87) C 88) C 89) D 90) C 91) C 92) C 93) B 94) D 95) D 96) A 97) C 98) C 99) B 100) C 101) D 102) B 103) D 104) A 105) A 106) D 107) B 108) D 109) D 110) B 111) D 112) A 113) B 114) C 115) B 116) C 117) A 118) D 119) C 120) D 121) B 122) A 123) A 124) D 125) C 53

Answer Key Testname: CHAPTER 6 126) B 127) D 128) D 129) B 130) C 131) B 132) B 133) A 134) B 135) C 136) C 137) B 138) C 139) D 140) A 141) B 142) A 143) B 144) C 145) A 146) A 147) D 148) C 149) B 150) B 151) D 152) B 153) D 154) D 155) A 156) D 157) C 158) D 159) B 160) A 161) A 162) B 163) C 164) A 165) D 166) A 167) D 168) A 169) A 170) D 171) B 172) D 173) A 174) A 175) C 54

Answer Key Testname: CHAPTER 6 176) B 177) B 178) A 179) B 180) B 181) D 182) C 183) B 184) C 185) D 186) B 187) B 188) B 189) C 190) A 191) C 192) C 193) D 194) A 195) A 196) A 197) A 198) A 199) A 200) D 201) A 202) A 203) C 204) C 205) D 206) D 207) C 208) A 209) B 210) A 211) C 212) D 213) A 214) B 215) A 216) B 217) C 218) D 219) D 220) D 221) B 222) C 223) A 224) D 225) D 55

Answer Key Testname: CHAPTER 6 226) A 227) D 228) B 229) D 230) B 231) C 232) B 233) B 234) C 235) A 236) D 237) A 238) A 239) D 240) D 241) C 242) A 243) B 244) A 245) D 246) C 247) D 248) C 249) B 250) B 251) B 252) B 253) C 254) B 255) A 256) C 257) B 258) A

Chapter 7 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) 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 cannot possibly be independent. C) S and T must also be independent. 2) 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) A and C B) C only C) B and C D) B only

E) A and B

3) In a large casino, the house wins on its blackjack games with a probability of 50.7%. Which of the following 3) 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) B D) D 4) When using the counting rules to count the number of possible outcomes, the permutation 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 unimportant C) When repetitions are allowed and the order of arrangement is important D) When repetitions are not allowed and the order of arrangement is important

5) 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 4 times as many combinations as permutations. B) There are 24 times as many permutations as combinations. C) There are 4 times as many permutations as combinations. D) There are 24 times as many combinations as permutations.

6) Given that P(E) = 1, what must be true about the event E? A) The event E is possible but not likely. B) The event E is certain. C) The event E is impossible. D) The event E is probable but not certain.

7) An insurance company sells an insurance policy for $1000. If there is no claim on a policy, the company7) 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 only B) A and C C) C only D) B and C 8) 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 archeological discoveries at different locations, at the same time D) Two consecutive wins by a football team

9) When using the counting rules to count the number of possible outcomes, the combinations formula can be used in which of the following situations? A) When repetitions are allowed and the order of arrangement is unimportant B) When repetitions are not allowed and the order of arrangement is unimportant C) When repetitions are not allowed and the order of arrangement is important D) When repetitions are allowed and the order of arrangement is important

10) Event A is that it rains in Santa Cruz tomorrow. Event B is that rains in Paris, France tomorrow. Are events 10) A and B: A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent? A) D

B) C

C) B

D) A

11) Event A is that Lisa votes for Candidate A in the gubernatorial election and event B is that she votes for11) candidate B. Are events A and B: A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

A) C

B) D

C) B

D) A

12) A card is selected at random from a standard deck of 52 cards. Let

12)

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 D B) A and C

C) B and C

D) B and D

13) 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) A C) C

13)

B) B D) All are equally likely

14) 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) Theoretical method B) Empirical method C) Relative frequency method D) Subjective method

14)

15) A knight may win a tournament. He may also fail to win the love of his lady. Are these events overlapping? Why or why not? A) Yes, because some ladies love winners B) Yes, because not all ladies love all winners C) No, because not all ladies love all winners D) No, because all ladies love all winners

15)

16) When a balanced die is rolled, the probability that a four will appear is

1 . 6

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) A and B B) All of them C) B and C D) B only E) C only

16)

17) A game involves tossing a fair coin 200 times. For each tail that appears you lose $1. For each head that17) 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) A and C B) B and C C) B only D) A only

18) Sean flipped a coin 100 times and got heads 42 times. He concludes that the probability of getting heads on a flip of his coin is 0.42. Which method did Sean use? A) Subjective method B) Multiplication method C) Empirical method D) Theoretical method

18)

19) 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 is selected at random, the most likely number of siblings for the student is 1. 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 selected at random has 2 siblings, the next student selected will have no siblings.

19)

20) A fair coin is tossed 5 times. Which of the following statements is (are) true?

20)

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) B and D B) A and D C) A and C

D) B and C

21) The permutation formula can be used to determine which of the following?

21)

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) A only B) B and C C) A and B D) A and C E) C only

22) Melissa estimates that the probability that she will marry her boyfriend is 0.6. Which method for determining probabilities did she use? A) Empirical method B) Relative frequency method C) Theoretical method D) Subjective method

22)

23) 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) B and C B) All of them C) A and C D) C only E) A only

23)

24) Which of the following statements makes sense?

24)

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) All of them B) B and C C) A only D) C only E) A and C

25) The combination formula can be used to determine which of the following?

25)

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

26) Event A is that the weather forecast predicts sun for your hometown tomorrow. Event B is that it rains tomorrow in your home town. Are events A and B:

26)

A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

A) B

B) C

C) D

D) A

27) Which pair(s) of events is (are) independent?

27)

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) A and B C) C and D

D) Both pairs

28) Which of the following events has a probability of 1? 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) A and C B) All of them C) B only D) A and B E) B and C

28)

29) 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? 1 A) Greater than but less than 1 B) 1 6

C) 0

1 6

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 30) A card is selected randomly from a standard deck of 52 cards. Let

30)

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.

31) A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run, the player 31) 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

32) 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?

32)

33) For a particular game at a casino, the expected winning for the player is -$0.87. How would you interpret this statement?

33)

34) Suppose a mathematician computed the expected winnings (to the player) of each of seven different games in a casino. What would you expect to be true for all expected winnings?

34)

29)

35) Explain what is wrong with the statement below. It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of winning $100,000 is only 0.000000512.

35)

36) Explain what is wrong with the statement below. It's quite a coincidence - the chance that I would have the birthday I do have is only 1/365.

36)

37) If you flip a fair coin 10 times would you be surprised if the coin comes up the same way every37) 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? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer to 2 decimal places when necessary. 38) The population of a certain country is about 105 million. The overall birth rate is 19.9 births per 1000. Approximately how many births were there in the country? A) 20,900 births B) 2.09 million births C) 20.9 million births D) 209,000 births Find the expected value. 39) In a large casino, the house wins on one of its games with a probability of 50,600%. 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 $400,000 on this game in one evening, how much should the casino expect to earn? A) $485,280,000 B) $404,400,000 C) $202,200,000 D) $202,400,000 Find the indicated probability. Round your answer to 6 decimal places when necessary. 40) In one town, 64% of adults have health insurance. What is the probability that 8 adults selected at random from the town all have health insurance? A) 0.125 B) 5.12 C) 0.028147 D) 0.64 Solve the problem. 41) Find the odds for getting two tails and a head when three fair coins are flipped. A) 3 to 5 B) 5 to 3 C) 1 to 7 D) 3 to 8 Find the indicated probability. Round your answer to 6 decimal places when necessary. 42) The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.06. Find the probability that the region will be hit by a hurricane in 3 consecutive years. A) 0 B) 0.0036 C) 0.000216 D) 0.18 Decide whether events A and B are overlapping or non-overlapping. 43) 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

38)

39)

40)

41)

42)

43)

Solve the problem. 44) In a certain lottery, 3 different numbers between 1 and 13 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) 2197 B) 1716 C) 286 D) 6 Find the indicated probability. Round your answer to 6 decimal places when necessary. 45) If a person is randomly selected, find the probability that his or her birthday is not on New Year's Day. Ignore leap years. 1 11 364 30 A) B) C) D) 365 12 365 31 Determine whether the events A and B are independent. 46) 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

44)

45)

46)

B) No

Solve the problem. 47) 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) 21 B) 10,000,000 C) 720 D) 120 Solve the problem. Round your answer to 5 decimal places when necessary. 48) The table shows the leading causes of death for one country in a single recent year.

47)

48)

Cause of Death Deaths Heart Disease 188,100 Cancer 136,800 AIDS 84,645 Stroke 51,300 Pulmonary Disease 48,051 Accidents 45,315 Diabetes 20,691 Pneumonia 19,152 Kidney Disease 10,089 Assume a population of 85.5 million. How much greater is the risk of death by cancer than the risk of death by accident? A) 30.18868 B) 3.01887 C) 2.71698 D) 0.00107

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 49) Every week, Joe plays chess with his father. Of the last 50 games, Joe has won 63% of the games. 49) What is the probability that Joe will win the next game? A) 0.63 B) 1 C) 0.063 D) 0.5

Find the indicated probability. Round your answer to 6 decimal places when necessary. 50) If two fair dice are rolled, what is the probability of not rolling a sum of 12? 1 35 5 1 A) B) C) D) 6 36 6 36 Find the indicated probability. 51) The table below describes the smoking habits of a group of asthma sufferers.

50)

51)

Light Heavy Nonsmoker smoker smoker Total Men 393 60 83 536 Women 376 88 68 532 Total 769 148 151 1068 If one of the 1068 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) 0.498 B) 0.352 C) 0.707 D) 0.489

Use the at least once rule to find the indicated probability. 52) The probability of winning $20 in a particular lottery is 0.02. What is the probability that you will get at least one $20 winner if you buy 50 tickets? A) 0.364 B) 0.980 C) 0.636 D) 0.007 Solve the problem. 53) 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) 9295 B) 13 C) 715 D) 728

52)

53)

54) How many 3-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) 1000 B) 999 C) 27 D) 6

54)

55) How many different five-card hands can be dealt from a deck that has no face cards (40 cards altogether)? A) 319,865 B) 639,730 C) 658,008 D) 127,946

55)

Determine whether the events A and B are independent. 56) 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) No B) Yes Use the at least once rule to find the indicated probability. 57) Find the probability of at least one queen when you draw cards from a standard deck 8 times; assume you replace the card each time you draw , so there are always 52 cards to draw from. A) 0.473 B) 0.044 C) 0.527 D) 0.900

56)

57)

Evaluate the factorial expression. 4! 58) 6!

58)

A) 2!

1 2!

C) 30

1 30

Solve the problem. Round your answer to 2 decimal places when necessary. 59) A U.S. city with a population of 1.8 million reports 37,853 births in one year. How many people are born per day in the city? A) 104 births per day B) 4932 births per day C) 95 births per day D) 728 births per day Solve the problem. 60) How many 5-letter passwords can be formed from the letters P, A, Y, M, E, N, T if no repetition of letters is allowed? A) 1260 B) 35 C) 2520 D) 42 Find the indicated probability. Round your answer to 6 decimal places when necessary. 61) 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. 2 13 1 4 A) B) C) D) 13 102 663 663

59)

60)

61)

Find the indicated probability. 62) The following table displays a distribution for a group of retired people by career and age at retirement. 62)

163

191

184

300

172

714

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) 0.253 B) 0.507 C) 0.063 D) 0.444

Decide whether events A and B are overlapping or non-overlapping. 63) You roll a red die and a blue die. 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

63)

Solve the problem. 64) At a lumber company, shelves are sold in 4 types of wood, 2 different widths and 5 different lengths. How many different types of shelves could be ordered? A) 11 B) 30 C) 40 D) 32 Find the indicated probability. Round your answer to 6 decimal places when necessary. 65) A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? 1 3 1 1 A) B) C) D) 5 14 3 11 Solve the problem. 66) A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand? A) 125 B) 13 C) 75 D) 30 Find the indicated probability. Round your answer to 6 decimal places when necessary. 67) Find the probability of selecting either a non-smoker or a woman when you select a person at random from a group composed of 20 female smokers, 35 male smokers, 25 female non-smokers, and 50 male non-smokers. A) 0.923 B) 0.192 C) 0.731 D) 0.2 Evaluate the factorial expression. 5! 68) 3! A) 20

64)

65)

66)

67)

68) B) 2!

C) 5

5 3

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 69) You count 61 heads when you toss a coin 100 times. If you don't know whether the coin is fair, 69) what is the probability that the next toss will be heads? A) 0.61 B) 0.061 C) 0.5 D) 1 Solve the problem. Round your answer to 2 decimal places when necessary. 70) In a recent year, there were 45 accidents in commercial aviation among major airlines over 15.0 million flight hours. Find the accident rate in units of accidents per 100,000 flight hours. A) 0.30 accidents per 100,000 flight hours B) 3 accidents per 100,000 flight hours C) 4.5 accidents per 100,000 flight hours D) 0.45 accidents per 100,000 flight hours

70)

Solve the problem. 71) 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. 2 5 6 1 A) B) C) D) 7 6 11 6 72) If 6 newborn babies are randomly selected, how many different gender sequences are possible? A) 36 B) 720 C) 64 D) 12 Find the expected value. 73) 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. 35 25 A) 6 B) 4 C) D) 6 4

71)

72)

73)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 74) Of the last 100 people who failed the lie detector test, 23 turned out to be telling the truth. What is 74) the probability that the next person who fails the test is actually telling the truth? A) 0.5 B) 0 C) 0.23 D) 0.77 Decide whether events A and B are overlapping or non-overlapping. 75) 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 Make a probability distribution for the given set of events. 76) 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)

75)

76)

(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. A) B) C) D) x P(X = x) x P(X = x) x P(X = x) x P(X = x) 1 1/6 1 11/36 1 5/18 1 5/18 2 1/6 2 1/4 2 2/9 2 1/4 3 1/6 3 7/36 3 1/6 3 7/36 4 1/6 4 5/36 4 1/9 4 5/36 5 1/6 5 1/12 5 1/18 5 1/9 6 1/6 6 1/36 6 0 6 1/36

Solve the problem. 77) A musician plans to perform 5 selections for a concert. If he can choose from 9 different selections, how many ways can he arrange his program? A) 15,120 B) 59,049 C) 45 D) 126 Determine whether the events A and B are independent. 78) 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) Yes

77)

78)

B) No

Find the expected value. 79) A contractor is considering a sale that promises a profit of $23,000 with a probability of .7 or a loss (due to bad weather, strikes, and such) of $12,000 with a probability of .3. What is the expected profit? A) $12,500 B) $11,000 C) $24,500 D) $16,100 Solve the problem. 80) 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"

79)

80)

B) 1.7556 × 105 three-number "combinations"

C) 3.5112 × 105 three-number "combinations"

D) 9240 three-number "combinations"

81) How many different 4-letter sequences can be made using the first 9 letters of the alphabet? Assume that repetition of letters is allowed. A) 126 B) 3024 C) 24 D) 6561

81)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 82) Of 1485 people who came into a blood bank to give blood, 328 people had high blood pressure. 82) Estimate the probability that the next person who comes in to give blood will have high blood pressure. A) 0.27 B) 0.22 C) 0.14 D) 0.19 Solve the problem. 83) Mark can remember only the first 3 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 24 seconds to try each one, how long would it take to try every possibility? A) 4000.8 minutes B) 400.1 minutes C) 16 minutes D) 3600 minutes Evaluate the factorial expression. 10! 84) (10 - 4)! A) 10

83)

84) B) 720

C) 1

D) 5040

Use the at least once rule to find the indicated probability. 85) Find the probability of at least one 3 in 7 rolls of a fair die. A) 0.056 B) 0.992 C) 0.279

D) 0.721

Find the indicated probability. 86) A die is rolled 50 times with the following results. Outcome Frequency

85)

86)

1 2 3 4 5 6 7 11 12 12 0 8

Compute the empirical probability that the die comes up a 5. 1 2 A) B) C) 0 3 25

Determine whether the events A and B are independent. 87) 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

1 6

87)

B) Yes

88) 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) No B) Yes Solve the problem. Round your answer to 2 decimal places when necessary. 89) A six mile strip of Sprinkle Road had 48 traffic fatalities last year. There were 2.2 million miles driven along this stretch. Determine the traffic fatality rate per 100,000 miles driven. A) 4583.33 fatalities per 100,000 miles driven B) 2.18 fatalities per 100,000 miles driven C) 22 fatalities per 100,000 miles driven D) 21.82 fatalities per 100,000 miles driven Find the expected value. 90) In a large casino, the house wins on one of its games with a probability of 51%. 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) $0.020 B) -$0.010 C) -$0.020 D) -$0.510 Decide whether events A and B are overlapping or non-overlapping. 91) 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) Non-overlapping B) Overlapping Find the indicated probability. Round your answer to 6 decimal places when necessary. 92) 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 3? 2 4 48 A) B) 16 C) D) 13 13 52

88)

89)

90)

91)

92)

Use the at least once rule to find the indicated probability. 93) A study conducted at a certain college shows that 61% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 8 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. A) 0.125 B) 0.999 C) 0.610 D) 0.981 Solve the problem. 94) 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) 60 B) 10 C) 120 D) 125

93)

94)

95) Find the odds against drawing a diamond when a card is drawn at random from a normal deck of 52 playing cards. A) 1 to 4 B) 1 to 3 C) 4 to 1 D) 3 to 1

95)

96) 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) -$0.83 C) -$1.00 D) -$0.85

96)

97) 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 7 questions on the survey? A) 720 B) 49 C) 5040 D) 7

97)

98) A license plate is to consist of 3 letters followed by 3 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) 1,386,000 B) 9,072,000 C) 1,296,000 D) 162,000

98)

99) If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.01, what are the odds against an earthquake? A) 99 to 1 B) 98 to 1 C) 100 to 1 D) 1 to 100

99)

Use the at least once rule to find the indicated probability. 100) The probability that a certain region in Mexico will be hit by a hurricane in any given year is 0.07. What is the probability that the region will be hit by at least one hurricane in the next 6 years? A) 0.930 B) 0.049 C) 0.647 D) 0.353

100)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 101) In a poll, respondents were asked whether they were planning to vote in the local election. 255 101) respondents indicated that they were planning to vote and 235 said that they were not. What is the probability that the next respondent questioned will indicate that they are planning to vote? A) 0.52 B) 1.09 C) 0.5 D) 0.48 Use the at least once rule to find the indicated probability. 102) An unprepared student makes random guesses on all questions of her multiple choice test. If there are 19 questions and each question has 5 possible answers, what is the probability she will answer at least one question correctly? A) 0.969 B) 0.004 C) 0.014 D) 0.986

102)

Solve the problem. Round your answer to 2 decimal places when necessary. 103) At an intersection in Normal, Illinois, there were 83 vehicle accidents with 168,212 vehicles passing through the intersection. Determine the accident rate per 1000 vehicles. A) 2,026,650.6 accidents per 1000 vehicles B) 168.21 accidents per 1000 vehicles C) 0 accidents per 1000 vehicles D) 0.49 accidents per 1000 vehicles Find the indicated probability. Round your answer to 6 decimal places when necessary. 104) If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second. 1 1 1 13 A) B) C) D) 16 169 204 204 Solve the problem. Round your answer to 5 decimal places when necessary. 105) The table shows the leading causes of death for one country in a single recent year.

103)

104)

105)

Cause of Death Deaths Heart Disease 143,850 Cancer 102,750 AIDS 61,650 Stroke 39,730 Pulmonary Disease 38,497 Accidents 31,510 Diabetes 16,577 Pneumonia 15,344 Kidney Disease 8083 Assume a population of 68.5 million. What is the empirical probability of death by AIDS during a single year? A) 0.62 B) 0.009 C) 0.00090

D) 0.00009

Solve the problem. 106) The table shows the prizes and probabilities of winning (on a single $1 ticket) for a particular state lottery. 106) Find the expected value of the winnings for a single lottery ticket. Prize (dollars) Probability 3 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) -$0.79

B) -$0.75

C) $0.21

D) -$0.84

Solve the problem. Round your answer to 2 decimal places when necessary. 107) In a recent year, there were 62 accidents in commercial aviation among major airlines over 8.5 million departures. Find the accident rate in units of accidents per 100,000 departures. A) 7.3 accidents per 100,000 departures B) 0.73 accidents per 100,000 departures C) 1.4 accidents per 100,000 departures D) 73 accidents per 100,000 departures Solve the problem. 108) A singer-songwriter wishes to compose a melody. Each note in the melody must be one of the 20 notes in her vocal range. How many different sequences of 6 notes are possible? A) 3,200,000 B) 27,907,200 C) 120 D) 64,000,000 Solve the problem. Round your answer to 2 decimal places when necessary. 109) A U.S. city with a population of 1.8 million reports 14,938 deaths. What is the death rate in deaths per 1000 people? A) 12.05 deaths per 1000 people B) 83 deaths per 1000 people C) 0.83 deaths per 1000 people D) 8.3 deaths per 1000 people Solve the problem. 110) Find the odds against correctly guessing the answer to a multiple choice question with 7 possible answers. A) 6 : 7 B) 6 : 1 C) 7 : 6 D) 7 : 1 Find the indicated probability. Round your answer to 6 decimal places when necessary. 111) Of the 53 people who answered "yes" to a question, 8 were male. Of the 78 people who answered "no" to the question, 14 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) 0.573 B) 0.168 C) 0.151 D) 0.511 112) Find the probability of rolling 5 successive 2s with 5 rolls of a fair die. A) 0.03125 B) 0.000772 C) 0.8333

D) 0.000129

Solve the problem. 113) License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? A) 100,000 B) 11,881,376 C) 175,760 D) 1,757,600 Find the expected value. 114) 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) -$0.40 B) -$0.42 C) -$0.50 D) -$1.00

107)

108)

109)

110)

111)

112)

113)

114)

Find the indicated probability. 115) In a poll of registered voters shortly before a mayoral election, people were asked which candidate they115) were planning to vote for. The results are shown in the table. Candidate Frequency Ford 380 Anderson 250 Garcia 520 Wong 667 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) 0.004 B) 0.138 C) 0.217 D) 250

Solve the problem. 116) 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) 1,512 B) 2,999 C) 2,997 D) 2,000 Use the at least once rule to find the indicated probability. 117) In a blood testing procedure, blood samples from 6 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) 0.000000262 B) 0.394 C) 0.606 D) 1.00 Find the indicated probability. Round your answer to 6 decimal places when necessary. 118) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 7. 12 1 1 9 A) B) C) D) 13 10 13 10 Make a probability distribution for the given set of events. 119) 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)

116)

117)

118)

119)

(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.

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 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 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 1/18 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

Determine whether the events A and B are independent. 120) A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is 120) selected at random. Event A: A club is selected on the first draw Event B: An ace is selected on the second draw A) No B) Yes

Find the indicated probability. Round your answer to 6 decimal places when necessary. 121) A sample of 4 different calculators is randomly selected from a group containing 46 that are defective and 23 that have no defects. What is the probability that all four of the calculators selected are defective? A) 18.4286 B) 0.1888 C) 0.0625 D) 0.1975 Solve the problem. 122) A tourist in France wants to visit 5 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order? 1 1 1 A) B) C) 120 D) 25 5 120

121)

122)

123) How many different 3-topping pizzas can be made if there are 10 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) 720 B) 1000 C) 6 D) 120

123)

124) In a certain lottery, 3 different numbers between 1 and 12 inclusive are drawn at random. These are the winning numbers. If you choose 3 different numbers at random between 1 and 12, what is the probability you will match the winning numbers? Assume that the order of the numbers is unimportant. 1 1 1 1 A) B) C) D) 220 1320 1728 6

124)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 125) A bag contains 15 balls numbered 1 through 15. What is the probability that a randomly selected ball has an even number? 15 2 1 7 A) B) C) D) 7 15 2 15 126) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.186. Find the probability that in a given year it will not snow on January 1st in that town. A) 1.186 B) 0.229 C) 5.376 D) 0.814 Find the indicated probability. 127) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

125)

126)

127)

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) 0.942 B) 0.69 C) 0.17 D) 0.772

Find the indicated probability. Round your answer to 6 decimal places when necessary. 128) One card is selected from a deck of cards. Find the probability of selecting a black card or a queen. 7 1 15 27 A) B) C) D) 13 26 26 52 Use the at least once rule to find the indicated probability. 129) In a batch of 8000 clock radios 7% are defective. A sample of 11 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) 0.550 B) 0.0700 C) 0.450 D) 0.0909 Find the expected value. 130) 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) -$0.40 B) $0 C) -$0.50 D) -$0.25 Solve the problem. 131) Suppose you are playing a game of chance. If you bet $6 on a certain event, you will collect $174 (including your $6 bet) if you win. Find the odds used for determining the payoff. A) 174 : 180 B) 29 : 1 C) 28 : 1 D) 1 : 28 Decide whether events A and B are overlapping or non-overlapping. 132) 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 133) 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 indicated probability. 134) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

128)

129)

130)

131)

132)

133)

134)

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) 0.89 B) 0.742 C) 0.082 D) 0.66

Find the expected value. 135) Experience shows that a ski lodge will be full (162 guests) if there is a heavy snow fall in December, while only partially full (80 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) 64.8 B) 112.8 C) 129.2 D) 97.2 Solve the problem. 136) 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) 0.00952 C) 0.01333 D) 0.01619

135)

136)

Find the expected value. 137) A commercial building contractor is trying to decide which of two projects to commit her company to.137) Project A will yield a profit of $50,000 with a probability of 0.6, a profit of $84,000 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: $47,200 B) Project A: $48,000 Project B: $52,200 Project B: $48,666 Contractor should choose project B Contractor should choose project A C) Project A: $56,200 D) Project A:$56,200 Project B: $60,200 Project B: $52,200 Contractor should choose project B Contractor should choose project A Evaluate the factorial expression. 138) 15! A) 8.7178 × 1010

B) 6.5385 × 1011

C) 1.3077 × 1012

D) 2.6154 × 1012

Solve the problem. 139) A sports shop sells tennis rackets in 4 different weights, 2 types of string, and 3 grip sizes. How many different rackets could they sell? A) 24 B) 18 C) 9 D) 32

138)

139)

140) There are 6 finalists in a singing competition. 140) If a person guesses randomly the top three winners (in any order), what is the probability that they will guess correctly? 1 1 1 1 A) B) C) D) 120 18 20 216 Find the expected value. 141) You are given 14 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 $14 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) $0.06 B) -$0.91 C) $2.75 D) -$0.06

141)

Solve the problem. Round your answer to 2 decimal places when necessary. 142) The overall U.S. death rate for 60 year-olds is approximately 12 deaths per 1000 people. Suppose that a life insurance company insures 2000 60-year-old people. The cost of the premium is $760 per year, and the death benefit is $55,000. What is the expected profit or loss for the insurance company? A) $200,000 profit B) $181,760 profit C) $1,320,000 loss D) $310,000 profit 143) A certain U.S. city had 50 traffic fatalities last year. There were 3 million miles driven in the city.. Determine the traffic fatality rate per 1,000,000 miles driven. A) 0.06 fatalities per 1,000,000 miles driven B) 1.67 fatalities per 1,000,000 miles driven C) 16.67 fatalities per 1,000,000 miles driven D) 16,666,666.67 fatalities per 1,000,000 miles driven Find the indicated probability. 144) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

142)

143)

144)

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) 0.69 B) 0.942 C) 0.772 D) 0.17

Solve the problem. Round your answer to 5 decimal places when necessary. 145) The table shows the leading causes of death for one country in a single recent year.

145)

Cause of Death Deaths Heart Disease 166,100 Cancer 128,350 AIDS 61,910 Stroke 43,035 Pulmonary Disease 42,431 Accidents 33,975 Diabetes 18,271 Pneumonia 16,912 Kidney Disease 8909 Assume a population of 75.5 million. In a typical city of 500,000 , how many people would you expect to die by accident in a year? A) Approximately 2250 people B) Approximately 16,987.5 people C) Approximately 225 people D) Approximately 1699 people

Solve the problem. 146) How many different five-card hands can be dealt from a deck that has only clubs (13 cards altogether)? A) 2,574 B) 3,861 C) 1,287 D) 143

146)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 147) An IRS auditor randomly selects 3 tax returns from 49 returns of which 6 contain errors. What is the probability that she selects none of those containing errors? A) 0.6758 B) 0.0011 C) 0.6698 D) 0.0018 148) 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? 1 1 1 5 A) B) C) D) 32 120 16 16 Decide whether events A and B are overlapping or non-overlapping. 149) 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 Find the indicated probability. Round your answer to 6 decimal places when necessary. 150) A die with 6 sides is rolled. What is the probability of rolling a number less than 5? 1 5 2 A) B) C) 4 D) 6 6 3 Solve the problem. 151) Ten thousand raffle tickets are sold. One first prize of $1600, 4 second prizes of $1000 each, and 8 third prizes of $300 each are to be awarded, with all winners selected randomly. If you are given one ticket, what are your expected winnings? A) 128 cents B) 29 cents C) 108 cents D) 80 cents Evaluate the factorial expression. 10! 152) 7! 3! A) 120

147)

148)

149)

150)

151)

152) B) 720

C) 1

D) 10

Solve the problem. Round your answer to 2 decimal places when necessary. 153) In a given year, the population of a certain country is about 159 million. The overall birth rate is 15.8 births per 1000. The overall death rate is 10.8 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) 2613 million C) 245,000 D) 24,500 Find the indicated probability. Round your answer to 6 decimal places when necessary. 154) What is the probability of not rolling a number larger than 4 with a fair die? 2 5 1 1 A) B) C) D) 3 6 2 3

153)

154)

Solve the problem. Round your answer to 5 decimal places when necessary. 155) The table shows the leading causes of death for one country in a single recent year.

155)

Cause of Death Deaths Heart Disease 212,400 Cancer 168,150 AIDS 86,730 Stroke 53,985 Pulmonary Disease 49,737 Accidents 40,710 Diabetes 21,417 Pneumonia 19,824 Kidney Disease 10,443 Assume a population of 88.5 million. What is the death rate due to heart disease in deaths per 100,000 of the population? A) 240 deaths per 100,000 B) 2.124 deaths per 100,000 C) 24 deaths per 100,000 D) 21.24 deaths per 100,000

156) The table shows the leading causes of death for one country in a single recent year.

156)

Cause of Death Deaths Heart Disease 147,600 Cancer 92,250 AIDS 52,890 Stroke 34,440 Pulmonary Disease 34,563 Accidents 33,210 Diabetes 14,883 Pneumonia 13,776 Kidney Disease 7257 Assume a population of 61.5 million. What is the empirical probability of death by stroke during a single year? A) 0.056 B) 0.000056 C) 0.00056

D) 0.0056

Find the indicated probability. Round your answer to 6 decimal places when necessary. 157) Find the probability of correctly answering the first 4 questions on a multiple choice test if random guesses are made and each question has 3 possible answers. 4 1 1 3 A) B) C) D) 3 64 81 4

157)

Determine whether the events A and B are independent. 158) Eight friends are drawing straws. The one who picks the short straw must cook dinner for the others. 158) Event A: The first person does not pick the short straw Event B: The second person picks the short straw A) No B) Yes

Find the indicated probability. Round your answer to 6 decimal places when necessary. 159) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 5? 8 5 1 A) B) C) 4 D) 9 6 9

159)

160) Among the contestants in a competition are 47 women and 26 men. If 5 winners are randomly selected, what is the probability that they are all men? A) 0.04288 B) 0.00438 C) 0.11063 D) 0.05181

160)

161) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. 31 11 31 334 A) B) C) D) 334 12 365 365

161)

Evaluate the factorial expression. 4! 162) 3! A)

4 3

162) B) 4!

C) 1

D) 4

Solve the problem. Round your answer to 5 decimal places when necessary. 163) The table shows the leading causes of death for one country in a single recent year.

163)

Cause of Death Deaths Heart Disease 203,500 Cancer 175,750 AIDS 74,925 Stroke 52,725 Pulmonary Disease 51,985 Accidents 45,325 Diabetes 22,385 Pneumonia 20,720 Kidney Disease 10,915 Assume a population of 92.5 million. What is the empirical probability of death by accident during a single year? A) 0.000049 B) 0.00049 C) 0.0049

D) 0.45

Find the indicated probability. Round your answer to 6 decimal places when necessary. 164) Three fair coins are tossed. Find the probability of getting the same thing on all three coins. 1 1 3 1 A) B) C) D) 8 4 8 2 165) 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 4. 7 1 2 1 A) B) C) D) 36 4 9 36

164)

165)

166) 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? 4 1 1 625 A) B) C) D) 9 6561 1296 1,679,616

166)

Find the indicated probability. 167) A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. 167) Sum 2 Frequency 4

3 1

4 2

5 6

6 4

7 4

8 3

9 3

10 11 12 14 9 0

Compute the empirical probability of getting a sum greater than 9. 3 23 1 A) B) C) 50 50 6

13 25

Solve the problem. 168) Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In how many ways can a person travel from A to C via B? A) 36 ways B) 24 ways C) 16 ways D) 10 ways Evaluate the factorial expression. 10! 169) 8! 2! A) 45

168)

169) B) 1

C) 90

D) 10

Solve the problem. 170) A baseball manager has 10 players of the same ability. How many 9 player starting lineups can he create? A) 10 B) 362,880 C) 90 D) 3,628,800 Solve the problem. Round your answer to 2 decimal places when necessary. 171) At an intersection in Normal, Illinois, there were 156 vehicle accidents with 255,590 vehicles passing through the intersection. Determine the accident rate per 10,000 vehicles. A) 6.1 accidents per 10,000 vehicles B) 0 accidents per 10,000 vehicles C) 255.59 accidents per 10,000 vehicles D) 1,638,397.44 accidents per 10,000 vehicles Find the indicated probability. Round your answer to 6 decimal places when necessary. 172) 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? 5 3 2 A) B) C) D) 6 3 5 5 173) 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. 9 3 3 3 A) B) C) D) 56 32 28 8

170)

171)

172)

173)

Find the expected value. 174) An insurance policy sells for $720. Based on past data, an average of 1 in 70 policyholders will file a $10,000 claim, an average of 1 in 100 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) $252 B) $468 C) $276 D) $282

174)

Make a probability distribution for the given set of events. 175) Suppose that you start with a normal deck of 52 cards and remove everything except the twos, threes, and 175) 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

Solve the problem. Round your answer to 2 decimal places when necessary. 176) The population of a certain country is about 132 million. The overall death rate is 12.2 deaths per 1000. Approximately how many deaths are there in the country? A) 1.61 million deaths B) 16,100 deaths C) 16.1 million deaths D) 161,000 deaths

176)

Solve the problem. 177) A shirt company has 4 designs each of which can be made with short or long sleeves. There are 5 different colors available. How many different shirts are available from this company? A) 11 B) 40 C) 20 D) 9 178) Find the odds for drawing an jack when a card is drawn at random from a normal deck of 52 playing cards. A) 1 to 13 B) 13 to 1 C) 1 to 12 D) 12 to 1

177)

178)

Find the indicated probability. 179) Three coins are tossed 80 times and the number of heads is recorded. The results are shown in the table179) below. Outcome Frequency

0 heads 1 head 2 heads 3 heads 28 26 19 7

Compute the empirical probability that at most two heads occur. 1 45 3 A) B) C) 2 2 4

Solve the problem. 180) Find the odds for getting two heads when two fair coins are flipped. A) 4 to 1 B) 1 to 4 C) 3 to 1

73 80

D) 1 to 3

180)

181) A company wants to hire a software engineer, an administrative assistant, and a sales representative. There are 4 possible candidates for the position of software engineer, 4 for the position of administrative assistant, and 3 for the position of sales representative. How many ways are there to choose the three people who will be hired? A) 11 B) 48 C) 64 D) 24

181)

182) There are 9 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible? A) 15,120 B) 120 C) 126 D) 59,049

182)

Find the indicated probability. Round your answer to 6 decimal places when necessary. 183) On a multiple choice test, each question has 5 possible answers. If you make a random guess on the first question, what is the probability that you are correct? 1 A) 1 B) 5 C) 0 D) 5

183)

Solve the problem. Round your answer to 5 decimal places when necessary. 184) The table shows the leading causes of death for one country in a single recent year.

184)

Cause of Death Deaths Heart Disease 196,650 Cancer 136,800 AIDS 76,095 Stroke 51,300 Pulmonary Disease 48,051 Accidents 42,750 Diabetes 20,691 Pneumonia 19,152 Kidney Disease 10,089 Assume a population of 85.5 million. In a typical city of 500,000, how many people would you expect to die of cancer in a year? A) Approximately 68,400 people B) Approximately 800 people C) Approximately 8000 people D) Approximately 6840 people

Provide an appropriate response. 185) Which of the following could not possibly be probabilities?

185)

A. -0.26 13 B. 7 C. 0 D. 0.87 A) A and B B) B and C C) A, B, and C D) A and C E) A and D

Find the expected value. 186) You are given 5 to 1 odds against tossing 2 tails in 2 tosses of a fair coin. This means that you win $5 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) $0.50 C) $1.25 D) -$0.50 Evaluate the factorial expression. 9! 187) 4!(9 - 4)! A) 120

186)

187) B) 2

C) 756

D) 126

Solve the problem. Round your answer to 2 decimal places when necessary. 188) A U.S. city with a population of 1.8 million reports 31,604 births. What is the birth rate in births per 1000 people? A) 17.56 births per 1000 people B) 1.76 births per 1000 people C) 56.95 births per 1000 people D) 176 births per 1000 people

188)

Decide whether events A and B are overlapping or non-overlapping. 189) 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 Solve the problem. 190) How many ways can an IRS auditor select 5 of 13 tax returns for an audit? A) 1287 B) 120 C) 154,440

189)

D) 371,293

Find the indicated probability. Round your answer to 6 decimal places when necessary. 191) 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 9? 5 3 1 1 A) B) C) D) 12 2 54 4 Solve the problem. Round your answer to 2 decimal places when necessary. 192) In a given year, the population of a certain country is about 185 million. The overall birth rate is 17.6 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) 0.13 million people B) 3.26 million people C) 1.33 million people D) 13.32 million people Use the at least once rule to find the indicated probability. 193) Find the probability of at least one club when you draw cards from a standard deck 11 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from. A) 0.014 B) 0.042 C) 0.585 D) 0.958 Decide whether events A and B are overlapping or non-overlapping. 194) 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

190)

191)

192)

193)

194)

Find the indicated probability. 195) The following table displays the number of siblings for students at one middle school. Find the probability 195) that a randomly selected student in the school has 2 siblings. Round your answer to the nearest thousandth. Number of siblingsFrequency 0 192 1 242 2 138 3 59 4 25 5 10 6 6 7 1

A) 0.205

B) 0.125

C) 0.287

D) 0.217

Solve the problem. 196) The library is to be given 6 books as a gift. The books will be selected from a list of 23 titles. If each book selected must have a different title, how many possible selections are there? A) 6,436,343 B) 72,681,840 C) 148,035,889 D) 100,947 Solve the problem. Round your answer to 2 decimal places when necessary. 197) The overall U.S. death rate for 60-62 year-olds is approximately 13 deaths per 1000 people. If there are about 14,954 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) 194 deaths B) 1944 deaths C) 19 deaths D) 87 deaths Solve the problem. 198) A license plate is to consist of 2 letters followed by 4 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted. A) 3,276,140 B) 3,276,000 C) 3,275,980 D) 6,760,000 Find the indicated probability. Round your answer to 6 decimal places when necessary. 199) A class consists of 17 women and 78 men. If a student is randomly selected, what is the probability that the student is a woman? 17 78 1 17 A) B) C) D) 95 95 95 78 200) A fair die is rolled. What is the probability of rolling an odd number or a number less than 3? 2 5 1 A) B) C) D) 1 3 6 2

196)

197)

198)

199)

200)

Find the indicated probability. 201) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

201)

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) 0.46 C) 0.942 D) 0.29

Solve the problem. 202) The odds on (against) your bet are 5 to 3. If you bet $60 and win, how much will you gain? Use the definition of odds in betting. A) $160 B) $60 C) $36 D) $100

202)

203) In Morse code, each symbol is either a dot or a dash. How many sequences of 10 symbols are possible? A) 3,628,800 B) 100 C) 20 D) 1024

203)

204) 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) 16,900 B) 35,152 C) 456,976 D) 33,800

204)

Find the indicated probability. 205) The following table show the results of a clinical trial for an allergy drug.

Improvement No improvement Total

205)

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) 0.11 B) 0.858 C) 0.458 D) 0.748

Find the indicated probability. Round your answer to 6 decimal places when necessary. 206) 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) 0.245 B) 0.490 C) 0.250 D) 0.500 Solve the problem. 207) In a certain town, 5% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle? A) 1 : 20 B) 1 : 19 C) 19 : 20 D) 19 : 1

206)

207)

Find the expected value. 208) 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 2 or a 3, nothing otherwise. What is your expected net winnings? A) $0.00 B) $3.00 C) -$1.00 D) $1.00 209) An insurance company will insure a $260,000 home for its total value for an annual premium of $560. 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) $220 B) -$260 C) $270 D) $300 Determine whether the events A and B are independent. 210) 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) No B) Yes Find the expected value. 211) Find the expected number of girls in a family of 4. A) 1.5 B) 2

C) 2.5

D) 1.75

208)

209)

210)

211)

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. 212) Sebastian lives in a rainy city. In his city, in 15 of the past 36 years there have been more than 100 212) 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. 7 15 1 5 A) B) C) D) 12 100 2 12 Provide an appropriate response. 213) Which (if any) of the following statements is/are true?

213)

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) A only C) Neither statement is true. D) B only

Decide whether events A and B are overlapping or non-overlapping. 214) 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

214)

Find the indicated probability. 215) The table shows the year and political party of a random sample of students from a certain college. Party Freshman Sophomore Independent 14 12 Democrat 24 27 Republican 12 14

Junior 28 12 24

215)

Senior 27 14 27

Find the empirical probability that a student at the college is an Independent. Round your answer to the nearest thousandth. A) 0.345 B) 0.115 C) 0.328 D) 0.333

Solve the problem. 216) The table shows the prizes and probabilities of winning (on a single $1 ticket) for a particular state lottery. 216) Prize (dollars) Probability 17 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 = $143 B) Expected loss = $230 C) Expected loss = $238 D) Expected loss = $222

Use the at least once rule to find the indicated probability. 217) Find the probability of getting at least one tail when tossing 8 fair coins. A) 0.996 B) 0.031 C) 0.004

D) 0.5

Find the indicated probability. Round your answer to 6 decimal places when necessary. 218) A fair die is rolled. What is the probability of rolling a 3 or a 6? 1 1 1 A) 2 B) C) D) 36 6 3 Solve the problem. 219) Find the odds for getting a sum of 7 when two fair dice are rolled. A) 5 to 1 B) 1 to 6 C) 6 to 1 Determine whether the events A and B are independent. 220) Event A: It will rain today in Seattle, Washington Event B: It will rain tomorrow in Seattle, Washington A) Yes B) No

D) 1 to 5

217)

218)

219)

220)

Solve the problem. 221) A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 9 different flags available, how many possible signals can be flown? A) 27 B) 84 C) 729 D) 504 Find the indicated probability. Round your answer to 6 decimal places when necessary. 222) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. 25 1 13 25 A) B) C) D) 102 2652 51 51 Solve the problem. 223) A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous? 1 1 1 1 A) B) C) D) 32,748 16,384 32,768 210 Solve the problem. Round your answer to 2 decimal places when necessary. 224) In a recent year, there were 649 deaths in general aviation over 8.8 billion miles flown. Find the fatality rate in units of deaths per 1 billion miles flown. A) 0.01 deaths per billion miles flown B) 571.12 deaths per billion miles flown C) 73.75 deaths per billion miles flown D) 7.38 deaths per billion miles flown Solve the problem. 225) 8 basketball players are to be selected to play in a special game. The players will be selected from 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 8 1 A) B) C) D) 40,320 2,220,075 27 213,127,200

221)

222)

223)

224)

225)

Find the expected value. 226) 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 226) 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. [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) 22.5 minutes B) 21.7 minutes C) 43.3 minutes D) 15 minutes

Find the indicated probability. Round your answer to 6 decimal places when necessary. 227) 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. 11 1 1 17 A) B) C) D) 36 3 2 36

227)

Solve the problem. 228) There are 6 women running in a race. 228) 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? 1 1 1 1 A) B) C) D) 216 18 120 20 229) A restaurant offers pizzas with 2 types of crust, 8 different toppings, and in 5 different sizes. How many different pizzas could be ordered? A) 15 B) 32 C) 80 D) 50 Find the expected value. 230) In a large casino, the house wins on one of its games with a probability of 50.5%. All bets are 1 : 1 . 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 $101.00 B) Win $2.00 C) Lose $2.00 D) Lose $1.00 231) In a game, you have a 1/45 probability of winning $115 and a 44/45 probability of losing $4. What is your expected winning? A) -$1.36 B) -$3.91 C) $6.47 D) $2.56 Find the indicated probability. Round your answer to 6 decimal places when necessary. 232) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good 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 Determine whether the events A and B are independent. 233) Event A: A couple's first child is a girl. Event B: The couple's second child is a girl A) Yes

229)

230)

231)

232)

233) B) No

Find the indicated probability. Round your answer to 6 decimal places when necessary. 234) One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 7 . (Note: The ace is considered a low card.) 35 7 15 31 A) B) C) D) 52 13 26 52

234)

Find the expected value. 235) The following table gives the distribution of heights for female students at one U.S. college. Height category (inches) Percentage 57-59 7.8 60-62 20.6 63-65 36.2 66-68 20.3 69-71 10.3 72 and over 4.8

235)

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.

Find the indicated probability. 236) You toss four coins and record the number of tails. You repeat this many times. The results are shown 236) below. Result 0 tails 1 tail 2 tails 3 tails 4 tails

Frequency 4 6 14 4 2

Find the empirical probability of getting 4 tails. Round your answer to the nearest thousandth. A) 0.067 B) 0.071 C) 0.063 D) 0.267

Make a probability distribution for the given set of events. 237) 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. A) B) Result Probability Result Probability 0T 1/16 0T 1/16 1T 1/8 1T 1/4 2T 3/8 2T 3/8 3T 1/8 3T 1/4 4T 1/16 4T 1/16 C) D) Result Probability Result Probability 0T 1/16 1T 1/4 1T 3/16 2T 7/16 2T 1/2 3T 1/4 3T 3/16 4T 1/16 4T 1/16

237)

Solve the problem. Round your answer to 5 decimal places when necessary. 238) The table shows the leading causes of death for one country in a single recent year.

238)

Cause of Death Deaths Heart Disease 170,500 Cancer 147,250 AIDS 71,300 Stroke 47,275 Pulmonary Disease 43,555 Accidents 32,550 Diabetes 18,755 Pneumonia 17,360 Kidney Disease 9145 Assume a population of 77.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke? A) 3.60656 B) 0.00159 C) 3.2459 D) 36.06557

Find the indicated probability. Round your answer to 6 decimal places when necessary. 239) The probability that Luis will pass his statistics test is 0.39. Find the probability that he will fail his statistics test. A) 0.64 B) 0.61 C) 2.56 D) 0.20

239)

Find the indicated probability. 240) The following table displays a distribution for a group of retired people by career and age at retirement. 240)

164

166

164

291

173

690

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) 0.282 B) 0.119 C) 0.238 D) 0.422

Find the indicated probability. Round your answer to 6 decimal places when necessary. 241) Find the probability of tossing 3 tails, then 3 heads, on the first 6 tosses of a fair coin. A) 3 B) 0.03125 C) 0.125 D) 0.015625 242) 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 of rain on three randomly selected consecutive days in January. A) 0.144 B) 0.064 C) 0.216 D) 0.090

241)

242)

Make a probability distribution for the given set of events. 243) The following table displays a frequency distribution of the number of siblings for students at one middle 243) school. Make a probability distribution for number of siblings. Number of siblings 0 1 2 3 4 5 6 7 Frequency 200 245 135 56 21 9 6 1 A) B) Siblings Probability Siblings Probability 0 0.312 1 0.518 1 0.349 2 0.285 2 0.212 3 0.118 3 0.071 4 0.044 4 0.031 5 0.019 5 0.013 6 0.013 6 0.009 7 0.002 7 0.001 C) D) Siblings Probability Siblings Probability 0 0.125 0 0.297 1 0.125 1 0.364 2 0.125 2 0.201 3 0.125 3 0.083 4 0.125 4 0.031 5 0.125 5 0.013 6 0.125 6 0.009 7 0.125 7 0.001

Solve the problem. 244) Four married couples have reserved eight seats in a row at the theater. If they arrange themselves randomly, what is the probability that all the women will sit in adjacent seats and all the men will sit in adjacent seats? 1 1 2 1 A) B) C) D) 70 840 315 35 Find the indicated probability. Round your answer to 6 decimal places when necessary. 245) What is the probability that 4 randomly selected people all have different birthdays? A) 0.9891 B) 0.9918 C) 0.9729 D) 0.9836

244)

245)

Solve the problem. 246) A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 3 colors. How many choices of carpet are there? A) 51 B) 44 C) 42 D) 47 Find the indicated probability. Round your answer to 6 decimal places when necessary. 247) 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? 5 1 1 A) B) 3 C) D) 18 12 18 Find the indicated probability. 248) A die is rolled 100 times with the following results. Outcome Frequency

246)

247)

248)

1 2 3 4 5 6 10 12 10 27 28 13

Compute the empirical probability that the die comes up 2 or 3. 1 12 10 A) B) C) 6 100 100

22 100

Solve the problem. 249) A pizza restaurant advertises 286 different 3-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) 14 B) 11 C) 13 D) 7 250) There are 7 women running in a race. How many different ways could first, second, and third place finishers occur? A) 21 B) 35 C) 343 D) 210 Find the indicated probability. Round your answer to 6 decimal places when necessary. 251) Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2? 1 1 11 13 A) B) C) D) 4 3 36 36

249)

250)

251)

Solve the problem. Round your answer to 5 decimal places when necessary. 252) The table shows the leading causes of death for one country in a single recent year.

252)

Cause of Death Deaths Heart Disease 217,200 Cancer 171,950 AIDS 82,355 Stroke 55,205 Pulmonary Disease 50,861 Accidents 45,250 Diabetes 21,901 Pneumonia 20,272 Kidney Disease 10,679 Assume a population of 90.5 million. What is the death rate due to accident in deaths per 100,000 of the population A) 0.4525 deaths per 100,000 B) 4.525 deaths per 100,000 C) 50 deaths per 100,000 D) 500 deaths per 100,000

Solve the problem. Round your answer to 2 decimal places when necessary. 253) A country with a population of 115 million has 23,805 traffic fatalities. Find the fatality rate in deaths per 100,000 population. A) 2381 deaths per 100,000 people B) 207 deaths per 100,000 people C) 20.7 deaths per 100,000 people D) 2.07 deaths per 100,000 people Find the expected value. 254) You are given 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice, meaning you win $7 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. A) $0.97 B) $0 C) $0.27 D) $0.11

253)

254)

Find the indicated probability. Round your answer to 6 decimal places when necessary. But 255) In January in a certain city the unconditional probability of rain on any given day of the month is 0.400.255) 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) 0.045 B) 0.072 C) 0.038 D) 0.024 256) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. 1 31 1 1 A) B) C) D) 12 365 31 365

256)

Solve the problem. 257) Determine the probability that in a class of 30 students, at least two students have the same birthday. 257) 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) 0.786 B) 0.706 C) 0.746 D) 0.294

Find the indicated probability. Round your answer to 6 decimal places when necessary. 258) 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. 2 7 1 3 A) B) C) D) 3 8 4 4 Evaluate the factorial expression. 259) 10! A) 7,257,600

B) 362,880

C) 1,814,400

D) 3,628,800

258)

259)

Find the indicated probability. 260) The following table displays a distribution for a group of retired people by career and age at retirement. 260)

183

184

172

323

177

727

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) 0.327 B) 0.250 C) 0.025 D) 0.099

Find the indicated probability. Round your answer to 6 decimal places when necessary. 261) If three fair coins are tossed, what is the probability of not tossing three heads? 7 2 1 1 A) B) C) D) 8 3 8 3

261)

Answer Key Testname: CHAPTER 7 1) B 2) D 3) C 4) D 5) B 6) B 7) D 8) C 9) B 10) D 11) B 12) D 13) C 14) A 15) B 16) E 17) D 18) C 19) C 20) D 21) E 22) D 23) D 24) C 25) C 26) A 27) C 28) E 29) D 30) 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. 31) The expected winnings are -$0.46. the game is not fair, and it favors the owner of the game. 32) 0.000798; yes 0.550; no 33) Answers will vary. Possible answer: In the long run, the average amount lost by the player per game is 87 cents. 34) The expected winnings would be negative for the player, as casinos are designed to make money. 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. 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. 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) + ....... = + 365 1 1 + + ....... = 1. 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".

Answer Key Testname: CHAPTER 7 37) yes; 0.00195; approximately 4 people 38) B 39) B 40) C 41) A 42) C 43) B 44) C 45) C 46) B 47) D 48) B 49) A 50) B 51) B 52) C 53) A 54) A 55) C 56) B 57) A 58) D 59) A 60) C 61) D 62) D 63) A 64) C 65) B 66) C 67) C 68) A 69) A 70) A 71) A 72) C 73) C 74) C 75) B 76) B 77) A 78) B 79) A 80) D 81) D 82) B 83) D 84) D 85) D 45

Answer Key Testname: CHAPTER 7 86) C 87) B 88) A 89) B 90) C 91) B 92) C 93) B 94) A 95) D 96) B 97) C 98) C 99) A 100) D 101) A 102) D 103) D 104) A 105) C 106) A 107) B 108) D 109) D 110) B 111) D 112) D 113) D 114) A 115) B 116) C 117) B 118) A 119) A 120) B 121) B 122) D 123) D 124) A 125) D 126) D 127) C 128) A 129) A 130) C 131) C 132) B 133) B 134) D 135) B 46

Answer Key Testname: CHAPTER 7 136) B 137) D 138) C 139) A 140) C 141) D 142) A 143) C 144) C 145) C 146) C 147) C 148) A 149) B 150) D 151) D 152) A 153) C 154) A 155) A 156) C 157) C 158) A 159) D 160) B 161) D 162) D 163) B 164) B 165) C 166) B 167) B 168) B 169) A 170) D 171) A 172) B 173) C 174) A 175) A 176) A 177) B 178) C 179) D 180) D 181) B 182) C 183) D 184) B 185) A 47

Answer Key Testname: CHAPTER 7 186) B 187) D 188) A 189) B 190) A 191) D 192) C 193) D 194) B 195) A 196) D 197) A 198) B 199) A 200) A 201) D 202) D 203) D 204) D 205) D 206) B 207) D 208) A 209) C 210) A 211) B 212) D 213) D 214) B 215) A 216) D 217) A 218) D 219) D 220) B 221) D 222) A 223) B 224) C 225) B 226) B 227) D 228) C 229) C 230) C 231) A 232) A 233) A 234) D 235) A 48

Answer Key Testname: CHAPTER 7 236) A 237) B 238) A 239) B 240) B 241) D 242) A 243) D 244) D 245) D 246) C 247) C 248) D 249) C 250) D 251) B 252) C 253) C 254) D 255) A 256) B 257) B 258) D 259) D 260) B 261) A

Chapter 8 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Earthquakes usually cause damage in all but which one of the following related ways? A) Tsunamis B) Collapsed building due to inferior construction C) Landslides D) Fires caused by heat from the earth's interior.

2) Which of the following sounds would you expect to have the highest decibel measurement? A) Rustling leaves B) Background noise in an average home C) Ordinary conversation D) Afternoon traffic in New York City

3) Which of the following are factors in the amount of damage caused by an earthquake? A) All of these B) The type of surface bedrock near the quake C) The economy of the region hit by the earthquake D) The amount of energy released in surface waves as compared to interior waves

4) The half-life of a radioactive substance is 65 years. If you start with some amount of this substance, what fraction will remain in 139 years? A) 0.23 B) 4.40 C) 0.01 D) 0.05

5) True or False? The world population growth rate is equal to the birth rate subtracted from the death rate. A) False B) True

6) True or False? Bases have a pH higher than 7. A) False

B) True

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 7) The price of computer memory is decreasing at a rate of 10% per year. If a memory chip costs $79 today, what will it cost in two years? A) Exponential; $71.30 B) Exponential; $63.99 C) Linear; $94.80 D) Linear; $63.20 Provide an appropriate response. 8) Use the growth rate of 1.8% to estimate the population of a growing country in 2050. Start from the 2000 population of 37 million. Use the approximate doubling time formula. A) 57.1 million B) 90.2 million C) 60.7 million D) 63.4 million Use the decibel scale to answer the question. 9) What is the loudness, in decibels, of a sound 53 million times as loud as the softest audible sound? A) 77 dB B) 93 dB C) 62 dB D) 108 dB

Use the pH scale to answer the question. 10) 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) Decreases by a factor of 40; more basic B) Increases by a factor of 40; more acidic C) Increases by a factor of 10,000; more acidic D) Decreases by a factor of 10,000; more basic Provide an appropriate response. 11) 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) 7.50 years B) 17.50 years C) 1.08 years D) 8.75 years

11)

12) Consider a population that begins growing exponentially at a base rate of 6% per year and then follows a logistic growth pattern. If the carrying capacity is 90 million, find the actual growth rate when the population is 88 million. A) 0.15% B) 0.13% C) 0.12% D) 0.14%

12)

13) Use the growth rate of 0.5% to estimate the population of a growing country in 2080. Start from the 2000 population of 27 million. Use the approximate doubling time formula. A) 40.1 million B) 54.0 million C) 90.8 million D) 59.6 million

13)

Use the earthquake magnitude scale to answer the question. 14) 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) 6.3 times as much energy

14)

B) 3.6 times as much energy D) 4.2 times as much energy

Provide an appropriate response. 15) True or False? log102,000,000 is between 7 and 8.

15)

A) True

B) False

Use the pH scale to answer the question. 16) What is the pH of a solution with a hydrogen ion concentration of 0.00001 mole per liter? Is this solution an acid or a base? A) pH = 7; neutral B) pH = 5; acid C) pH = 8; base D) pH = 6; acid Solve.

10)

17) Use the bacteria parable to determine how many bacteria are in the bottle at 11:10. A) 12 bacteria B) 2 10 bacteria C) 2 9 bacteria D) 20 bacteria

Provide an appropriate response. 18) Use the 1960s peak annual growth rate of 4.1% and population of 2 million to predict the current growth rate with a logistic model. Assume a current country population of 8 million. Assume the carrying capacity is 24 million. A) 4.47% B) 7.45% C) 4.10% D) 2.98% 19) True or False? The carrying capacity of our planet depends on our consumption of energy. A) False B) True

16)

17)

18)

19)

20) True or False? The carrying capacity is the largest population the environment can support for extended periods of time. A) False B) True

20)

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). 21) Use the average growth rate between 1850 and 1950, which was about 1.5%. 21) A) 57 years; population in 50 years = 181,145 B) 42 years; population in 50 years = 156,142 C) 49 years; population in 50 years = 243,803 D) 47 years; population in 50 years = 210,151

Use the earthquake magnitude scale to answer the question. 22) How much energy, in joules, is released by an earthquake of magnitude 6? A) 2.5 × 1013 joules B) 2.5 × 1010 joules C) 2.5 × 1016 joules

22)

D) 2.4 × 1013 joules

Provide an appropriate response. 23) Inflation is causing prices to rise at a rate of 9% per year. Use the approximate double time formula to determine what the price will be in 11 years if the item costs $100 today. A) $533.06 B) $266.53 C) $313.83 D) $109.32

23)

24) True or False? Earthquake strength is described in pH, the loudness of sounds is described in magnitudes, and the acidity of household cleansers is described by decibels. A) False B) True

24)

25) True or False? An earthquake of magnitude 6 will do twice as much damage as an earthquake of magnitude 3. A) False B) True

25)

Use the decibel scale to answer the question. 26) How many times as loud as the softest audible sound is the sound of threshold of pain for human ear (90 decibels)? A) 1090 B) 1018 C) 109

26) D) 103

Provide an appropriate response. 27) The doubling time of a population of flies is 4 hours. By what factor does the population increase in 48 hours? A) 2 48 B) 48 C) 2 1/12 D) 2 12

27)

28) The Consumer Price Index is increasing at a rate of 4% per year. By what factor will prices increase in 2 years? Use the approximate doubling time formula (rule of 70). A) 1 B) 4.08 C) 16 D) 1.08

28)

29) Given log10 2 = 0.3010 and log10 3 = 0.4771, find log10 54 without using a calculator.

29)

A) 1.7323

B) 1.3801

C) 0.4096

D) 0.4308

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). 30) Use the average growth rate between 1970 and 2000, which was about 1.4%. 30) A) 45 years; population in 50 years = 151,572 B) 60 years; population in 50 years = 174,110 C) 52 years; population in 50 years = 229,740 D) 50 years; population in 50 years = 200,000

Provide an appropriate response. 31) _______ growth occurs when a quantity grows by the same relative amount in each unit of time. A) Linear B) Exponential C) Static D) None of the above Use the decibel scale to answer the question. 32) How much louder (more intense) is a 57-dB sound than a 40-dB sound? A) 1.4 times as loud B) 238 times as loud C) 50 times as loud D) 25,118,864 times as loud Provide an appropriate response. 33) Suppose a population has a doubling time of 20 years. By what factor will it grow in 20 years? A) 4 B) 2 C) 3 D) 1

31)

32)

33)

Use the pH scale to answer the question. 34) What is the pH of a solution with a hydrogen ion concentration of 10-12 mole per liter? Is this solution an acid or a base? A) pH = 7; neutral B) pH = 6; acid C) pH = 12; base D) pH = 13; base Provide an appropriate response. 35) True or False? The earthquake magnitude scale relates the magnitude to the amount of energy released. A) True B) False

34)

35)

36) Consider a population that begins growing exponentially at a base rate of 5% per year and then follows a logistic growth pattern. If the carrying capacity is 39 million, find the actual growth rate when the population is 17 million. A) 3.19% B) 2.54% C) 2.82% D) 3.02%

36)

37) Suppose a radioactive substance has a half-life of 1000 years. What fraction will be left after 1000 years? 1 1 A) 2 B) C) 4 D) 4 2

37)

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). 38) Use the current annual growth rate which is about 2.8%. 38) A) 35 years; population in 50 years = 303,143 B) 20 years; population in 50 years = 229,740 C) 27 years; population in 50 years = 527,803 D) 25 years; population in 50 years = 400,000

Provide an appropriate response. 39) True or False? The loudness of a sound in decibels is defined by the formula intensity of the sound 10 log10 . intensity of loudest audible sound A) False

39)

B) True

Use the decibel scale to answer the question. 40) How does the intensity of sound form a concert speaker at a distance of 1 meter compare to the intensity at a distance of 7 meters? A) Factor of 107 weaker at 7 m. B) Factor of 21 weaker at 7 m. C) Factor of 7 weaker at 7 m.

40)

D) Factor of 49 weaker at 7 m.

41) How does the intensity of sound form a concert speaker at a distance of 1 meter compare to the intensity at a distance of 900 meters? A) Factor of 2700 weaker at 900 m. B) Factor of 10900 weaker at 900 m. C) Factor of 810,000 weaker at 900 m.

41)

D) Factor of 900 weaker at 900 m.

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 42) The price of a gallon of gasoline is increasing by 5¢ per week. If the price is $3.08 per gallon today, what will it be in ten weeks? A) Linear; $3.58 B) Exponential; $3.24 C) Linear; $3.53 D) Exponential; $5.02 Provide an appropriate response. 43) True or False? 100.897 is between 10 and 100. A) False

42)

43)

B) True

44) Given log10 2 = 0.3010 and log10 3 = 0.4771, find log10 12 without using a calculator.

44)

45) True or False? Our town is growing with a doubling time of 10 years, so its population will triple in 30 years. A) True B) False

45)

46) A nation of 100 million people is growing at a rate of 8% per year. Use the exact double time formula to determine what the population will be in 33 years. A) 104 million B) 623 million C) 1268 million D) 356 million

46)

47) 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) Annual growth rate B) Collapse C) Overshoot D) Logistic growth

47)

48) True or False? Suppose you had a magic bank account in which your balance doubled each day. If you started with just $1, you'd be a millionaire in less than a month. A) True B) False

48)

A) 1.2552

B) 0.2872

C) 0.5677

D) 1.0791

Solve.

49) The number of cells in a tumor doubles every 2.8 months. If the tumor begins as a single cell, how many cells will there be after 3 years? A) 2 cells B) 71 cells C) 7420 cells D) 101 cells

49)

50) Using the chessboard parable, how many grains of wheat should be placed on square 6 of the chessboard? A) 32 grains B) 16 grains C) 64 grains D) 10 grains

50)

Provide an appropriate response. 1 is between 0 and 1. 51) True or False? log10 11

51)

A) True

B) False

52) The Consumer Price Index is increasing at a rate of 8% per year. What is its doubling time? Use the approximate doubling time formula (rule of 70). A) 16 years B) 256 years C) 5.6 years D) 8.75 years

52)

53) True or False? Pure water is neutral and has a pH of 0. A) True B) False

53)

Use the earthquake magnitude scale to answer the question. 54) How much energy, in joules, is released by an earthquake of magnitude 4.6? A) 7.9 × 1012 joules B) 1.0 × 109 joules C) 2.0 × 1011 joules

Solve.

54)

D) 1.9 × 1011 joules

55) Using the chessboard parable, find the total weight (in pounds ) when all squares up to and including 19 are filled. Assume that each grain of wheat weighs 1/7000 pound. Round your answer to the nearest pound. A) 75 pounds B) 37 pounds C) 5 pounds D) 19 pounds

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 56) The value of your house is rising by $17,125 per year. If it is worth $159,166 today, what will it be worth in three years? A) Exponential; $528,873.00 B) Linear; $494,623.00 C) Linear; $210,541.00 D) Exponential; $216,266.78 57) During the worst periods of inflation in America, the price of food increased at a rate of 6% per month. If your food bill was $100 one month during this period, what was it two months later? A) Linear; $212.00 B) Linear; $112.00 C) Exponential; $112.36 D) Exponential; $106.09 Provide an appropriate response. 58) Given that log102 = 0.301, find log10 A) -4.000

1 without using a calculator. 4

B) 0.027

C) -0.602

55)

56)

57)

58) D) -1.806

Solve.

59) Use the bacteria parable to determine what fraction of the bottle is full at 11:33. 1 1 1 7 full full full full A) B) C) D) 12 2 27 2 26 2 28

Provide an appropriate response. 60) Urban encroachment is causing the area of a forest to decline at a rate of 3% per year. Use the approximate half-life formula to determine the fraction that remains in 63 years. A) 0.970731 B) 1.350000 C) 0.535887 D) 0.153893 61) A community of deer begins with an initial population of 1000 and grows 2.3% per year. Find the doubling time of the population. Round to the nearest year. A) 1 year B) 87 years C) 13 years D) 30 years Use the decibel scale to answer the question. 62) How does the intensity of sound from a concert speaker at a distance of 20 meters compare to the intensity at a distance of 100 meters? A) Factor of 50 weaker at 100 m. B) Factor of 100 weaker at 100 m. C) Factor of 5 weaker at 100 m. D) Factor of 25 weaker at 100 m. Provide an appropriate response. 63) Real populations sometimes increase beyond their environment's carrying capacity in a relatively short period of time. What is the name of this phenomenon? A) Overshoot B) Annual growth rate C) Logistic growth D) Collapse

Solve.

59)

60)

61)

62)

63)

64) What are the conditions in which the approximate doubling time formula works well? A) large growth rates and breaks down for growth rates below 15% B) large growth rates and breaks down for growth rates below 30% C) small growth rates and breaks down for growth rates over 15% D) small growth rates and breaks down for growth rates over 30%

64)

65) The doubling time of a city's population is 15 years. How long does it take for the population to quadruple. A) 154 years B) 2 15 years C) 4 years D) 30 years

65)

66) Use the magic penny parable to determine how much money you would have after 21 days. A) $20,971.52 B) $41,943.04 C) $4.40e+10 D) $10,485.76

66)

Provide an appropriate response. 67) The initial population of a town is 18,208 and it grows with a doubling time of 14 years. What will the population be in 8 years? A) 27,057 people B) 291,328 people C) 145,664 people D) 18,214 people Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 68) The population of Scoville is increasing at a rate of 336 people per year. If the population is 327 today, what will it be in three years? A) Linear; 1317 people B) Linear; 1335 people C) Exponential; 37,933,383 people D) Exponential; 34,966,119 people 7

67)

68)

Provide an appropriate response. 69) A community of rats begins with an initial population of 100 and grows 7% per month. Find the doubling time of the population. Round to the nearest month. A) 9 months B) 16 months C) 10 months D) 23 months Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 70) The value of your house is rising by 21% per year. If it is worth $268,900 today, what will it be worth in three years? A) Exponential; $329,414.06 B) Exponential; $476,372.75 C) Linear; $438,307.00 D) Linear; $381,838.00 Provide an appropriate response. 71) True or False? Birth rates have increased rapidly throughout the world during the past 50 years. A) True B) False

69)

70)

71)

72) Use the 1960s peak annual growth rate of 0.7% and population of 8 million to predict the current growth rate with a logistic model. Assume a current country population of 17 million. Assume the carrying capacity is 26 million. A) 1.36% B) 0.35% C) 0.70% D) 0.53%

72)

73) True or False? When the population is small relative to the carrying capacity, logistic growth is exponential with a fractional growth rate close to the base growth rate r. A) False B) True

73)

74) A certain radioactive isotope decays at a rate of 0.225% per year. Determine the half-life of this isotope, to the nearest year. A) 134 years B) 308 years C) 222 years D) 3 years

74)

75) The initial population of a town is 121,473 and it grows with a doubling time of 55 years. What will the population be in 26 years? A) 3,158,298 people B) 121,491 people C) 168,572 people D) 6,316,596 people

75)

Use the decibel scale to answer the question. 76) 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 3 weaker at 60 m. B) Factor of 30 weaker at 60 m. C) Factor of 36 weaker at 60 m. D) Factor of 9 weaker at 60 m.

76)

Provide an appropriate response. 77) The following table gives the birth and death rates for four countries in three different years:

77)

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 Littleton's net growth rate due to births and deaths in year 3. A) 0.9 per 100 B) 0.4 per 100 C) 0.8 per 100

D) 0.6 per 100

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). 78) Use the average growth rate between 1850 and 1950, which was about 0.2%. 78) A) 360 years; population in 50 years = 108,244 B) 345 years; population in 50 years = 106,121 C) 352 years; population in 50 years = 112,617 D) 350 years; population in 50 years = 110,409

Provide an appropriate response. 79) Poaching is causing a population of elephants to decline by 5% per year. Use the approximate half-life formula to determine the fraction that remains in 59 years if there are 8661 elephants today. A) 4829 elephants B) 18,250 elephants C) 8243 elephants D) 467 elephants Use the pH scale to answer the question. 80) What is the hydrogen ion concentration of a solution with pH 2.5? A) 3.2 x 10-5 B) 3.2 x 10-4 C) 3.2 x 10-3

80) D) 3.2 x 10-2

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 81) The population of Oak Forest is increasing at a rate of 4% per year. If the population is 87,224 today, what will it be in three years? A) Linear; 272,139 people B) Linear; 112,224 people C) Exponential; 98,115 people D) Exponential; 90,760 people Provide an appropriate response. 82) In 2000, the population of Littletown was 17 thousand. Use the given doubling time to predict the population in 2060. Assume a doubling time of 32 years. A) 32.6 thousand B) 3.7 thousand C) 32,640 thousand D) 62.4 thousand Use the decibel scale to answer the question. 83) What is the loudness, in decibels, of a sound 33 trillion times as loud as the softest audible sound? A) 189 dB B) 135 dB C) 162 dB D) 108 dB

79)

81)

82)

83)

Provide an appropriate response. 84) Inflation is causing prices to rise at a rate of 6% per year. Use the exact double time formula to determine what the price will be in 7 years if the item costs $100 today. A) $100.49 B) $100.06 C) $100.42 D) $150.36 Solve.

85) Using the chessboard parable, find the total number of grains when all squares up to and including 18 are filled. A) 262,143 grains B) 65,536 grains C) 34 grains D) 131,072 grains

Provide an appropriate response. 86) True or False? Exponential growth leads to repeated doublings. With each doubling, the amount of increase is approximately equal to the sum of all preceding doublings. A) False B) True

84)

85)

86)

87) True or False? If you decrease the amount of water in the cup, you'll decrease the pH of the water in the cup. A) False B) True

87)

88) True or False? Within the next decade, world population will grow by more than eight times the current population of the United States. A) False B) True

88)

89) In 2000, the population of Littletown was 9 thousand. Use the given doubling time to predict the population in 2010. Assume a doubling time of 33 years. A) 1.2 thousand B) 2970 thousand C) 11.1 thousand D) 13.7 thousand

89)

90) 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

90)

91) Oil consumption is increasing at a rate of 2.6% per year. By what factor will oil consumption increase in 3 years? Use the approximate doubling time formula (rule of 70). A) 1.08 B) 15.6 C) 2.68 D) 1.01

91)

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. 92) The value of your car is decreasing by 13% per year. If the car is worth $10,840 today, what will it be worth in two years? A) Exponential; $9476.60 B) Linear; $12,249.20 C) Linear; $13,658.40 D) Exponential; $8204.80 Provide an appropriate response. 93) True or False? Repeated doubling, in which each doubling occurs in the same amount of time, is a hallmark of linear growth. A) True B) False 94) 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) 2.72 B) 0.37 C) 0.14 D) 0.05

92)

93)

94)

Solve.

95) In 2000, the population of Littletown was 10 thousand. Use the given doubling time to predict the population in 2100. Assume a doubling time of 40 years. A) 320.0 thousand B) 5.7 thousand C) 56.6 thousand D) 40,000 thousand

95)

96) The current population of a threatened animal species is 1 million, but it is declining with a half-life of 18 years. How many animals will be left in 80 years? A) 45,929 animals B) 230 animals C) 22,965 animals D) 46 animals

96)

97) Use the magic penny parable to determine how many days would elapse before you had a total of over 913,659. A) 30 days B) 26 days C) 18 days D) 35 days

97)

Provide an appropriate response. 98) True or False? Exponential growth cannot continue indefinitely. After only a relatively large number of doublings, exponentially growing quantities reach possible proportions. A) True B) False 99) Given that log103 = 0.477, find log109 without using a calculator. A) 0.954

B) 6

C) 0.109

99) D) 12

Use the earthquake magnitude scale to answer the question. 100) How many times as much energy is released by an earthquake of magnitude 4 as by one of magnitude 2? A) 103 times as much energy B) 104 times as much energy C) 102 times as much energy

98)

100)

D) 106 times as much energy

Provide an appropriate response. 101) True or False? 102.950 is between 1000 and 10,000. A) True

B) False

Use the pH scale to answer the question. 102) If the pH of a solution decreases by 1.7, 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 17; more acidic B) Decreases by a factor of 17; more basic C) Increases by a factor of 50; more acidic D) Decreases by a factor of 50; more basic Solve. 103) Use the magic penny parable to determine how many days would elapse before you had a total of over $2,048,947. A) 28 days B) 37 days C) 32 days D) 20 days

101)

102)

103)

Answer Key Testname: CHAPTER 8 1) D 2) D 3) A 4) A 5) B 6) B 7) B 8) B 9) A 10) D 11) D 12) B 13) A 14) C 15) B 16) B 17) B 18) D 19) B 20) B 21) D 22) A 23) B 24) A 25) A 26) C 27) D 28) D 29) A 30) D 31) B 32) C 33) B 34) C 35) A 36) C 37) D 38) D 39) A 40) D 41) C 42) A 43) A 44) D 45) B 46) C 47) B 48) A 49) C 50) A 12

Answer Key Testname: CHAPTER 8 51) B 52) D 53) B 54) C 55) A 56) C 57) C 58) C 59) B 60) D 61) D 62) D 63) A 64) C 65) D 66) A 67) A 68) B 69) C 70) B 71) B 72) B 73) B 74) B 75) C 76) D 77) C 78) D 79) D 80) C 81) C 82) D 83) B 84) D 85) A 86) B 87) A 88) A 89) C 90) A 91) A 92) D 93) B 94) B 95) C 96) A 97) B 98) B 99) A 100) A 13

Answer Key Testname: CHAPTER 8 101) B 102) C 103) A

Chapter 9 Exam 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) Independend variable, book title; dependent variable, copyright year C) does not describe a function

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, distance traveled; dependent variable, time B) Independend variable, time; dependent variable, distance traveled C) does not describe a function SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 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. 3) 3)

Plot and label the given points. 4) (5, 2), (-2, -2)

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. 5) 5)

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) (time spent studying, percentage on exam)

Plot and label the given points. 8) (3, -6), (-6, 4)

Plot and label the given points. 10) (-2, -6), (-5, 1)

10)

11)

Plot and label the given points. 12) (1, 4), (-6, 2)

12)

Plot and label the given points. 14) (0, 6), (0, 4)

14)

15)

Plot and label the given points. 16) (4, 2), (6, -6)

16)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 17) The population of a town with an initial population of 72,526 is decreasing at a rate of 3.5% per year. Create an exponential function of the form Q = Q0 × (1 + r)t. A) Q = 72,526 × (1.035)t C) Q = 72,526 × (1.07)t

B) Q = 72,526 × (-2.5)t

D) Q = 72,526 × (0.965)t

Write an equation for the linear function and use it to answer the given question. 18) The Math Club plans to pay a visitor $74 to speak at a fundraiser. Tickets will be sold for $5 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 = 74 + 5n; 15 people B) p = -74 + 5n; 30 people C) p = -74 + 5n; 15 people D) p = 74 - 5n; 30 people Solve the equation for the unknown quantity x. 19) 12x = 44 A) 2.28

17)

B) 0.66

C) 1.52

D) 1.02

Write a short statement that expresses a possible function between the given variables. 20) (slope of hill, speed of bicycle) A) If you are coasting down a hill on a bicycle, the wider the hill, the slower you will coast. B) If you are coasting down a hill on a bicycle, the steeper the hill, the slower you will coast. C) If you are coasting down a hill on a bicycle, the steeper the hill, the faster you will coast. D) If you are coasting down a hill on a bicycle, the narrower the hill, the faster you will coast. Provide an appropriate response. 21) True or False? After 80 years, a population growing at a rate of 8% per year will have grown by twice as many people as a population growing at a rate of 4% per year. A) True B) False

18)

19)

20)

21)

22) Cars sold

22)

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) 550 cars B) 400 cars C) 350 cars D) 500 cars

23) True or False? If you create a graph showing how heart rate depends on running speed, the range should be heart rates from 60 to 180. A) True B) False

23)

24) True or False? Exponential functions are useful for modeling lottery numbers. A) False B) True

24)

25) A toxic radioactive substance with a density of 2 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 47 years ago. If the half-life of the substance is 20 years, what was the density of the substance when it was deposited 47 years ago? A) 25.49 mg/cm2 B) 2.69 mg/cm2 C) 0.39 mg/cm2 D) 10.2 mg/cm2

25)

26) Q = Q0 × 2 t/Tdouble is the equation for ________.

26)

A) doubling time C) half-life

B) growth or decay D) None of the above.

Write an equation for the linear function and use it to answer the given question. 27) Normaltown High School's pool record for the 100-yard freestyle was 46.7 in 1990. Assume that the record falls at a constant rate of 0.07 second per year. What does the model predict for the record in 2017? A) R = 46.7t - 0.07; 1260.83 seconds B) R = 46.7t + 0.07; 1260.97 seconds C) R = 46.7 + 0.07t; 48.59 seconds D) R = 46.7 - 0.07t; 44.81 seconds Write a short statement that expresses a possible function between the given variables. 28) (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 price of the bag of oranges increases, the weight of the bag decreases. C) As the weight of the bag of oranges increases, the price of the bag increases. D) As the weight of the bag of oranges decreases, the price of the bag increases.

27)

28)

Provide an appropriate response. 29) True or False? The slope is defined as the amount that the graph rises horizontally for a given distance that it runs vertically. A) False B) True 30) What is the most compact mathematical representation of a function? A) Equation B) Data table C) Domain Solve the equation for the unknown quantity x. 31) 4 4x = 30 A) 3.68

B) 1.64

C) 1.63

D) Graph

D) 0.61

Create the required linear function an use it to answer the question. 32) Suppose that you were 24 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 9 and 31. A) h = 24 + 2.4a; 45.6 inches; 98.4 inches B) h = 24 + 7.2a; 45.6 inches; 247.2 inches C) h = 24 + 12a; 88.8 inches; 396 inches D) h = 24 - 2.4a; 2.4 inches; -50.4 inches

29)

30)

31)

32)

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. 33) You drive along the highway at a constant speed of 62 miles per hour. How far do you travel in 4.1 33) hours? In 6.3 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 62 miles per hour. The rate of change is 62 mi/hr. In 4.1 hours, you travel 190.65 miles. In 6.3 hours, you travel 292.95 miles. B) Your distance traveled changes with respect to time at a rate of 62 miles per hour. The rate of change is 62 mi/hr. In 4.1 hours, you travel 317.75 miles. In 6.3 hours, you travel 488.25 miles. C) Your distance traveled changes with respect to time at a rate of 62 miles per hour. The rate of change is 62 mi/hr. In 4.1 hours, you travel 127.1 miles. In 6.3 hours, you travel 195.3 miles. D) Your distance traveled changes with respect to time at a rate of 62 miles per hour. The rate of change is 62 mi/hr. In 4.1 hours, you travel 254.2 miles. In 6.3 hours, you travel 390.6 miles.

Provide an appropriate response. 34) There are currently 70 million cars in a certain country, decreasing by 3.1% annually. How many years will it take for this country to have 48 million cars? Round to the nearest year. A) 22 years B) 12 years C) 7 years D) 100 years Draw a graph of the function and use the graph to answer the question.

34)

35) 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) $1125

B) $1925

C) $2325

D) $2175

Provide an appropriate response. 36) The given table represents a function. Make a clear graph of the function. Date Average High Temperature Jan. 1 45° F Feb. 1 38° F Mar. 1 50° F Apr. 1 60° F May 1 68° F June 1 78° F

35)

36)

July 1 Aug. 1 Sep. 1 Oct. 1 Nov. 1 Dec. 1 Dec. 31 A)

83° F 86° F 82° F 75° F 51° F 45° F 42° F

37) The general shape of an exponential growth function is a ______. A) rising curve B) rising line C) falling line

D) falling curve

37)

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 38) y = 3x + 1 1 A) slope = ; y intercept = (1, 0) B) slope = 3; y intercept = (0, 1) 3

C) slope = 3; y intercept = (1, 0)

D) slope =

1 ; y intercept = (0, 1) 3

38)

Provide an appropriate response. 39) The population of a town with an initial population of 56,112 grows at a rate of 3.3% per year. Make a graph of the exponential function. A) B)

Year

39)

Year

40) What is comprised of the values of the dependent variable? A) Domain B) Range C) Periodic function D) Model

40)

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 41) y = -x + 1 A) slope = 1; y intercept = (1, 0) B) slope = -1; y intercept = (0, 1)

C) slope = -1; y intercept = (1, 0)

41)

D) slope = 1; y intercept = (0, 1)

Create the required linear function an use it to answer the question. 42) In 1995 the United States recovered 22% 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 2003. A) 31.7% B) 30% C) 28.1% D) 26.4%

42)

Provide an appropriate response. 43) The population of a town with an initial population of 57,655 grows at a rate of 2.7% per year. Create a table showing the value of the quantity Q for the first 5 years or growth or decay. A) B) Year Population Year Population 0 57,655 0 57,655 1 213,324 1 56,098 2 789,297 2 54,584 3 2,920,399 3 53,110 4 10,805,475 4 51,676 5 39,980,258 5 50,281 C) D) Year Population Year Population 0 57,655 0 57,655 1 60,768 1 59,212 2 64,050 2 60,810 3 67,509 3 62,452 4 71,154 4 64,138 5 74,996 5 65,870 44) If prices increase at a monthly rate of 0.5%, by what percentage do they increase in a year? A) 4.6% B) 7.7% C) 6% D) 6.2% Draw a graph of the function and use the graph to answer the question. 45) 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 63 inches. Graph the equation and use the graph to estimate the depth of snow on January 28th.

A) 15 inches

B) 12 inches

43)

44)

45)

C) 7 inches

D) 35 inches

Write an equation for the linear function and use it to answer the given question. 46) You can purchase a motorcycle for $7980 or lease it for a down payment of $573 and $212 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 = 573 - 212m; 40 months B) L = 573 - 212m; 34 months C) L = 573 + 212m; 34 months D) L = 573 + 212m; 40 months Provide an appropriate response. 47) The following graph represents a function. Describe the function in words.

46)

47)

A) The function shows a steadily decreasing average age of death between 1980 and 2004. B) The function shows that the average age of death increases between 1980 and 1992 and does not change between 1992 and 2004. C) The function shows a steadily increasing average age of death between 1980 and 2004. D) The function shows that the average age of death per year does not change between 1980 and 2004. Create the required linear function an use it to answer the question. 48) 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 + 17 B) P = 0.6t + 24 C) P = 0.3t - 17 D) P = -0.6t + 7

48)

Write a short statement that expresses a possible function between the given variables. 49) (price of a DVD player, demand for DVD player) A) As the demand of a DVD player increases, the price generally decreases. B) As the price of a DVD player increases, the demand generally decreases. C) As the price of a DVD player increases, the demand generally increases. D) As the demand of a DVD player decreases, the price generally increases.

49)

50) (number of SUVs on road, air quality) A) As the quality of the air deteriorates, the number of SUVs on the road increases. B) As the number of SUVs on the road increases, the quality of the air generally deteriorates. 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 decreases, the quality of the air generally deteriorates. Provide an appropriate response. 51) What is a mathematical representation of a function that provides detailed information but can become unwieldy? A) Equation B) Data table C) Graph D) Domain

50)

51)

52) A computer is purchased for $4500. Its value each year is about 77% of the value the preceding year. Find the value of the computer after 3 years. A) $10,395.00 B) $1218.05 C) $2054.40 D) $1581.89

52)

53) True or False? A linear function has a constant rate of change and a curved graph. A) True B) False

53)

Write an equation for the linear function and use it to answer the given question. 54) The cost of renting a car is a flat $26, plus an additional 0.13 cents per mile that you drive. How far can you drive for $99? A) r = 26m + 0.13; 4 miles B) r = 26 + 0.13m; 562 miles C) r = 26 - 0.13m; 962 miles D) r = 26m - 0.13; 4 miles Provide an appropriate response. 55) Between 1998 and 2002, the average rate of inflation for a particular country was about 4% per year. If a cart of groceries cost $83 in 1998, what did it cost in 2002? A) $97.10 B) $100.98 C) $93.36 D) $112.92 Solve the equation for the unknown quantity x. 56) log10x = 2 A) 22

54)

55)

56)

B) 121

C) 20

D) 100

Provide an appropriate response. 57) The population of a town with an initial population of 69,064 is decreasing at a rate of 2.8% per year. Create a table showing the value of the quantity Q for the first 5 years or growth or decay. A) B) Year Population Year Population 0 69,064 0 69,064 1 68,097 1 65,196 2 67,144 2 61,545 3 66,204 3 58,099 4 65,277 4 54,845 5 64,363 5 51,774 C) D) Year Population Year Population 0 69,064 0 69,064 1 67,130 1 70,998 2 65,251 2 72,986 3 63,424 3 75,029 4 61,648 4 77,130 5 59,922 5 79,290 58) True or False? The rate of change is equal to the slope of the graph. A) True B) False

57)

58)

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 59) y = -4x + 3 1 A) slope = - ; y intercept = (3, 0) B) slope = -4; y intercept = (3, 0) 4

C) slope = -4; y intercept = (0, 3)

D) slope = -

1 ; y intercept = (0, 3) 4

Create the required linear function an use it to answer the question. 60) 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 791. 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 = 3.8475t - 495.75 B) s = 4.275t + 491.75 C) s = 3.8475t + 495.75 D) s = -4.275t + 491.75

59)

60)

Provide an appropriate response. 61) The given table represents a function. Identify the independent and dependent variables, and describe 61) the domain and range. Date Average High Temperature Jan. 1 45° F Feb. 1 38° F Mar. 1 46° F Apr. 1 57° F May 1 65° F June 1 75° F July 1 81° F Aug. 1 89° F Sep. 1 85° F Oct. 1 74° F Nov. 1 55° F Dec. 1 47° F Dec. 31 41° F

A) The variables are (time, temperature) or (date, temperature). The domain is all days over the course of a year. The range is temperatures between 38° and 89°. B) The variables are (temperature, time) or (temperature, date). The domain is all temperatures between 38° and 89° and the range is all days over the course of a year. C) The variables are (time, temperature) or (date, temperature). The domain is all days over the course of a year. The range is temperatures between 45° and 41°. D) The variables are (temperature, time) or (temperature, date). The domain is all temperatures between 45° and 41° and the range is all days over the course of a year.

62) The population of a town with an initial population of 52,576 is decreasing at a rate of 4% per year. Make a graph of the exponential function. A) B)

Year

62)

63) The following graph represents a function. Identify the independent and dependent variables and describe 63) 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 ages between 0 and 82. The range is the years between 1980 and 2004. C) 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. 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. Solve the equation for the unknown quantity x. 64) 5 x = 26 A) 0.49

B) 3.04

C) 1.35

D) 2.02

Provide an appropriate response. 65) The population of a town with an initial population of 62,828 grows at a rate of 2.4% per year. Create an exponential function of the form Q = Q0 × (1 + r)t. A) Q = 62,828 × (0.976)t C) Q = 62,828 × (1.024)t

64)

65)

B) Q = 62,828 × (3.4)t

D) Q = 62,828 × (0.952)t

66) True or False? An exponential function grows (or decays) by the same relative amount per unit time. A) False B) True

66)

Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10. 67) y = -4x - 1 1 A) slope = - ; y intercept = (0, -1) B) slope = -4; y intercept = (-1, 0) 4

D) slope = -

C) slope = -4; y intercept = (0, -1)

Solve the equation for the unknown quantity x. 68) log10(2 + x) = 1 A) 2

69) log10x = -1.3 A) 0.2725

67)

1 ; y intercept = (-1, 0) 4

68)

B) 8

C) -2

D) 12

B) -13

C) 0.0501

D) -14.3

69)

Provide an appropriate response. 70) A certain drug is eliminated from the bloodstream exponentially with a half-life of 12 hours. Suppose that a patient receives an initial dose of 25 milligrams of the drug at midnight. Estimate when the drug concentration will reach 20% of its initial level. A) 16 hours B) 28 hours C) 40 hours D) 58 hours 71) True or False? The demand for movie tickets is a function of their price. A) False B) True

70)

71)

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. 72) A gas station owner finds that for every penny increase in the price of gasoline, she sells 1657 fewer 72) gallons of gas per week. How much more or less gas will she sell if she raises the price by 6 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 1657 gallons per cent. The rate of change is -1657 gallons per cent. If the price is increased by 6 cents per gallon, the change in gas sales is -12,427.5 gallons. If the price is decreased by 2 cents, gas sales increase by -4142.5 gallons. B) At a particular gas station, sales decrease with respect to price by 1657 gallons per cent. The rate of change is 1657 gallons per cent. If the price is increased by 6 cents per gallon, the change in gas sales is 4971 gallons. If the price is decreased by 2 cents, gas sales increase by -1657 gallons. C) At a particular gas station, sales decrease with respect to price by 1657 gallons per cent. The rate of change is 1657 gallons per cent. If the price is increased by 6 cents per gallon, the change in gas sales is 7456.5 gallons. If the price is decreased by 2 cents, gas sales increase by 2485.5 gallons. D) At a particular gas station, sales decrease with respect to price by 1657 gallons per cent. The rate of change is -1657 gallons per cent. If the price is increased by 6 cents per gallon, the change in gas sales is -9942 gallons. If the price is decreased by 2 cents, gas sales increase by 3314 gallons.

Provide an appropriate response. 73) A certain drug is eliminated from the bloodstream exponentially with a half-life of 24 hours. Suppose that a patient receives an initial dose of 30 milligrams of the drug at midnight. How much of the drug is in the patient's blood at noon the next day? A) 0.71 mg B) 21.21 mg C) 7.5 mg D) 10.61 mg 74) The _____ the rate of change, the steeper the slope. A) greater C) more dependent

B) smaller D) more independent

73)

74)

75) If prices of gold decrease at a monthly rate of 0.7%, by what percentage do they decrease in a year. A) 8.4% B) 10.1% C) 8.1% D) 8.7%

75)

76) True or False? A positive slope means a line rising right. A) True B) False

76)

77) The process of measuring the ages of rocks, bones, pottery, or other solid objects that contain radioactive elements is called ________. A) doubling time B) half-life C) radioactive measuring D) radioactive decay

77)

Write an equation for the linear function and use it to answer the given question. 78) You can rent time on computers at the local copy center for a $7 setup charge and an additional $4 for every 10 minutes. How much time can you rent for $24? A) r = 7t - 0.4; 3.49 minutes B) r = 7t + 0.4; 3.37 minutes C) r = 7 + 0.4t; 42.5 minutes D) r = 7 - 0.4t; 77.5 minutes

78)

Provide an appropriate response. 79) What is comprised of the values of the independent variable? A) Model B) Range C) Domain D) Periodic function Solve the equation for the unknown quantity x. 80) 2 × 6 x = 33 A) 4.77

B) 2.12

C) 0.31

79)

D) 1.56

Create the required linear function an use it to answer the question. 81) 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 795. 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 54-hour review course. Round your answer to the tenths place. A) 725.0 B) 717.7 C) 729.2 D) 739.0 Solve the equation for the unknown quantity x. 82) 8 x/2 = 44 A) 0.27

B) 1.36

C) 2.43

D) 3.64

Write an equation for the linear function and use it to answer the given question. 83) In the town of Oak Forest, a 3% local sales tax and a 5% 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 $49 before taxes? A) T = 0.08p + 1; $4.92 B) T = 1.08p; $52.92 C) T = 0.98p; $48.02 D) T = 0.92p; $45.08 84) The price of a particular model car is $11,730 today and rises with time at a constant rate of $1125 per year. How much will a new car cost in 3.2 years? A) p = 11,730 + 1125t; $15,330.00 B) p = 11,730 - 1125t; $8130.00 C) p = 11,730t - 1125; $36,411.00 D) p = 1125 + 11,730t; $38,661.00 Provide an appropriate response. 85) In the algebraic equation of a line, the y-intercept is denoted by the letter ______. A) y B) m C) x D) b

80)

81)

82)

83)

84)

85)

Answer Key Testname: CHAPTER 9 1) C 2) B 3) a) Snow depth increases with time. b) 2 in. per day. c) Good model if snowfall rate is constant for 5 days. 4)

5) a) On a long trip, distance from home increases with time. b) 80 miles per hour. c) Good model if speed is constant for 8 hours. 6) a) The number of students sick with the flu increases with time. b) 16 students sick per day. c) Good model if the flu rate is constant for 5 weeks. 7) 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.

Answer Key Testname: CHAPTER 9 8)

9) 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)

10)

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.

Answer Key Testname: CHAPTER 9 11) 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)

12)

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).

13) a) As the length of the race increases, the average speed decreases. b) -0.7 (km/hr)/km hour. c) The model is a rough approximation. 14)

Answer Key Testname: CHAPTER 9 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)

16)

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.

17) D 18) C 19) C 20) C 21) B 22) A 23) A 24) A 25) D 26) A 27) D 28) C 29) A 30) A 31) D 29

Answer Key Testname: CHAPTER 9 32) A 33) D 34) B 35) D 36) C 37) A 38) B 39) B 40) B 41) B 42) B 43) D 44) D 45) C 46) C 47) C 48) A 49) B 50) B 51) B 52) C 53) B 54) B 55) A 56) D 57) C 58) A 59) C 60) B 61) A 62) B 63) C 64) D 65) C 66) B 67) C 68) B 69) C 70) B 71) B 72) D 73) B 74) A 75) C 76) A 77) D 78) C 79) C 80) D 81) A 30

Answer Key Testname: CHAPTER 9 82) D 83) B 84) A 85) D

Chapter 10 Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) How long is the perimeter of a snowflake island? A) 2 times the height C) it is infinite

B) 3 times the height D) it is the same as the area

2) The process of repeating a rule over and over to generate a self-similar fractal is called . A) iteration

B) fractalization

C) interpretation

3) In fractal geometry, the perimeter of a region is

D) repetition

and the area is

A) unlimited; unlimited C) unlimited; limited

B) limited; limited D) limited; unlimited

4) Define a self-similar fractal. A) has a fractal dimension greater than 2 B) can be created by finding the fractal dimension C) looks similar to itself when examined at different scales D) has a fractal dimension between 0 and 1

5) What mathematical tool is helpful in finding the fractal dimension? A) tangent B) integration C) iteration 6) In fractal geometry, the shorter the ruler

D) logarithm

A) the less accurate the measurement C) the more accurate the measurement

B) the shorter the perimeter D) the longer the perimeter

7) The Sierpinski sponge has a fractal dimension between A) 1 and 2

B) 3 and 4

8) Solving for fractal dimension, we use the rule that

C) 2 and 3

D) 0 and 1 .

A) log a x = x log a

B) log(a + b) = log(a) log(b)

C) log ab = log a + log b

D) log

a = log a - log b b

9) To create a Sierpinski triangle, start with a solid black triangle and iterate what rules? A) Delete the middle third of each line segment of the triangle. B) Draw an isosceles triangle extending from each side. C) Connect the midpoints of the sides and remove the resulting inner triangle. D) Connect the endpoints of the sides and inserting an isosceles triangle.

10) To create the Snowflake curve, the first step is to

10)

A) find the fractal dimension B) divide the line segment in half C) use a smaller ruler D) divide the line segment into three equal pieces 11) Define a random iteration. A) an iteration that doesn't produce a fractal. B) an iteration that is self-similar. C) an iteration with slight variations in every iteration.

11)

12) The fractal dimension of a coastline

12)

A) is between 1 and 2 C) is greater than 2

B) is less than 1 D) is between 0 and 1

13) Define a fractal object. A) An object with several edges that can be revealed at larger scales. B) An object that reveals new features at smaller scales. C) An object that can be magnified. D) An object with many jagged edges. Convert the given degree measure into degrees, minutes, and seconds of arc. 14) 66.13° A) 66°7 38 B) 66°17 48 C) 66°17 38

13)

D) 66°7 48

Find the area of the triangle. 15)

15)

32 yd 37 yd A) 1184 yd2

14)

B) 296 yd2

C) 512 yd2

D) 592 yd2

Solve the problem. 16) Earth has a radius of approximately 6400 kilometers, and Saturn has a radius of approximately 60,300 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

16)

1.10 × 1012 cubic kilometers, surface area of Saturn is about 4.57 × 1010 square kilometers, volume of Saturn is about 9.18 × 1014 cubic kilometers

(ii) Saturn has the larger surface-area-to-volume ratio. B) (i) Surface area of Earth is about 4.57 × 1010 square kilometers, volume of Earth is about 9.18 × 1014 cubic kilometers, surface area of <a> is about 5.15 × 108 square kilometers, volume of Saturn 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 4.57 × 1010 square kilometers, volume of Earth is about

9.18 × 1014 cubic kilometers, surface area of Saturn is about 5.15 × 108 square kilometers, volume of Saturn is about 1.10 × 1012 cubic kilometers

(ii) Saturn 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 Saturn is about 4.57 × 1010 square kilometers, volume of Saturn is about 9.18 × 1014 cubic kilometers (ii) Earth has the larger surface-area-to-volume ratio.

The two triangles below are similar. Find the missing lengths. 17) 22

17)

A) x = 41

27 36

B) x = 44

C) x = 36

D) x = 55

Determine if the pair of triangles are similar. 18)

18)

A) Similar Solve.

B) Not similar

19) Determine the area of a circular enclosure and a square enclosure made with 236 meters of fence. A) Circular: 3022 m 2 ; square: 3481 m 2 B) Circular: 3022 m 2 ; square: 13,924 m 2 C) Circular: 4432 m 2 ; square: 3481 m 2

D) Circular: 4432 m 2 ; square: 13,924 m 2

19)

Solve the problem. 20) If you magically tripled in size, how much more material will be required for your new set of clothes? A) 27 B) 9 C) 2 D) 3 Find the area of the triangle. 21) 23 m

20)

21)

20 m

26.5 m A) 230 m 2

Find the perimeter. 22) 12 ft

A) 30 ft

B) 530 m 2

C) 200 m 2

D) 265 m 2

22)

6 ft

13 ft

B) 25 ft

C) 39 ft

D) 31 ft

Provide an appropriate response. 23) True or False? A geometric line is formed by the shortest path between any 2 points. A) False B) True

23)

Solve. Round your answer to the nearest tenth. 24) Find the circumference of a circle with a diameter of 32 feet. A) 100.5 ft B) 201.0 ft C) 50.2 ft

24)

Solve.

D) 803.8 ft

25) Determine the area of a circular enclosure and a square enclosure made with 778 feet of fence. Use = 3.1416. A) Circular: 48,167 ft2 ; square: 151,321 ft2 B) Circular: 48,167 ft2 ; square: 37,830 ft2 C) Circular: 32,835 ft2 ; square: 151,321 ft2

D) Circular: 32,835 ft2 ; square: 37,830 ft2

Provide an appropriate response. 26) True or False? The closer away an object is located from you, the smaller it will appear in angular size. A) False B) True The two triangles below are similar. Find the missing lengths. 27) 75

A) x = 21

7 72

25)

27)

24 B) x = 28

C) x = 12

26)

D) x = 7

Use the formula relating angular size, physical size and distance. 28) What is the angular size of a quarter viewed from a distance of 71 yards? A) 0.05° B) 0.81° C) 1.18° Refer to the given map. Assume that the length of each east-west block is block is

D) 0.02°

28)

1 mile and the length of each north-south 8

1 mile. 4

29) 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) 1.25 mi D) 1.50 mi Convert the given angle measure into degrees and decimal fractions of a degree. 30) 171°4'2'' A) 171.127° B) 171.077° C) 171.067°

D) 171.027°

Provide an appropriate response. 31) True or False? In Euclidean geometry, a triangle with two acute angles and one obtuse angle is impossible to construct. A) True B) False Solve the problem. 32) Find the area of the skating rink. Round to the nearest tenth. 36 ft

29)

30)

31)

32)

9 ft

A) 1156.7 ft2

B) 832.7 ft2

C) 902.3 ft2

Provide an appropriate response. 33) What is the approximate grade of a path that rises 1070 feet every mile? A) 20.27% B) 16.21% C) 1.22%

D) 578.3 ft2

D) 0.61%

33)

Use the formula relating angular size, physical size and distance. 34) A planet has an angular diameter of about 1.4° and a distance of about 167 million kilometers. What is its true diameter? A) 31.54 million kilometers B) 27.46 million kilometers C) 8.16 million kilometers D) 4.08 million kilometers Solve the problem. 35) If you magically tripled in size, by what factor has your waist size increased? A) 2 B) 3 C) 9

D) 27

36) If you magically quadrupled in size, by what factor has your weight increased? A) 4 B) 64 C) 3 D) 16 Provide an appropriate response. 37) What is the slope of a 2 in 11 roof? 11 11 = 5.5 = 0.85 A) B) 2 13

2 = 0.15 C) 13

2 = 0.18 D) 11

Find the dimension of the object and state whether or not it is a fractal. 38) In measuring the length 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 4. A) The dimension is 1 and the object is ordinary (non-fractal). B) The dimension is 1.262 and the object is fractal. C) The dimension is 0.792 and the object is fractal. D) The dimension is 2.262 and the object is fractal. Find the perimeter and area of the figure. 39) A square with sides of length 7.6 feet A) P = 115.52 ft, A = 57.76 ft2

B) P = 30.4 ft, A = 57.76 ft2

C) P = 40.4 ft, A = 115.52 ft2

34)

35)

36)

37)

38)

39)

D) P = 15.2 ft, A = 115.52 ft2

Provide an appropriate response. 40) Optimization problems seek what type of solution? A) Largest B) Average

C) Best possible

D) Smallest

Use the formula relating angular size, physical size and distance. 41) A planet has an angular diameter of about 1.5° and a distance of about 67 million kilometers. What is its true diameter? A) 11.8 million kilometers B) 1.75 million kilometers C) 3.51 million kilometers D) 13.56 million kilometers Find the fraction of a circle that encloses the given angle. 42) 24° 1 1 A) B) 50 25

1 C) 15

Convert the given angle measure into degrees and decimal fractions of a degree. 43) 66°18' A) 66.36° B) 66.26° C) 66.30°

1 D) 5

D) 66.31°

40)

41)

42)

43)

Solve the problem. 44) Steve is 11% taller than Andy but proportioned in exactly the same way. If Andy's waist is 34 inches, what is Steve's waist? A) 38 in. B) 39 in. C) 41 in. D) 36 in. Solve. Round your answer to the nearest tenth. 45) Find the area of a circle with a diameter of 21 centimeters. A) 346.2 cm2 B) 1384.7 cm2 C) 65.9 cm2

D) 131.9 cm2

Convert the given angle measure into degrees and decimal fractions of a degree. 46) 38°4'24'' A) 38.083° B) 38.033° C) 38.073°

D) 38.133°

Find the degree measure of the angle created by the given part of a circle. 3 47) circle 4 A) 270°

B) 30°

C) 180°

44)

45)

46)

47) D) 135°

Provide an appropriate response. 48) Determine which surface is steeper between a road with a 25% grade or a road with a pitch of 1 in 4. A) a road with a 25% grade B) a road with a pitch of 1 in 4

48)

Solve the problem. 49) If you magically quadrupled in size, by what factor has your arm length increased? A) 3 B) 64 C) 4 D) 16

49)

Provide an appropriate response. 50) How much does a road with a 1% grade rise for each horizontal foot? A) 0.008 ft B) 0.009 ft C) 0.01 ft

50)

Solve.

D) 0.011 ft

51) Determine the area of a circular enclosure and a square enclosure made with 1116 yards of fence. Use = 3.1416. A) Circular: 99,110 yd2 ; square: 311,364 yd2 B) Circular: 67,562 yd2 ; square: 77,841 yd2 C) Circular: 67,562 yd2 ; square: 311,364 yd2

D) Circular: 99,110 yd2 ; square: 77,841 yd2

51)

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

52) Find the straight-line distance between the bus stop and the library. A) 1.85 mi B) 1.44 mi C) 1.35 mi Solve.

D) 1.62 mi

53) A 12-foot fence on the property line would cast a 20-foot shadow on the shortest day of the year, and the north side of the house is set back 50 feet from the property line. Find the maximum allowed height of the house. A) 42 ft B) 49 ft C) 35 ft D) 30 ft

Find the fraction of a circle that encloses the given angle. 54) 6° 1 1 A) B) 45 40

1 C) 58

1 D) 60

Solve. Round your answer to the nearest tenth. 55) Find the area of a circle with a diameter of 37 feet. A) 116.2 ft2 B) 4298.7 ft2

C) 232.4 ft2

D) 1074.7 ft2

Solve the problem. 56) Suppose you build an architectural model of a new office complex using a scale factor of 52. 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) 104 times as much B) 140,608 times as much C) 2704 times as much D) 52 times as much Find the perimeter and area of the figure. 57) A square with sides of length 4.7 feet A) P = 44.18 ft, A = 22.09 ft2

B) P = 18.8 ft, A = 22.09 ft2 D) P = 28.8 ft, A = 44.18 ft2

C) P = 9.4 ft, A = 44.18 ft2

Find the degree measure of the angle created by the given part of a circle. 1 58) circle 2 A) 210°

B) 120°

C) 180°

52)

53)

54)

55)

56)

57)

58) D) 90°

Solve the problem. 59) A semi-circular transom above a door is to contain a stained glass window. If the stained glass window costs $0.75 per square inch, how much will the window cost?

32 in. | A) $301.44

B) $602.88

C) $2411.52

59)

D) $1205.76

60) Suppose you build an architectural model of a new office complex using a scale factor of 50. How will the height of the actual office complex compare to the height of the scale model? A) 25 times as great B) 100 times as great C) 50 times as great D) 2500 times as great Provide an appropriate response. 61) True or False? Two triangles are similar if they have the same size, but not necessarily the same shape. A) True B) False

60)

61)

Find the area in acres of the property under the given assumptions. Refer to the figure.

62) The stream frontage is 664 feet in length and the property line is 2699 feet in length. A) 29.91 acre B) 19.94 acre C) 39.88 acre D) 9.97 acre

62)

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

63) Find the straight-line distance between the bus stop and the grocery store. A) 1.22 mi B) 1.06 mi C) 1.43 mi

D) 0.96 mi

Find the area of the triangle. 64)

48 cm 36.5 cm

A) 882 cm2

63)

64) 42 cm

B) 766.5 cm2

C) 1008 cm2

D) 1533 cm2

Solve the problem. 65) (i) In general terms, how does the surface-area-to-volume ratio of a rat compare to that of a 65) gorilla? (ii) Which animal must maintain a higher rate of metabolism to replace the heat lost through the skin? A) (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. B) (i) The surface-area-to-volume ratio of a rat is equal to the surface-area-to-volume ratio of a gorilla. (ii) Both animals must maintain the same rate of metabolism. C) (i) The surface-area-to-volume ratio of a rat is lower than the surface-area-to-volume ratio of a gorilla. (ii) The gorilla must maintain a higher rate of metabolism. D) (i) The surface-area-to-volume ratio of a rat is higher than the surface-area-to-volume ratio of a gorilla. (ii) The rat must maintain a higher rate of metabolism. Provide an appropriate response. 66) If a roof with a pitch of 2 in 13 rises in the horizontal direction for 2.62 feet, how high is it vertically? A) 0.35 ft B) 17.03 ft C) 2.62 ft D) 2.27 ft

66)

Solve.

67) A 15-foot fence on the property line would cast a 30-foot shadow on the shortest day of the year, and the north side of the apartment building is set back 80 feet from the property line. Find the maximum allowed height of the apartment building. A) 51.33 ft B) 55 ft C) 40 ft D) 47.67 ft

Find the perimeter and area of the figure. 68) A parallelogram with sides of length of 2.5 feet and 5 feet, and a distance between the 5-foot sides of 0.4 foot. A) P = 4.1 ft, A = 0.3 ft2 B) P = 4.1 ft, A = 0.7 ft2 C) P = 15 ft, A = 4.1 ft2

68)

D) P = 15 ft, A = 2.0 ft2

Solve the problem. 69) City A is at about latitude 54°S and longitude 19°E. City B is at about latitude 15°N and longitude 19°E. About how far apart are the two cities? A) 3900 mi B) 2730 mi C) 4830 mi D) 6900 mi 70) Steve is 15% taller than Andy but proportioned in exactly the same way. If Andy is 235 pounds, how much does Steve weigh? A) 357 lb B) 406 lb C) 459 lb D) 313 lb Refer to the given map. Assume that the length of each east-west block is block is

67)

69)

70)

1 mile and the length of each north-south 8

1 mile. 4

71) Find the straight-line distance between the bus stop and the theater. A) 1.33 mi B) 1.27 mi C) 1.50 mi

D) 1.58 mi

71)

Solve the problem. 72) A driveway is shaped like a parallelogram. How much asphalt (in square yards) is needed to pave the 72) driveway?

4.75 yd

2 yd

A) 9.5 yd2

B) 4.75 yd2

C) 5.15 yd2

D) 19 yd2

Provide an appropriate response. 73) True or False? Slope is the term used when expressing the rise over run of a road as a percentage. A) False B) True

73)

Solve. Round your answer to the nearest tenth. 74) Find the circumference of a circle with a diameter of 22 feet. A) 379.9 ft B) 69.1 ft C) 138.2 ft

74)

D) 34.5 ft

Solve the problem. 75) Steve is 11% taller than Andy but proportioned in exactly the same way. If Andy is 70 inches tall, how tall is Steve? A) 81 in. B) 85 in. C) 74 in. D) 78 in. 76) The water reservoir for a city is shaped like a rectangular prism 238 meters long, 188 meters wide, and 18 meters deep at the end of the day, the reservoir is 60% full. How much water must be added overnight to fill the reservoir? A) 322,157 m 3 B) 442,966 m 3 C) 1,127,549 m 3 D) 1,248,358 m 3 Find the perimeter and area of the figure. 77) A rectangle with a length of 2 yards and a width of 9 yards A) P = 8 yd, A = 36 yd2 B) P = 11 yd, A = 36 yd2 C) P = 14 yd, A = 18 yd2

75)

76)

77)

D) P = 22 yd, A = 18 yd2

Find the dimension of the object and state whether or not it is a fractal. 78) In measuring the volume 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 27. A) The dimension is 3 and the object is a fractal. B) The dimension is 2 and the object is ordinary (non-fractal). C) The dimension is 1 and the object is ordinary (non-fractal). D) The dimension is 3 and the object is ordinary (non-fractal). The two triangles below are similar. Find the missing lengths. 79)

78)

79)

A) x = 11.25; y = 15.75 C) x = 6; y = 12

B) x = 20; y = 28 D) x = 13.5; y = 18

Solve the problem. 80) A competition swimming pool is 25 meters long, 24 meters wide, and 4 meters deep. How much water does the pool hold? A) 14,400 m 3 B) 400 m 3 C) 15,000 m 3 D) 2400 m 3

80)

Find the dimension of the object and state whether or not it is a fractal. 81) In measuring the length 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 5. A) The dimension is 5 and the object is a fractal. 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 area of the triangle. 82)

51 in. 35 in.

A) 805 in.2

82) 46 in.

B) 1058 in.2

C) 1173 in.2

Refer to the given map. Assume that the length of each east-west block is block is

81)

D) 1610 in.2 1 mile and the length of each north-south 8

1 mile. 4

83) Find the shortest possible walking distance (following the streets) between the bus stop and the library. A) 1.50 mi B) 1.25 mi C) 1.75 mi D) 2.0 mi Solve the problem. 84) Find the latitude and longitude of the location on Earth precisely opposite the point located at latitude 43°N, longitude 33°W. A) 43°S, 147°E B) 43°N, 147°W C) 43°N, 33°E D) 43°S, 147°W Convert the given degree measure into degrees, minutes, and seconds of arc. 85) 148.1314° A) 148°7 57 B) 148°45 13 C) 148°7 53

D) 148°7 45

83)

84)

85)

Determine if the pair of triangles are similar. 86)

86)

A) Not similar

B) Similar

Provide an appropriate response. 87) In a right triangle, the square of the length of the hypotenuse is equal to the ________. A) sum of the lengths of the other two sides B) sum of the squares of the other two sides C) area of the triangle D) square root of the sum of the other two side Solve. Round your answer to the nearest tenth. 88) Find the area of a circle with a radius of 11.5 yards. A) 1661.1 yd2 B) 72.2 yd2

C) 415.3 yd2

D) 144.4 yd2

Find the dimension of the object and state whether or not it is a fractal. 89) 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 36. A) The dimension is 6 and the object is a fractal. B) The dimension is 2 and the object is ordinary (non-fractal). C) The dimension is 3 and the object is ordinary (non-fractal). D) The dimension is 1 and the object is ordinary (non-fractal). Solve the problem. 90) Suppose you build an architectural model of a new concert hall using a scale factor of 25. How will the height of the actual concert hall compare to the height of the scale model. A) 13 times as great B) 625 times as great C) 50 times as great D) 25 times as great Provide an appropriate response. 91) True or False? Longitude measures positions north or south position. A) False B) True 92) How many dimensions does a line have? A) 3 B) 2

C) 1

93) The word geometry means __________. A) earth measure C) shape measure

B) mountain shape D) triangle forming

87)

88)

89)

90)

91)

D) 0

92)

93)

Find the perimeter. 94)

23 m

14 m A) 46 m

94)

23 m

B) 161 m

C) 60 m

D) 58 m

Solve the problem. 95) Suppose you build an architectural model of a new concert hall using a scale factor of 19. How will the surface area of the actual concert hall compare to the surface area of the scale model? A) 19 times as great B) 6859 times as great C) 38 times as great D) 361 times as great 96) City A is nearly at the same longitude as City B, but City A's latitude is 58°S while City B's latitude is 16°S. About how far away is City A from City B? A) 5180 mi B) 4200 mi C) 2940 mi D) 7400 mi Provide an appropriate response. 97) True or False? A circle is an example of a solid. A) True

95)

96)

97)

B) False

Find the area in acres of the property under the given assumptions. Refer to the figure.

98) The stream frontage is169 feet in length and the property line is 462 feet in length. A) 0.42 acre B) 1.67 acre C) 0.83 acre D) 1.25 acre Find the fraction of a circle that encloses the given angle. 99) 30° 1 1 A) B) 12 2

1 C) 10

Convert the given degree measure into degrees, minutes, and seconds of arc. 100) 182.13° A) 182°5 13 B) 182°7 13 C) 182°8 48

1 D) 4

D) 182°7 48

98)

99)

100)

Find the dimension of the object and state whether or not it is a fractal. 101) 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 equal to 1 and the object is ordinary (non-fractal). B) The dimension is between 1 and 2 and the object is fractal (Cantor set). C) The dimension is less than 1 and the object is fractal (Cantor set). D) The dimension is greater than 2 and the object is ordinary (non-fractal). Solve the problem. 102) Find the area of the window. Round to the nearest tenth.

101)

102)

11 ft

6 ft

A) 179 ft2

B) 122.5 ft2

C) 70.7 ft2

D) 80.1 ft2

103) Suppose you build an architectural model of a new concert hall using a scale factor of 12. How will the volume of the actual concert hall compare to the volume of the square model? A) 1728 times as great B) 144 times as great C) 36 times as great D) 12 times as great Solve. Round your answer to the nearest tenth. 104) Find the circumference of a circle with a radius of 12.5 yards. A) 490.6 yd B) 78.5 yd C) 15.9 yd Refer to the given map. Assume that the length of each east-west block is block is

D) 39.3 yd

103)

104)

1 mile and the length of each north-south 8

1 mile. 4

105) Find the shortest possible walking distance (following the streets) between the bus stop and the grocery store. A) 1.63 mi B) 1.38 mi C) 1.25 mi D) 1.50 mi

105)

106) Find the shortest possible walking distance (following the streets) between the grocery store and the library. A) 0.75 mi B) 1.25 mi C) 0.50 mi D) 1.0 mi Solve the problem. 107) A heat duct in the college library has a circular cross section with a radius of 4 inches and a length of 25 feet. How much paint (in square feet) is needed to paint the duct? A) 628 ft2 B) 314 ft2 C) 26.2 ft2 D) 52.3 ft2 Find the degree measure of the angle created by the given part of a circle. 1 circle 108) 180 A) 8°

B) 1°

C) 2°

D) 4°

Solve. 110) Suppose you are designing a cardboard box that must have a volume of 42 cubic feet. The cost of the cardboard is $9 per square foot. How much will the material for each box cost? A) $652.47 B) $869.96 C) $326.23 D) $434.98 Convert the given degree measure into degrees, minutes, and seconds of arc. 111) 284.8706° A) 284°52 87 B) 284°13 87 C) 284°53 13

D) 284°52 14

Provide an appropriate response. 112) How many dimensions does a point have? A) 1 B) 2

D) 0

Use the formula relating angular size, physical size and distance. 113) What is the angular size of a quarter viewed from a distance of 17 yards? A) 0.21° B) 0.09° C) 4.94°

D) 3.37°

Find the perimeter. 114) 8 cm 18 cm A) 33 cm

107)

108)

Solve the problem. 109) You build an architectural model of a new office complex using a scale factor of 71. 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) 357,911 times as many B) 71 times as many C) 5041 times as many D) 213 times as many

C) 3

106)

109)

110)

111)

112)

113)

114) 7 cm

B) 34 cm

C) 63 cm

D) 32 cm

Provide an appropriate response. 115) Determine which surface is steeper between a roof with a pitch of 1 in 3 or a roof with a slope of B) a roof with a slope of

A) a roof with a pitch of 1 in 3

Refer to the given map. Assume that the length of each east-west block is block is

3 . 4

115)

3 4

1 mile and the length of each north-south 8

1 mile. 4

116) Find the straight-line distance between the grocery store and the library. A) 0.63 mi B) 0.48 mi C) 0.75 mi

D) 0.56 mi

Find the dimension of the object and state whether or not it is a fractal. 117) 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. 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. Find the perimeter and area of the figure. 118) A square with sides of length 2.6 yards A) P = 20.4 yd, A = 13.52 yd2

B) P = 10.4 yd, A = 6.76 yd2 D) P = 13.52 yd, A = 6.76 yd2

C) P = 5.2 yd, A = 13.52 yd2

Find the dimension of the object and state whether or not it is a fractal. 119) In measuring the volume 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 36. A) The dimension is 3.262 and the object is fractal. B) The dimension is 4.262 and the object is fractal. C) The dimension is 0.307 and the object is fractal. D) The dimension is 33 and the object is ordinary (non-fractal). Convert the given degree measure into degrees, minutes, and seconds of arc. 120) 335.76° A) 335°45 36 B) 335°45 76 C) 335°46 35

D) 335°35 76

116)

117)

118)

119)

120)

Find the perimeter. 121)

22 yd

121)

22 yd

22 yd A) 44 yd

B) 66 yd

C) 242 yd

D) 65 yd

Provide an appropriate response. 122) Who was the first mathematician to summarize many of the ideas of geometry? A) Euclid B) Pascal C) Newton D) Pythagoras

122)

Convert the given angle measure into degrees and decimal fractions of a degree. 123) 241°26'4'' A) 241.434° B) 241.444° C) 241.494°

123)

D) 241.394°

Solve the problem. 124) A toy ball has a diameter of 6.48 inches. What are its volume and surface area? A) 146.2 in.3 ; 142.3 in.2 B) 142.4 in.3 ; 131.8 in.2 C) 145.8 in.3 ; 236.8 in.2

124)

D) 461.4 in.3 ; 427.2 in.2

Convert the given degree measure into degrees, minutes, and seconds of arc. 125) 27.97° A) 27°58 97 B) 27°58 0 C) 27°58 18 Provide an appropriate response. 126) How many dimensions does a cube have? A) 1 B) 2

C) 4

D) 27°58 12

D) 3

Find the area of the triangle. 127) 24 ft 21 ft 38 ft A) 798 ft2

125)

126)

127)

B) 252 ft2

Provide an appropriate response. 128) How many dimensions does a plane have? A) 3 B) 1

C) 399 ft2

D) 220.5 ft2

C) 0

D) 2

128)

Answer Key Testname: CHAPTER 10 1) C 2) A 3) C 4) C 5) D 6) D 7) C 8) A 9) C 10) D 11) C 12) A 13) B 14) D 15) D 16) D 17) B 18) B 19) C 20) B 21) D 22) D 23) B 24) A 25) B 26) A 27) A 28) D 29) D 30) C 31) B 32) C 33) A 34) D 35) B 36) B 37) D 38) B 39) B 40) C 41) B 42) C 43) C 44) A 45) A 46) C 47) A 48) B 49) C 50) C 20

Answer Key Testname: CHAPTER 10 51) D 52) C 53) A 54) D 55) D 56) C 57) B 58) C 59) A 60) C 61) B 62) B 63) B 64) B 65) D 66) C 67) B 68) D 69) C 70) A 71) B 72) A 73) A 74) B 75) D 76) A 77) D 78) D 79) A 80) D 81) B 82) A 83) C 84) A 85) C 86) B 87) B 88) C 89) B 90) D 91) A 92) C 93) A 94) C 95) D 96) C 97) B 98) C 99) A 100) D 21

Answer Key Testname: CHAPTER 10 101) C 102) D 103) A 104) B 105) D 106) A 107) D 108) C 109) A 110) A 111) D 112) D 113) B 114) A 115) B 116) D 117) D 118) B 119) A 120) A 121) B 122) A 123) A 124) B 125) D 126) D 127) C 128) D

Chapter 11 Exam 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) octagon C) dodecahedron

D) hexagon

2) Which of the following is an example of exponential growth? A) the number of notes in a song B) the change in height of a newborn baby C) the better the quality of sound D) the increase in frequencies in scale

3) Which subject was not a part of the quadrivium - the standard curriculum in medieval universities? A) music B) astronomy C) geometry D) history

4) Which of the following is not a type of symmetry? A) translation B) rotation

C) repetition

D) All of these.

5) What types of instruments create music digitally? A) pianos B) synthesizers

C) guitars

D) trombones

6) When making a tiling using only regular hexagons A) the tiles fill all of the space, but 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 do not fill all of the space, there is some overlap of the tiles.

7) Which item is not related to the golden ratio? A) the golden rectangle C) the golden pitch

B) logarithmic spiral D) Fibonacci sequences

8) Which symbol do we use to denote the golden ratio? A) B) C) 9) Which letter is an example of reflective symmetry? A) R B) K

C) Q

D) G

10) The golden ratio divides a line into how many pieces? A) two B) four C) one

D) three

11) In how many ways does the golden ratio occur in a pentagram? A) none B) five C) eight

D) at least ten

12) The golden ratio was used in A) the building of the atomic bomb. C) the value of

B) Greek architecture. D) the discovery of gold.

10)

11)

12)

13) Which of the following is a method for storing digital music? A) compact disk B) floppy disk C) sheet music

D) vinyl records

14) The golden ratio is an example of the use of A) symmetry. B) perspective.

C) proportion.

D) multiplication.

15) One of the most basic qualities of sound is A) analog. B) string.

C) octave.

D) pitch.

13)

14)

15)

16) What question led Greek scholars to formulating the golden ratio? A) What is the best way to divide a line? B) What is the square root of 2? C) How to find ? D) How are pitch and vibration related?

16)

17) 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.

17)

18) Which regular polygon can be used to make a tiling? A) triangle B) parallelogram C) octagon

D) pentagon

19) What fraction is approximately equal to the golden ratio? 8 1 3 A) B) C) 5 2 5

1 D) 5

18)

19)

20) The vanishing point of a picture with perspective is A) the point where you cannot see anything on the picture. B) the point where parallel lines meet. C) the point where two perpendicular lines intersect. D) the point where two curves intersect.

20)

21) Which music principle did the Greeks discover? A) the shorter the string, the lower the pitch C) the shorter the string, the higher the pitch

21)

B) the longer the string, the higher the pitch D) the longer the string, the shorter the pitch

22) 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 prime C) if each number is a multiple of the next D) if their ratio is approximately the same as the golden ratio

22)

23) In mathematics, the word symmetry is used A) to describe an operation that leaves something unchanged. B) when a solution to an equation is unknown. C) to describe an operation that changes appearance. D) to draw an obtuse angle.

23)

24) The golden ratio is a(n) A) rational number. C) irrational number.

24)

B) natural number D) whole number.

25) What is the first principle of perspective? A) All shapes and sizes must remain equal, regardless of their distance from the viewer. B) All parallel lines never intersect, they remain the same distance apart. C) All lines that are parallel in the real scene and perpendicular to the canvas must intersect at the principal vanishing point of the painting. D) None of these.

25)

26) 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 to be the same size as the ones in the foreground. B) appear larger than the ones in the foreground. C) appear smaller than the ones in the foreground. D) None of these.

26)

27) When an object can be shifted, say to the left or right, and still remains the same, this is an example of symmetry.

27)

A) reflection

B) relation

C) translation

D) rotation

28) Which of these is not a type of picture of music? A) color B) digital

C) analog

D) All of the above

29) What are the most pleasing combinations of notes? A) fifths C) fourths

B) first harmonics D) consonant tones

30) Which letter is an example of rotation symmetry? A) R B) T

C) C

29)

30)

D) S

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)

31)

Provide an appropriate response. 32) Draw two cubes, one with perspective and one without.

32)

33) Draw an object with rotation symmetry.

33)

34) Draw an object with translation symmetry.

34)

Find the frequencies of the first 6 notes of the scale that starts at the given note. 35) A# above middle C; this A# has a frequency of 463

28)

35)

Form a tiling from the given figure using translations and reflections. 36)

36)

Provide an appropriate response. 37) Draw an object with reflection symmetry.

37)

Form a tiling from the given figure using translations and reflections. 38)

38)

Find the frequencies of the first 6 notes of the scale that starts at the given note. 39) C# above middle C; this C# has a frequency of 275

39)

Form a tiling from the given figure using translations and reflections. 40)

40)

41)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 42) Starting at middle G with a frequency of 390 cps, find the frequency of the note a fifth above middle G. A) 372 B) 579 C) 606 D) 584 Solve.

42)

43) Given 2.3 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 = 1.62. A) 3.73 in. or 1.42 in. B) 6.03 in. or 0.88 in. C) 3.73 in. or 0.70 in. D) 6.03 in. or 1.14 in.

43)

44) A line is subdivided according to the golden ratio, with the smaller piece having a length of 4 meters. What is the length of the entire line? A) 20.8 m B) 8 m C) 6.4 m D) 10.4 m

44)

Provide an appropriate response. 45) Starting at middle A with a frequency of 437 cps, find the frequency of the note five half-steps above middle A. A) 579 B) 584 C) 419 D) 606

Solve.

45)

46) Starting with a tone having a frequency of 153 cycles per second, find the frequency of the tone that is one octave higher. A) 306 cps B) 612 cps C) 23,409 cps D) 459 cps

46)

47) Given 1.5 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 = 1.62. A) 2.43 in. or 0.93 in. B) 3.93 in. or 1.75 in. C) 3.93 in. or 0.57 in. D) 2.43 in. or 1.08 in.

47)

48) Given 8.0 kilometers 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) 12.96 km or 4.94 km B) 12.96 km or 0.20 km C) 20.96 km or 0.33 km D) 20.96 km or 3.05 km

48)

Provide an appropriate response. 49) Starting with a tone having a frequency of 112 cycles per second, find the frequency of the tone that is four octaves higher. A) 448 cps B) 12,544 cps C) 1792 cps D) 896 cps

49)

50) Starting with middle G, at a frequency of 390 cycles per second, find the frequency of the next octave of G in the circle of fifths. A) 24,960 B) 32,760 C) 49,920 D) 474

50)

51) Starting with a tone having a frequency of 632 cycles per second, find the frequency of the tone that is three octaves higher. A) 1896 cps B) 399,424 cps C) 2528 cps D) 5056 cps

51)

Identify all of the symmetries in the following figure. 52)

52)

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. Provide an appropriate response. 53) Starting with a tone having a frequency of 192 cycles per second, find the frequency of the tone that is three octaves higher. A) 768 cps B) 1536 cps C) 36,864 cps D) 576 cps Identify all of the symmetries in the following figure. 54)

53)

54)

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, 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. C) 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. D) None of these.

Provide an appropriate response. 55) 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) 774 B) 779 C) 761 D) 801

55)

56) Starting with a tone having a frequency of 193 cycles per second, find the frequency of the tone that is two octaves higher. A) 772 cps B) 579 cps C) 37,249 cps D) 1544 cps

56)

57) The circle of fifths is generated by starting at a particular musical note and stepping upward by intervals of a fifth. By what factor does the frequency of a tone increase if it is raised by three fifths? A) 22.35 B) 1.22 C) 3.36 D) 6.05

57)

58) Starting with a tone having a frequency of 687 cycles per second, find the frequency of the tone that is two octaves higher. A) 5496 cps B) 2748 cps C) 471,969 cps D) 1374 cps

58)

Identify all of the symmetries in the following figure. 59)

59)

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 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. C) It has translation symmetry (if imagined to extend in both directions). It also has reflection symmetry (across a horizontal line between the jagged lines). D) None of these.

60)

A) It has rotation symmetry; it can be rotated through 270° and its appearance remains the same. B) It has rotation symmetry with angles of 360° ÷ 5 = 72° and multiples of 72°. C) 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. D) None of these. Provide an appropriate response. 61) Starting at middle E with a frequency of 328 cps, find the frequency of the note 36 half-steps above middle E. A) 2624 B) 2660 C) 2588 D) 2619 Solve.

62) Given 0.11 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) 0.29 cm or 23.82 cm B) 0.29 cm or 0.04 cm C) 0.18 cm or 0.07 cm D) 0.18 cm or 14.73 cm

61)

62)

Answer Key Testname: CHAPTER 11 1) D 2) D 3) D 4) C 5) B 6) C 7) C 8) C 9) B 10) A 11) D 12) B 13) A 14) C 15) D 16) A 17) B 18) A 19) A 20) B 21) C 22) D 23) A 24) C 25) C 26) C 27) C 28) A 29) D 30) D 31)

32) Possible answer:

Answer Key Testname: CHAPTER 11 33) Possible answer:

34) Possible answer:

A# B C C# D D# 35) Note Frequency 463 491 520 551 583 618

36) 37) Possible answer:

Answer Key Testname: CHAPTER 11 38)

C# D D# E F F# 39) Note Frequency 275 292 309 328 347 368 40)

41)

42) D 43) A 44) D 45) B 46) A 47) A 11

Answer Key Testname: CHAPTER 11 48) A 49) C 50) C 51) D 52) C 53) B 54) C 55) B 56) A 57) C 58) B 59) C 60) B 61) A 62) C

Chapter 12 Exam 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 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

2) 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 a Borda count, which of the following fairness criteria is violated? A) Fairness Criterion 3 B) Fairness Criterion 4 C) Fairness Criterion 2 D) None of these

3) 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

4) Which of the following voting methods does not always satisfy Fairness Criterion 3? A) Sequential runoff B) Pairwise comparison C) Borda count D) Plurality

5) Consider the following preference schedule.

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 3 B) Fairness Criterion 2 C) Fairness Criterion 1 D) None of these

6) Which of the following voting methods always satisfies Fairness Criterion 2? A) Pairwise comparison B) Plurality C) Borda count D) Sequential runoff

7) Which of the following voting methods always satisfies Fairness Criterion 2? A) Plurality B) Pairwise comparison C) Sequential runoff D) Borda count

8) Which of the following quantities does not vary from state to state? A) Standard quota B) Number of Representatives C) Standard divisor D) Minimum quota

9) 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 1 C) Fairness Criterion 3 D) None of these

10) Which of the following best describes how the modified quota is found? A) Divide the state's population by the modified divisor B) Trial and error C) Divide the state's population by the standard divisor D) Divide the state's population by the standard quota

10)

11) 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

11)

12) Consider the following preference schedule.

12)

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 4 B) Fairness Criterion 2 C) Fairness Criterion 3 D) All of these

13) Consider the following preference schedule.

13)

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 4 B) Fairness Criterion 3 C) Fairness Criterion 2 D) None of these

14) Consider the following preference schedule. First C Second A Third B 11

B C A 9

B A C 7

14)

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

15) Which of the following voting methods does not always satisfy Fairness Criterion 1? A) Plurality B) Borda count C) Pairwise comparison D) Sequential runoff

15)

16) Which of the following is the geometric mean of x and y? x+y xy A) x2 + y2 B) C) 2 2

16) D)

17) Consider the following preference schedule. First B Second A Third C 9

C B A 8

A C B 7

17)

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

18) Consider the following preference schedule. First B Second A Third C 9

C B A 8

A C B 7

18)

A B C 4

If the winner is selected by a Borda count, which of the following fairness criteria is violated? A) Fairness Criterion 3 B) Fairness Criterion 2 C) Fairness Criterion 4 D) None of these

19) Which of the following best describes the relationship between the standard divisor and the modified divisor? A) The quantities are unrelated. B) The modified divisor is bigger. C) The two quantities are equal. D) The standard divisor is bigger.

19)

20) Which of the following quantities varies from state to state? A) Standard divisor B) Standard quota C) Modified divisor D) Number of Senators

20)

21) Which method of apportionment never leads to a violation of the quota criterion? A) Jefferson's method B) Webster's method C) Hamilton's method D) Hill-Huntington method

21)

22) 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

22)

23) Consider the following preference schedule.

23)

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 3 B) Fairness Criterion 4 C) Fairness Criterion 2 D) None of these

24) Which method of apportionment can lead to an occurrence of the population paradox? A) Jefferson's method B) Hamilton's method C) Hill-Huntington method D) Webster's method

24)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 25) Refer to the figure, which shows the distribution of voters in a state with 14 Democratic voters 25) and 11 Republican, and five voters per district.

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.

26) Refer to the figure, which shows the geographical distribution of voters in a state with 64 voters26) 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.

Draw boundaries expected to result in the election of five Democratic and three Republican representatives.

Decide whether the statement makes sense. Explain your reasoning. 27) 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.

27)

Solve the problem. 28) Refer to the figure, which shows the geographical distribution of voters in a state with 64 voters28) 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.

Draw boundaries expected to result in the election of four Democratic and four Republican representatives.

Provide an appropriate response. 29) What has happened if the Alabama paradox has occurred? Decide whether the statement makes sense. Explain your reasoning. 30) Sunil and his brother live in different states. The population of Sunil's state has been 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.

29)

30)

31) Our state has 10 districts. 22% of the state's Republicans live in my district.

31)

32) In Debra's town, a new voting system will be used which will be guaranteed to always satisfy all four of the fairness criteria.

32)

Provide an appropriate response. 33) What has happened if the new states paradox has occurred? Decide whether the statement makes sense. Explain your reasoning. 34) 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.

33)

34)

35) 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.

35)

36) In the mayoral election, a top-two runoff system was used and all four of the fairness criteria were satisfied.

36)

37) Our state has 6 districts and 180,000 Democrats. I figure that roughly 30,000 Democrats live in each district.

37)

38) Stephanie won by approval voting even though more than half of the voters disapproved of her.

38)

39) 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.

39)

Provide an appropriate response. 40) What has happened if the population paradox has occurred? Solve the problem. 41) Devise a preference schedule with three candidates in which candidate A has a plurality of the votes, but loses by the sequential runoff method. Decide whether the statement makes sense. Explain your reasoning. 42) The defendant was found not guilty even though 11 of the 12 jurors voted for conviction.

40)

41)

42)

Solve the problem. 43) Given that there are 30 voters and 4 candidates, complete the following preference schedule so43) that the Borda count method violates Fairness Criterion 1. First Second Third Fourth

B C C DD D CB A AA B 16 ? ?

Decide whether the statement makes sense. Explain your reasoning. 44) Toni lost the election in a sequential runoff even though she received the majority of the first-place votes. Provide an appropriate response. 45) Explain what is meant by the fractional remainder.

44)

45)

Solve the problem. 46) Given that there are 30 voters and 3 candidates, complete the following preference schedule so46) that the Borda count method violates Fairness Criterion 1. First B C C Second C B A Third A A B 16 ? ?

Decide whether the statement makes sense. Explain your reasoning. 47) 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.

47)

48) Using the Hamilton apportionment method, a state was given 9 seats even though its standard quota was 9.94. Provide an appropriate response. 49) Explain briefly what Fairness Criterion 3 means and give a voting method that satisfies it. Decide whether the statement makes sense. Explain your reasoning. 50) In the U.S. presidential election, the candidate that wins the majority of the popular vote does not always become president.

48)

49)

50)

51) The 64 senators who were in favor of the bill were unable to end the filibuster so the bill did not pass.

51)

52) A school district decides to add new teachers after a new school opens in the district. They 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.

52)

Solve the problem. 53) Devise a preference schedule with three candidates in which the top-two runoff system violates Fairness Criterion 3. Explain.

53)

Decide whether the statement makes sense. Explain your reasoning. 54) Using the Hamilton apportionment method, a state was given 17 seats even though its standard quota was 15.98.

54)

Solve the problem. 55) Construct a preference schedule for 37 voters and 5 candidates where the majority candidate wins 4 pairwise comparison points and another candidate wins 3 pairwise points.

55)

56) Refer to the figure, which shows the distribution of voters in a state with 14 Democratic voters 56) and 11 Republican, and five voters per district.

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.

57) Devise a preference schedule with three candidates in which the Borda count method violates Fairness Criterion 1. Explain.

57)

Decide whether the statement makes sense. Explain your reasoning. 58) 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. 59) Using the Webster apportionment method, a state was given 7 seats even though its standard quota was 8.03. Provide an appropriate response. 60) Explain briefly what Fairness Criterion 2 means and give a voting method that satisfies it. 61) Explain briefly what Fairness Criterion 1 means and give a voting method that may violate this criterion. Decide whether the statement makes sense. Explain your reasoning. 62) Alex won by the Borda method, but Tom won by the method of sequential runoffs.

58)

59)

60) 61)

62)

63) Alison won the majority of the vote but not the plurality.

63)

64) Pierre won fewer votes than Anthony or Carol, yet in a single runoff, Pierre won the election.

64)

65) These days most congressional races are decided by small margins.

65)

66) In the last election 48% of the people voted for a Republican but Republicans won only 32% of our state's seats in the House of Representatives.

66)

67) Sunil and his brother live in different states. The population of Sunil's state has been growing fast while the population of his brother's state has been fairly stable. nevertheless, using the Webster apportionment method last year Sunil's state lost a seat while his brother's state gained a seat.

67)

68) 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.

68)

69) Darren lost in a plurality vote even though he is favored in pairwise races over every other candidate.

69)

Solve the problem. 70) 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.

70)

Decide whether the statement makes sense. Explain your reasoning. 71) Districts which are decided by a small margin are less likely to elect representatives with extreme partisan views than those which are decided by large margins.

71)

Provide an appropriate response. 72) Explain briefly what Fairness Criterion 4 means and give a voting method that may violate this criterion.

72)

Solve the problem. 73) Devise a preference schedule with three candidates in which candidate A has a majority of the votes, but loses by the Borda count method.

73)

Provide an appropriate response. 74) Briefly summarize Arrow's Impossibility Theorem.

74)

Decide whether the statement makes sense. Explain your reasoning. 75) The population of my state is roughly 8,701,000 and it has 15 districts. There are 200,000 people in my district. Provide an appropriate response. 76) Describe briefly how approval voting works.

75)

76)

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? 77) 77) Votes for RepublicanVotes for Democratic Republican Democratic candidates (1000s) candidates (1000s) seats seats Before redistricting 1341 1563 7 12 After redistricting 1356 1754 8 11

Decide whether the statement makes sense. Explain your reasoning. 78) My district is shaped like a horseshoe.

78)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Demographic data for a hypothetical state is given. Use the information to solve the problem. 79) 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) 14 Republicans, 6 Democrats C) 15 Republicans, 5 Democrats D) 6 Republicans, 14 Democrats

79)

Solve the problem. (F), 80) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida 80) San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference table. 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) Florida B) San Antonio

C) Hawaii

D) Alaska

81) 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

81)

S J C 8

Who is the winner of a sequential runoff? A) Clark C) Jones and Clark tie.

B) Jones D) Smith

Answer the question. 82) 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 83) 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

82)

83)

Use Hamilton's method to find the apportionment. 84) West End school district is purchasing 50 new computers to be distributed among the five schools in the 84) 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 b c d e A) School Number of Computers 12 9 9 10 10 a b c d e B) School Number of Computers 11 10 9 10 10 a b c d e C) School Number of Computers 12 9 10 10 9 a b c d e D) School Number of Computers 11 9 10 10 10

Solve the problem. 85) Refer to the following preference schedule. If the plurality method is used to determine the winner, is 85) 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

Use Webster's method to find the apportionment. 86) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned 86) 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) 26 B) 24 C) 23

D) 25

Answer the question about the preference schedule. 87) If candidate E withdrew from the election (and voters for the other candidates were moved up in the 87) 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 14 5 10 4 16 A) A-30, B-5, C-0, D-4 B) A-30, B-5, C-10, D-4 C) A-14, B-5, C-10, D-4 D) A-14, B-5, C-0, D-4 Provide an appropriate response. 88) 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) Jones wins the popular vote and becomes President. B) Atwood wins the popular vote and becomes President. C) Atwood wins the popular vote, but Jones becomes President. D) Jones wins the popular vote, but Atwood becomes President.

88)

Solve the problem. 89) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 89) 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 method of pairwise comparisons? A) S B) R C) P

D) T

Determine whether the specified paradox occurs. 90) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned 90) among the seven states; and the population of each state is shown below for the first and sixth years. 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. 91) The table below shows the population and number of electoral votes for three states. Rank the three states 91) in order of increasing voting power. State Michigan Oregon Florida

Population 10,096,000 3,708,000 18,090,000

Electoral votes 17 7 27

A) Florida, Oregon, Michigan C) Oregon, Michigan, Florida

B) Michigan, Oregon, Florida D) Florida, Michigan, Oregon

Determine which state is more poorly represented. 92) State A with a population of 653,064 and 12 representatives or state B with a population of 532,500 and 15 representatives. A) State B B) State A C) The two have equal representation.

92)

Solve the problem. 93) Consider an election in which the votes were cast as follows. How many of Grafton's votes would Howard 93) need to win the runoff election? Candidate Number of Votes Fuston 374 Grafton 118 Howard 245 A) 129 C) 104

B) 124 D) Howard cannot win the runoff election.

Make the requested preference schedule. 94) 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: 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. A) First AB B C Second B A C B Third C C A A 3 1 2 2 C) 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 First AB B C Second B A C A Third C C A B 3 2 1 2

94)

Solve the problem. the 95) If Jefferson's method is used to apportion 131 legislative seats to six states with the populations given in95) 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) e B) d C) f

D) b

96) If Jefferson's method is used to apportion 250 legislative seats to five states with the populations given in 96) 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) e B) b C) c

D) a

97) A condominium association is holding an election for president of the board of directors. Each member97) 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) Cleary B) Downs

C) Blake

D) Abbott

Use Jefferson's method to find the apportionment. 98) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned 98) 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 Jefferson's method. A) 24 B) 26 C) 23

D) 25

Determine which state is more poorly represented. 99) State A with a population of 256,000 and 10 representatives or state B with a population of 568,000 and 16 representatives. A) State A B) State B C) The two have equal representation.

99)

Solve the problem. 100) Suppose that candidates A and B have moderate political positions, while candidate C is quite conservative. 100) 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) B B) There is a tie. C) C D) A Determine whether the specified paradox occurs. 101) In a small country consisting of 5 provinces, 300 federal judges are apportioned according to the population 101) of each province. The population of each province is shown for the first and sixth years. 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

Use Hamilton's method to find the apportionment. 102) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned 102) 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 Hamilton's method. A) 25 B) 23 C) 26

D) 24

Determine whether the specified paradox occurs. 103) A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned 103) 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 Does the Alabama paradox occur using Hamilton's method if the number of seats is increased from 160 to 161? A) Yes B) No

Use the Hill-Huntington method to find the apportionment. 104) 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: 4; R: 5 B) P: 2; Q: 5; R: 4 C) P: 2; Q: 3; R: 6 D) P: 3; Q: 4; R: 4

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

Who is the winner of a sequential runoff? A) Jones C) Clark

B) Smith D) Jones and Clark tie.

(F), 106) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida 106) 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) yes B) no is 107) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 107) 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

108) 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) D

108)

C B D A 6

B) A

C) C

D) B

109) Consider an election in which the votes were cast as follows. How many of Umprey's votes would Stewart 109) need to win the runoff election? Candidate Number of Votes Stewart 237 Tilley 403 Umprey 181 A) 167 C) 173

B) 174 D) Stewart cannot win the runoff election.

110) Refer to the following preference schedule. If the plurality method is used to determine the winner, is 110) 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

111) Suppose that candidate A is quite conservative, while candidates B and C have moderate political positions. 111) 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) C B) There is a tie. C) A D) B (F), 112) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida 112) 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) Florida & Hawaii (tie) B) Alaska & Florida (tie) C) Alaska & Hawaii (tie) D) Alaska

Determine whether the specified paradox occurs. 113) 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.

113)

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

Solve the problem. (F), 114) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida 114) 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) Alaska B) Hawaii

C) San Antonio

D) Florida

115) 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

115)

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

Determine whether the specified paradox occurs. 116) A small country consists of 7 provinces with the following populations:

116)

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

Use Jefferson's method to find the apportionment. 117) A small country consists of 7 provinces with the following populations:

117)

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) 53 B) 55 C) 56 D) 54

Find the standard quota asked for. Round your answer to two decimal places if necessary. 118) A school district receives a grant to purchase 39 new computers to be apportioned among the 6 schools118) 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) 9.02 B) 9.84

C) 10.26

D) 7.8

Answer the question. 119) 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

119)

Use Hamilton's method to find the apportionment. 120) The table below gives the populations of four districts A, B, C, and D, among which a total of 60 seats are 120) to be apportioned. 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) 29 B) 28 C) 26

D) 27

Solve the problem. 121) Refer to the following preference schedule. First Second Third Fourth

121)

A B B C D D B C D A A C C A C D C B D D A B B A 14 12 14 26 11 13

Find the winner by a runoff of the top two candidates. A) B B) C C) D

D) A

122) 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

122)

C B D A 6

Find the winner by a runoff of the top two candidates. A) B B) C C) A

D) D

is 123) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 123) 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

is 124) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 124) 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

Make the requested preference schedule. 125) Ten voters are asked to rank 4 brands of cell phones: A, B, C, and D. The ten voters turn in the following 125) 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

A B C D

Make a preference schedule for these ballots. A) 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 C) 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 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

Solve the problem. 126) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 126) 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) T B) R C) P

D) S

127) Suppose that candidates A and C have moderate political positions, while candidate B is quite liberal. Voter 127) 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) C B) B C) There is a tie. D) A

Find the standard quota asked for. Round your answer to two decimal places if necessary. 128) The table below gives the populations of four districts A, B, C, and D, among which a total of 60 seats are 128) 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

Solve the problem. 129) 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

129)

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) no B) yes

130) 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

130)

D A B C 3

Find the winner of a sequential runoff. A) A B) B

C) D

D) C

131) In an election, each member ranks the candidates from first to third. The preference schedule below shows 131) the results of the preliminary nonbinding ballots with candidates Robbins (R), Kaplan (K), and Simpson (S). First K Second S Third R 14

S S K R R K 11 13

R K S 12

A second election is then held, which yields the following preference schedule: First K Second S Third R 14

K S R 11

S R K 13

R K S 12

If a run-off of the top two candidates is used to determine the winner, is Fairness Criterion 3 satisfied? A) yes B) no

Answer the question. 132) 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 Solve the problem. 133) 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

132)

133)

C S J 8

Determine the winner using the plurality method. A) Jones C) Clark

B) Smith D) Jones and Smith tie.

Determine whether the specified paradox occurs. 134) A country with two states has 16 seats in the legislature. The population of each state is given by: 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

134)

Solve the problem. is 135) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 135) 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

Determine which state is more poorly represented. 136) State A with a population of 544,220 and 10 representatives or state B with a population of 349,848 and 12 representatives. A) State A B) State B C) The two have equal representation. Find the standard quota asked for. Round your answer to two decimal places if necessary. 137) 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.

136)

137)

State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the standard quota for state C. A) 37.45 B) 33.42

C) 30.49

D) 36.79

Solve the problem. 138) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 138) 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) S B) P

C) T

D) R

Use the Hill-Huntington method to find the apportionment. 139) 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: 3; Y: 3; Z: 3 B) X: 2; Y: 4; Z: 3 C) X: 4; Y: 2; Z: 3 D) X: 3; Y: 4; Z: 2

139)

Determine which state is more poorly represented. 140) State A with a population of 417,204 and 12 representatives or state B with a population of 556,272 and 16 representatives. A) State A B) State B C) The two have equal representation. Solve the problem. 141) 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

140)

141)

D A B C 3

Find the winner by a Borda count. A) B B) C

C) A

D) D

142) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 142) 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

R P S T 6

Which choice wins using the Borda count method? A) R B) T

C) S

D) P

143) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 143) 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 30 60 36 34 20

S T R P 4

Which choice wins using the method of pairwise comparisons? A) P B) S C) T

D) R

Answer the question. 144) 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

144)

Use Hamilton's method to find the apportionment. in 145) A country has five states with populations as given in the table below and needs to apportion 250 seats145) 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 b c d e A) State Number of Representatives 28 35 142 23 22 a b c d e B) State Number of Representatives 29 35 141 23 22 a b c d e C) State Number of Representatives 29 35 141 23 21 a b c d e D) State Number of Representatives 28 35 143 23 21

Solve the problem. 146) 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

146)

C S J 8

Determine the winner using the Borda count method. A) Clark B) Jones and Smith tie. C) Smith D) Jones is 147) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 147) 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

Determine whether the specified paradox occurs. 148) A country with two states has 16 seats in the legislature. The population of each state (in thousands) is 148) 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

Find the standard quota asked for. Round your answer to two decimal places if necessary. 149) The faculty senate of a university has 45 senators to be apportioned among its four colleges based on 149) 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. College L S B E Number of Faculty 279 355 312 423 Find the standard quota for the College of Sciences. A) 13.06 B) 14.34

C) 11.67

D) 16.32

Determine whether the specified paradox occurs. 150) A country with two states has 75 seats in the legislature. The population of each state (in thousands) is 150) 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

Provide an appropriate response. 151) 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) Kemper wins the popular vote, but Gonzales becomes President. B) Gonzales wins the popular vote, but Kemper becomes President. C) Kemper wins the popular vote and becomes President. D) Gonzales wins the popular vote and becomes President.

151)

Solve the problem. C 152) Refer to the given preference schedule. If the Borda count method is used to determine the winner and 152) 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

Use the Hill-Huntington method to find the apportionment. 153) 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: 3; B: 2; C: 4 B) A: 4; B: 3; C: 2 C) A: 2; B: 3; C: 4 D) A: 3; B: 3; C: 3

153)

Use Jefferson's method to find the apportionment. 154) West End school district is purchasing 50 new computers to be distributed among the five schools in the 154) 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 b c d e A) School Number of Computers 11 10 9 10 10 a b c d e B) School Number of Computers 12 9 10 10 9 a b c d e C) School Number of Computers 12 9 9 10 10 a b c d e D) School Number of Computers 11 9 10 10 10

Answer the question. 155) 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

155)

Provide an appropriate response. 156) 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) Jones wins the popular vote, but Atwood becomes President. C) Atwood wins the popular vote, but Jones becomes President. D) Jones wins the popular vote and becomes President.

156)

Solve the problem. 157) A condominium association is holding an election for president of the board of directors. Each member157) 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) Downs B) Abbott C) Blake

D) Cleary

Answer the question. 158) 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 Solve the problem. 159) 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

158)

159)

B A D C 3

Find the winner by a runoff of the top two candidates. A) A B) B C) C

D) D

Provide an appropriate response. 160) 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) Gonzales wins the popular vote and becomes President. B) Gonzales wins the popular vote, but Kemper becomes President. C) Kemper wins the popular vote, but Gonzales becomes President. D) Kemper wins the popular vote and becomes President.

160)

Solve the problem. 161) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 161) 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 Borda count method? A) S B) T

C) P

D) R

Provide an appropriate response. 162) 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, but Roberts becomes President. B) Roberts wins the popular vote and becomes President. C) Simpson wins the popular vote and becomes President. D) Roberts wins the popular vote, but Simpson becomes President.

162)

Use Webster's method to find the apportionment. 163) West End school district is purchasing 50 new computers to be distributed among the five schools in the 163) 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. School a b c d e Population 210 165 160 175 190

a b c d e A) School Number of Computers 11 10 9 10 10 a b c d e B) School Number of Computers 11 9 10 10 10 a b c d e C) School Number of Computers 12 9 10 10 9 a b c d e D) School Number of Computers 12 9 9 10 10

Solve the problem. 164) Consider an election in which the votes were cast as follows. How many of Quincy's votes would Plaxton 164) need to win the runoff election? Candidate Number of Votes Plaxton 298 Quincy 304 Rasputin 325 A) 166 B) 152

C) 28

D) 139

Use Jefferson's method to find the apportionment. 165) The table below gives the populations of four districts A, B, C, and D, among which a total of 20 seats are 165) 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

Determine whether the specified paradox occurs. 166) A city has 204 police officers to be apportioned among 4 precincts based on the population of each precinct. 166) The populations are given in the following table. 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 Jefferson's method to find the apportionment. in 167) A country has five states with populations as given in the table below and needs to apportion 250 seats167) the legislature. Use Jefferson'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 b c d e A) State Number of Representatives 28 35 143 23 21 a b c d e B) State Number of Representatives 28 35 142 23 22 a b c d e C) State Number of Representatives 29 35 141 23 21 a b c d e D) State Number of Representatives 29 35 141 23 22

Use Webster's method to find the apportionment. 168) A small city has 50 police officers to be apportioned among 8 precincts based on the population of each168) precinct. The populations are given in the following table. 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) 6 B) 7 C) 5

D) 4

Provide an appropriate response. 169) 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. B) Furuya wins the popular vote and becomes President. C) Smith wins the popular vote and becomes President. D) Smith wins the popular vote, but Furuya becomes President.

169)

Find the standard quota asked for. Round your answer to two decimal places if necessary. 170) A university has 27 scholarships to be apportioned among the engineering students based on the 170) 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. Department M E C Enrollment 233 297 153 Find the standard quota for the Mechanical Engineering Department. A) 8.85 B) 9.21 C) 8.47

D) 7.89

Solve the problem. 171) Refer to the given preference schedule. If the plurality method is used to determine the winner and D 171) drops out, is Fairness Criterion 4 satisfied? First Second Third Fourth

A) Yes

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

B) No

Find the standard quota asked for. Round your answer to two decimal places if necessary. 172) A small city has 46 police officers to be apportioned among 8 precincts based on the population of each172) precinct. The populations are given in the following table. 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) 4.69 B) 6.91

C) 5.59

D) 5.27

Solve the problem. 173) If the population of the United States increased to 380 million and the number of representatives remained at 435, how many Americans, on average, would each representative serve? A) 873,563 people per representative B) 165,300 people per representative C) 1,144,737 people per representative D) 862,569 people per representative

173)

174) Refer to the given preference schedule. If candidate C drops out, does the method of pairwise comparisons 174) 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

175) Consider an election in which the votes were cast as follows. What percentage of Simpson's votes would 175) Gomez need to win the runoff election? Candidate Percentage of Vote Hughes 29% Simpson 47% Gomez 24% A) 55.3% B) 57.4%

C) 26%

D) 30%

Use the Hill-Huntington method to find the apportionment. 176) 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 X; Twelfth seat: State Y B) Eleventh seat: State Y; Twelfth seat: State Z C) Eleventh seat: State X; Twelfth seat: State Z D) Eleventh seat: State Y; Twelfth seat: State Y

176)

Make the requested preference schedule. 177) 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

C A D B

Make a preference schedule for these ballots. A) First B B CC Second A C A D Third C A D A Fourth D D B B 1 2 3 2 C) First B B CC Second A C A D Third C A D A Fourth D D B B 1 2 2 3

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 B D Third C A D A Fourth D D A B 1 2 2 3

Solve the problem. 178) 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

177)

178)

S C J 8

Who is the winner of a sequential runoff? A) Jones and Clark tie. C) Clark

B) Jones D) Smith

Use Hamilton's method to find the apportionment. 179) 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. Find the apportionment for province G using Hamilton's method. A) 54 B) 56 C) 55 D) 53

179)

Solve the problem. 180) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 180) 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) P

D) S

in 181) If Jefferson's method is used to apportion 200 legislative seats to four states with the populations given 181) 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) a B) b C) d

D) e

is 182) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 182) 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

B) No

183) 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

183)

D A B C 3

B) B

C) C

Determine whether any of the listed candidates has a majority. 184) Four candidates running for mayor receive votes as follows: Ito: 43,191, Johnson: 19,196, Kennedy: 9598, Lieberman: 14,397 A) Yes B) No

D) D

184)

Make the requested preference schedule. 185) Ten voters are asked to rank 3 brands of shoes: A, B, and C. The ten voters turn in the following ballots185) 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. A) First B B C Second A C A Third C A B 2 4 4 C) 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 First B B CC Second A C B A Third C A A B 2 3 4 1

Solve the problem. 186) Refer to the following preference schedule. First A Second B Third C 15

A C B 14

B A C 5

B C A 14

C A B 12

186)

C B A 9

Find the winner by a runoff of the top two candidates. A) No clear winner B) B C) A D) C

187) Refer to the given preference schedule. If the plurality method is used to determine the winner and C 187) 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

188) 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

188)

S C J 8

Determine the winner using the method of pairwise comparisons. A) Clark B) Jones C) Smith D) Jones & Clark (tie)

Use Jefferson's method to find the apportionment. 189) The table below gives the populations of four districts A, B, C, and D, among which a total of 60 seats are 189) to be apportioned. 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) 27 C) 26

D) 28

Solve the problem. 190) Refer to the given preference schedule. If candidate D drops out, does the Borda count method satisfy 190) Fairness Criterion 4? First Second Third Fourth

A) Yes

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

B) No

191) 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

S C J 8

Determine the winner using the Borda count method. A) Clark B) Jones C) Jones and Smith tie. D) Smith

191)

192) 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

192)

C B D A 6

Find the winner by the method of pairwise comparisons. A) C B) D C) A

D) B

193) If the population of the United States increased to 430 million and the number of representatives were set at the constitutional limit of one representative for every 30,000 people, how many representatives would there be in Congress? A) 6977 representatives B) 14,333 representatives C) 1290 representatives D) 1433 representatives Provide an appropriate response. 194) 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. B) Simpson wins the popular vote, but Roberts becomes President. C) Roberts wins the popular vote, but Simpson becomes President. D) Simpson wins the popular vote and becomes President. Solve the problem. 195) 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

A B C D 7

193)

194)

195)

A B D C 6

Find the winner by a runoff of the top two candidates. A) D B) B C) A

Answer the question about the preference schedule. 196) 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 14 7 10 3 18 A) 10 B) 42 C) 45

D) C

196)

D) 28

Solve the problem. 197) Suppose that candidates A and B have moderate political positions, while candidate C is quite liberal. Voter 197) 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) B C) A D) There is a tie. in 198) If Jefferson's method is used to apportion 132 legislative seats to four states with the populations given 198) the table, then a violation of the quota criterion occurs. State Population

a b c d 17,180 7,500 49,400 5,820

The apportionment for which state violates the quota criterion? A) b B) d C) a

D) c

199) 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

199)

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

200) Refer to the following preference schedule. If the winner is decided by sequential runoffs, is 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

200)

201) The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year's 201) 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) S B) P

C) R

D) T

Answer the question. 202) 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. 203) 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

202)

203)

C B D A 6

Find the winner by a Borda count. A) C B) B

C) D

D) A

204) Jackson Associates is planning a group vacation to one of the following locations: Alaska (A), Florida (F), 204) 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 Borda count method? A) Hawaii B) Florida

C) Alaska

D) San Antonio

205) 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

205)

S J C 8

Determine the winner using the Borda count method. A) Clark B) Smith C) Jones D) Jones and Smith tie.

206) 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

A B C D 7

206)

A B D C 6

Find the winner by the method of pairwise comparisons. A) B B) D C) A

D) C

207) An election is held in which each member ranks the candidates from first to third. The preference schedule 207) below shows the results of the preliminary nonbinding ballots with candidates A, B, and C. First B A Second A C Third C B 20 23

C B A 19

A second election is then held, which yields the following preference schedule: First B A Second A B Third C C 20 23

C B A 19

If a run-off of the top two candidates is used to determine the winner, is Fairness Criterion 3 satisfied? A) yes B) no

208) 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

208)

B A D C 3

Find the winner by the method of pairwise comparisons. A) D B) C C) A

D) B

Provide an appropriate response. 209) 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) Smith wins the popular vote, but Furuya becomes President. B) Furuya wins the popular vote, but Smith becomes President. C) Smith wins the popular vote and becomes President. D) Furuya wins the popular vote and becomes President. Solve the problem. 210) 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

209)

210)

D B A C 3

Find the winner of a sequential runoff. A) B B) A

C) D

D) C

Find the standard quota asked for. Round your answer to two decimal places if necessary. 211) A small country consists of 7 provinces with populations as indicated in the table. 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) 84.68 B) 72.68 C) 56.93 D) 66.61

211)

Use Webster's method to find the apportionment. in 212) A country has five states with populations as given in the table below and needs to apportion 250 seats212) the legislature. Use Webster'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 b c d e A) State Number of Representatives 29 35 141 23 21 a b c d e B) State Number of Representatives 28 35 143 23 21 a b c d e C) State Number of Representatives 29 35 141 23 22 a b c d e D) State Number of Representatives 28 35 142 23 22

Determine whether any of the listed candidates has a majority. 213) Four candidates running for congress receive votes as follows: Alberts: 44,935, Brown: 12,255, Cassimatis: 32,680, D'Amico: 28,595 A) Yes B) No Use Webster's method to find the apportionment. 214) A small country consists of 7 provinces with the following populations:

213)

214)

Solve the problem. 215) Imagine that a small company has four shareholders who hold 28%, 25%, 24%, and 23% 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% hold any effective power in voting? A) no B) yes

215)

is 216) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 216) 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 any of the listed candidates has a majority. 217) Four candidates running for senate receive votes as follows: Edwards: 100,206, Fong: 38,969, Goodman: 16,701, Haddad: 27,835 A) Yes B) No

217)

Solve the problem. is 218) Refer to the following preference schedule. If the Borda count method is used to determine the winner, 218) 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

219) Refer to the following preference schedule. First Second Third Fourth Fifth

219)

C D E E C B D B A B E C A A D 22 16 25

Find the winner by a runoff of the top two candidates. A) E B) A C) C

D) D

220) 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

220)

C S J 8

Determine the winner using the method of pairwise comparisons. A) Smith B) Jones & Clark (tie) C) Clark D) Jones

221) 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

221)

C B D A 6

Find the winner of a sequential runoff. A) D B) B

C) C

D) A

222) 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

222)

D A B C 3

Find the winner by the method of pairwise comparisons. A) A B) B C) D

D) C

Demographic data for a hypothetical state is given. Use the information to solve the problem. 223) A state has 20 representatives and a population of 16 million; party affiliations are 70% Republican and 30% 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) 20, 10 B) 19, 9 C) 19, 8 D) 20, 9 Solve the problem. 224) 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

223)

224)

D A B C 3

Find the winner by a runoff of the top two candidates. A) C B) A C) B

D) D

225) Consider an election in which the votes were cast as follows. How many of Burnaby's votes would Costello need to win the runoff election? Candidate Number of Votes Abbott 319 Burnaby 126 Costello 194 A) 125 B) 126

C) 63

D) 68

225)

(F), 226) Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida 226) 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 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) yes B) no

Answer Key Testname: CHAPTER 12 1) A 2) D 3) D 4) A 5) D 6) A 7) B 8) C 9) D 10) A 11) A 12) A 13) D 14) D 15) B 16) D 17) B 18) C 19) D 20) B 21) C 22) A 23) D 24) B 25) Answers may vary. One possible answer is:

26) Answers may vary. One possible answer is:

27) 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. 48

Answer Key Testname: CHAPTER 12 28) Answers may vary. One possible answer is:

29) The total number of available seats increased, yet one or more states lost a seat as a result. 30) 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. 31) 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. 32) 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. 33) The addition of seats for a new state changed the apportionment for existing states. 34) 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. 35) 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. 36) 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. 37) 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. 38) 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. 39) 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. 40) A slow-growing state gained a seat at the expense of a faster-growing state. 41) Possible answer: First A B C Second B C B Third C A A 10 5 4 42) Yes, this is possible. Some states require a unanimous vote in order for a defendant to be found guilty.

Answer Key Testname: CHAPTER 12 43) Answers will vary. Possible solution: First Second Third Fourth

B C C DD D CB A AA B 16 9 5 44) 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. 45) The fractional remainder is the fraction that remains in the standard quota after subtracting the minimum quota. 46) Answers will vary. Possible solution: First B C C Second C B A Third A A B 16 8 6 47) No, the statement does not make sense. It has been proved by mathematicians that such a system is impossible. 48) 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. 49) 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. 50) 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. 51) 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. 52) 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) 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 54) 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. 55) Answers will vary. Possible solution: First A B Second B D Third C E Fourth D C Fifth E A 19 18

Answer Key Testname: CHAPTER 12 56) Answers may vary. One possible answer is:

57) 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 58) 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. 59) 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. 60) If a candidate is favored over every other candidate in pairwise races, that candidate should be declared a winner; pairwise comparison 61) If a candidate receives a majority of the first-place votes, that candidate should be the winner; point system (Borda count) 62) Yes, this is possible. The different methods do not always produce the same winner. 63) 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). 64) 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. 65) 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. 66) 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. 67) 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 Webster apportionment method is not susceptible to this paradox. 68) 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. 69) 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. 70) 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

Answer Key Testname: CHAPTER 12 71) 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. 72) 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. 73) Possible answer: First A B C Second B C B Third C A A 10 5 4 74) It is impossible to create a voting system that always satisfies all four fairness criteria. 75) No, the statement does not make sense. All districts within a particular state must have very nearly equal populations. 76) Voters state whether or not they approve of each candidate, and the candidate with the most approval votes wins. 77) Votes: Before redistricting: Republican 46%, Democrat 54%; After redistricting: Republican 44%, Democrat 56%; Seats: Before redistricting: Republican 37%, Democrat 63%; After redistricting: Republican 42%, Democrat 58%; The distribution of House seats better reflects the distribution of votes after redistricting. 78) 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. 79) B 80) D 81) B 82) B 83) A 84) A 85) B 86) B 87) B 88) D 89) D 90) B 91) D 92) B 93) D 94) A 95) C 96) C 97) A 98) A 99) B 100) A 101) B 102) D 103) B

Answer Key Testname: CHAPTER 12 104) A 105) B 106) B 107) A 108) B 109) B 110) B 111) A 112) C 113) A 114) A 115) B 116) B 117) B 118) D 119) A 120) B 121) B 122) B 123) B 124) A 125) B 126) C 127) A 128) B 129) B 130) A 131) A 132) A 133) A 134) B 135) A 136) A 137) C 138) C 139) B 140) C 141) A 142) C 143) A 144) B 145) A 146) C 147) B 148) A 149) C 150) A 151) B 152) A 153) D 53

Answer Key Testname: CHAPTER 12 154) C 155) B 156) D 157) B 158) B 159) D 160) A 161) D 162) C 163) D 164) A 165) C 166) A 167) A 168) C 169) D 170) B 171) B 172) C 173) A 174) A 175) A 176) A 177) C 178) C 179) A 180) D 181) A 182) B 183) C 184) B 185) C 186) D 187) B 188) A 189) A 190) A 191) A 192) A 193) B 194) C 195) C 196) B 197) C 198) D 199) B 200) A 201) B 202) B 203) A 54

Answer Key Testname: CHAPTER 12 204) B 205) C 206) C 207) A 208) A 209) D 210) A 211) B 212) D 213) B 214) B 215) B 216) B 217) A 218) B 219) C 220) A 221) C 222) B 223) D 224) C 225) B 226) A