Chap005 by Hmad Alkhaldi

18.

Which of the following can be represented by a continuous random variable?

The time of a flight between Chicago and New York

B. The number of defective light bulbs in a sample of 5

C. The number of arrivals to a drive-thru bank window in a four-hou

D. The score of a randomly selected student on a five-question mul A discrete random variable assumes a countable number of possible values, whereas a continuous random variable is characterized by uncountable values. The time of a flight between Chicago and New York is the only one of the four random variables without a countable number of possible values; this time may take any value from a time interval.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-01 Distinguish between discrete and continuous random variables. Topic: Random Variables and Discrete Probability Distributions

19.

Which of the following can be represented by a continuous random variable?

The average temperature in Tampa, Florida, during a month July

B. The number of typos found on a randomly selected page of this

C. The number of students who will get financial assistance in a gro ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

selected students

D. The number of customers who visit a department store between on Mondays A discrete random variable assumes a countable number of possible values, whereas a continuous random variable is characterized by uncountable values. The average temperature is the only one of the four random variables without a countable number of possible values. (Measured temperatures are typically rounded to a single degree, but the measurements actually represent a continuous scale.)

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-01 Distinguish between discrete and continuous random variables. Topic: Random Variables and Discrete Probability Distributions

20.

What is a characteristic of the mass function of a discrete random variable X?

The sum of probabilities over all possible values x is 1.

B. For every possible value x, the probability C. Describes all possible values x with the associated probabilities D. All of the above. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-02 Describe the probability distribution of a discrete random variable. Topic: Random Variables and Discrete Probability Distributions

21.

What are the two key properties of a discrete ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

probability distribution?

and

The two key properties are

and

AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-02 Describe the probability distribution of a discrete random variable. Topic: Random Variables and Discrete Probability Distributions

22.

Exhibit 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is 0?

A. 0.1 0 B. 0.35 C. 0.55 D. 0.65 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Distractors: Wrong answers include the probability that X is -10, more than 0, and is at least 0.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-02 Describe the probability distribution of a discrete random variable. Topic: Random Variables and Discrete Probability Distributions

23.

Exhibit 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is greater than 0?

A. 0.1 0 B. 0.35 C. 0.55 D. 0.65

Distractors: Wrong answers include the probability that X is -10, 0, and at least 0.

ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

24.

Exhibit 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is negative?

A. 0.0 0 B. 0.10 C. 0.15 D. 0.35

Distractors: Wrong answers include the probability that X is 0 and X is 10.

25.

Exhibit 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is less than 5?

A. 0.1 0 B. 0.15 C. 0.35 D. 0.45

Distractors: Wrong answers include the probability that X is -10, 0, or 10.

26.

Exhibit 5-2. Consider the following cumulative distribution function for the discrete random variable X.

Refer to Exhibit 5-2. What is the probability that X is less than or equal to 2?

A. 0.1 4 B. 0.30 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

C. 0.44 D. 0.56

Distractors: Wrong answers include , and

27.

Exhibit 5-2. Consider the following cumulative distribution function for the discrete random variable X.

Refer to Exhibit 5-2. What is the probability that X equals 2?

A. 0.1 4 B. 0.30 C. 0.44 D. 0.56

Distractors: Wrong answers include , and

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Describe the probability distribution of a discrete random variable. Topic: Random Variables and Discrete Probability Distributions

28.

Exhibit 5-2. Consider the following cumulative distribution function for the discrete random variable X.

Refer to Exhibit 5-2. What is the probability that X is greater than 2?

A. 0.1 4 B. 0.30 C. 0.44 D. 0.56

Distractors: Wrong answers include , and

29.

We can think of the expected value of a random variable X as ________________.

The long-run averag

values generated ov repetitions

B. The long-run average of the random variable values generated o repetitions

C. The long-run average of the random variable values generated o independent repetitions

D. The long-run average of the random variable values generated o independent repetitions AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-03 Calculate and interpret summary measures for a discrete random variable. Topic: Expected Value, Variance, and Standard Deviation

30.

The expected value of a random variable X can be referred to or denoted as _____.

A. µ B. E(X

) C. The population mean D. All of the above The expected value of a random variable X is denoted by E(X), and can be referred to as the population mean for which the typical notation is μ.

AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-03 Calculate and interpret summary measures for a discrete random variable. Topic: Expected Value, Variance, and Standard Deviation

31.

Exhibit 5-3. Consider the following probability distribution. © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Refer to Exhibit 5-3. The expected value is ___.

A. 0.9 B. 1.5 C. 1.9 D. 2.5 = 0(0.1) + 1(0.2) + 2(0.4) + 3(0.3) = 1.9

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate and interpret summary measures for a discrete random variable. Topic: Expected Value, Variance, and Standard Deviation

32.

Exhibit 5-3. Consider the following probability distribution.

Refer to Exhibit 5-3. The variance is ____.

A. 0.8 9 B. 0.94 C. 1.65 D. 1.90 = 0(0.1) + 1(0.2) + 2(0.4) + 3(0.3) = 1.9 = (0 2

1.9) (0.1) + (1 - 1.9) (0.2) + (2 - 1.9) (0.4) + (3 2

1.9) (0.3) = 0.361 + 0.162 + 0.004 + 0.363 = 0.890 Distractors: Wrong answers include the mean and the standard deviation.

33.

Exhibit 5-3. Consider the following probability distribution.

Refer to Exhibit 5-3. The standard deviation is _________.

A. 0.8 9 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

B. 0.94 C. 1.65 D. 1.90 = 0(0.1) + 1(0.2) + 2(0.4) + 3(0.3) = 1.9 = (0 2

1.9) (0.1) + (1 - 1.9) (0.2) + (2 - 1.9) (0.4) + (3 2

1.9) (0.3) = 0.361 + 0.162 + 0.004 + 0.363 = 0.890

Distractors: Wrong answers include the mean and the variance.

34.

Exhibit 5-4. Consider the following probability distribution.

Refer to Exhibit 5-4. The expected value is _____.

A. 1.0 B. -0.1 C. 0.1 D. 1.0 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

= -2(0.2) + -1(0.1) + 0(0.3) + 1(0.4) = -0.1

35.

Exhibit 5-4. Consider the following probability distribution.

Refer to Exhibit 5-4. The variance is _____.

A. 1.1 4 B. 1.29 C. 1.65 D. 1.94 = -2(0.2) + -1(0.1) + 0(0.3) + 1(0.4) = -0.1 = (-2 2

+ 0.1) (0.2) + (-1 + 0.1) (0.1) + (0 + 0.1) (0.3) + (1 2

+ 0.1) (0.4) = 0.722 + 0.081 + 0.003 + 0.484 = 1.290 Distractors: Wrong answers include the standard ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

deviation.

36.

Exhibit 5-4. Consider the following probability distribution.

Refer to Exhibit 5-4. The standard deviation is ____.

A. 1.1 4 B. 1.29 C. 1.65 D. 1.94 = -2(0.2) + -1(0.1) + 0(0.3) + 1(0.4) = -0.1 = (-2 2

+ 0.1) (0.2) + (-1 + 0.1) (0.1) + (0 + 0.1) (0.3) + (1 2

+ 0.1) (0.4) = 0.722 + 0.081 + 0.003 + 0.484 = 1.290

Distractors: Wrong answers include the variance.

37.

An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year.

The expected value and the variance of this distribution are:

Optio nA

B. Option B C. Option C D. Option D

Distractors: Wrong answers include the unweighted average and the standard deviation.

38.

An analyst believes that a stock's return depends on the state of the economy, for which she has estimated the following probabilities:

According to the analyst's estimates, the expected return of the stock is ____.

A. 7.8 % B. 11.4% C. 11.7% D. 13.0% ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

= 0.15(0.1) + 0.13(0.6) + 0.07(0.3) = 0.114

39.

An analyst estimates that the year-end price of a stock has the following probabilities:

The stock's expected price at the end of the year is _______.

$87. 50

B. $88.50 C. $89.00 D. $90.00

= 80(0.1) + 85(0.3) + 90(0.4) + 95(0.02) = 88.50

40.

Exhibit 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the probability that the realtor will sell at least one house during a month?

A. 0.2 0 B. 0.40 C. 0.60 D. 0.80

Distractors: Wrong answers include , and

41.

Exhibit 5-5. The number of homes sold by a ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the probability that the realtor sells no more than one house during a month?

A. 0.2 0 B. 0.40 C. 0.60 D. 0.80

Distractors: Wrong answers include , and

42.

Exhibit 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the expected number of homes sold by the realtor during a month?

A. 1 B. 1.2 C. 1.5 D. 2 = 0(0.2) + 1(0.4) + 2(0.4) = 1. Distractors: Wrong answers include the unweighted mean

43.

Exhibit 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the standard deviation of the number of homes sold by the realtor during a month?

A. 0.5 6 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

B. 0.75 C. 1 D. 1.2

Distractors: Wrong answers include the variance, expected value, and unweighted mean.

44.

Exhibit 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the probability that the salesman will sell one car during a week?

A. 0.2 0 B. 0.40 C. 0.60 D. 0.80

Distractors: Wrong answers include , and

45.

Exhibit 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the probability that the salesman sells no more than one car during a week?

A. 0.2 0 B. 0.40 C. 0.60 D. 0.80

Distractors: Wrong answers include , and

AACSB: Analytic Blooms: Apply

Difficulty: 1 Easy Learning Objective: 05-02 Describe the probability distribution of a discrete random variable. Topic: Random Variables and Discrete Probability Distributions

46.

Exhibit 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the expected number of cars sold by the salesman during a week?

A. 0 B. 0.8 C. 1 D. 1.5 = 0(0.4) + 1(0.4) + 2(0.2) = 0. Distractors: Wrong answers include unweighted mean.

47.

Exhibit 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the standard deviation of the number of cars sold by the salesman during a week?

A. 0.5 6 B. 0.75 C. 0.80 D. 1

Distractors: Wrong answers include the variance, expected value, and unweighted mean.

48.

A consumer who is risk averse is best characterized as _______________.

A consumer who may ac

prospect even if the expe negative

B. A consumer who demands a positive expected gain as compens ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

C. A consumer who completely ignores risk and makes his/her dec expected values D. None of the above In general, consumers are risk averse and expect a reward for taking risk. A risk averse consumer demands a positive expected gain as compensation for taking risk. Distractors: Wrong answer choices include descriptions of risk loving and risk neutral consumers.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Differentiate among risk neutral; risk averse; and risk loving consumers. Topic: Expected Value, Variance, and Standard Deviation

49.

A consumer who is risk neutral is best characterized as ______________.

A consumer who may ac

prospect even if the expe negative

B. A consumer who demands a positive expected gain as compens

C. A consumer who completely ignores risk and makes his/her dec expected values D. None of the above In general, consumers are risk averse and expect a reward for taking risk. A risk neutral consumer, on the other hand, completely ignores risk and makes his/her decisions solely on the basis of expected values. ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Distractors: Wrong answer choices include descriptions of risk averse and risk neutral consumers.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-04 Differentiate among risk neutral; risk averse; and risk loving consumers. Topic: Expected Value, Variance, and Standard Deviation

50.

How would you characterize a consumer who is risk loving?

A consumer who may ac

prospect even if the exp negative.

B. A consumer who demands a positive expected gain as compens

C. A consumer who completely ignores risk and makes his/her dec of expected values. D. None of the above. In general, consumers are risk averse and expect a reward for taking risk. A risk loving consumer may accept a risky prospect even if the expected gain is negative. Distractors: Wrong answer choices include descriptions of risk averse and risk neutral consumers.

51.

Exhibit 5-7. An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-7. The correlation coefficient between the returns on Stocks A and B is _____.

A. 0.1 7 B. 0.20 C. 0.80 D. 4.97

The correlation indicates a weak positive linear relationship between the returns on Stocks A and B.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium

Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns. Topic: Portfolio Returns

52.

Refer to Exhibit 5-7. The expected return of the portfolio is ____.

2.60 %

B. 5.04% C. 7.64% D. 14.90%

wA = $120,000/$200,000 = 0.60 wB = $80,000/$200,000 = 0.40 E(Rp) = 0.60(8.4%) + 0.40(6.5%) = 7.64%

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns.

Topic: Portfolio Returns

53.

Refer to Exhibit 5-7. The portfolio variance is ______.

8.17 %

B. 13.80% C. 66.78 (%)

D. 190.70 (%)

wA = $120,000/$200,000 = 0.60 wB = $80,000/$200,000 = 0.40 = 2

(0.60) (11.82) + (0.40) (7.19) + 2(0.60)(0.40) (17.10) = 66.7758

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard

Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns. Topic: Portfolio Returns

54.

Exhibit 5-8. An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-8. The expected return of the portfolio is _____.

6.30 %

B. 6.75% C. 7.38% D. 13.50%

wA = $75,000/$100,000 = 0.75 wB = $25,000/$100,000 = 0.25 E(Rp) = 0.75(8.0%) + 0.25(5.5%) = 7.375%

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns.

Topic: Portfolio Returns

55.

Refer to Exhibit 5-8. The standard deviation of the portfolio is _____.

9.39 (%)

B. 14.19 (%) C. 88.23 (%)

D. 201.41 (%)

wA = $75,000/$100,000 = 0.75 wB = $25,000/$100,000 = 0.25 = 2

(0.75) (11.82) + (0.25) (7.9) + 2(0.75)(0.25) (17.10) = 88.2317

Distractors: Wrong answers include the variance. ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns. Topic: Portfolio Returns

56.

Given the information in the accompanying table, calculate the correlation coefficient between the returns on Stocks A and B.

0.21 2

B. -0.167 C. 0.167 D. 0.212

The correlation coefficient indicates a weak negative linear relationship between the returns on Stocks A and B. Distractors: Wrong answer choices include the covariance and the absolute values of the correlation coefficient and the covariance. ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns. Topic: Portfolio Returns

57.

Which of the following statements is most

accurate about a binomial random variable?

It has a bellshaped distribution.

B. It is a continuous random variable. C. It counts the number of successes in a given number of trials. D. It counts the number of successes in a specified time interval or AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

58.

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective?

0.007 29

B. 0.0081 C. 0.081 D. 0.03 There are n = 5 trials, and a defect is considered a success with p = 0.10 and q = 1 - p = 0.90. The probability of getting exactly x = 3 successes is ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

= 0.0081. This result can also be found using Excel's BINOM.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

59.

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?

0.00 10

B. 0.2916 C. 0.3439 D. 0.6561 There are n = 4 trials, and a defect is considered a success with p = 0.10 and q = 1 - p = 0.90. The probability of getting exactly x = 0 successes is

= 0.6561. This result can also be found using Excel's ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of exactly one calculator being defective, and at least one calculator being defective.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

60.

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

0.00 10

B. 0.2916 C. 0.3439 D. 0.6561 There are n = 4 trials, and a defect is considered a success with p = 0.10 and q = 1 - p = 0.90. The probability of getting at least one success is

. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answer choices include the probabilities of exactly 0 calculators and of exactly 1 calculator being defective.

AACSB: Analytic

Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

61.

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them has a degree in economics?

0.02 7

B. 0.300 C. 0.343 D. 0.900 There are n = 3 trials, with p = 0.30 and q = 1 - p = 0.70. The probability of getting exactly x = 0 successes is

= 0.343. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answer choices include the probability that all three have a degree in economics.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

62.

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that at least one of them has a degree in economics?

0.30 0

B. 0.343 C. 0.657 D. 0.900 There are n = 3 trials, with p = 0.30 and q = 1 - p = 0.70. The probability of getting at least one success is . This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answer choices include the probability that exactly 0 have a degree in economics.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

63.

Exhibit 5-9. On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected.

Refer to Exhibit 5-9. What is the probability that two light bulbs will be defective? ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

0.01 05

B. 0.0746 C. 0.3151 D. 0.5987 There are n = 10 trials, and a defect is considered a success with p = 0.05 and q = 1 - p = 0.95. The probability of getting exactly x = 2 successes is

= 0.0746. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answer choices include the probabilities that exactly zero, one, and three light bulbs are defective.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

64.

Exhibit 5-9. On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. Refer to Exhibit 5-9. What is the probability that none of the light bulbs will be defective?

0.01 05

B. 0.0746 C. 0.3151 D. 0.5987 There are n = 10 trials, and a defect is considered a success with p = 0.05 and q = 1 - p = 0.95. The probability of getting exactly x = 0 successes is

= 0.5987. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answer choices include the probabilities that exactly one, two, and three light bulbs are defective.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

65.

Exhibit 5-9. On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. Refer to Exhibit 5-9. What are the mean and variance of the number of defective bulbs?

0.475 and

0.475 B. 0.475 and 0.6892 C. 0.50 and 0.475 D. 0.50 and 0.6892

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

66.

Exhibit 5-10. According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries (National Vital Statistics Report, Volume 60, Number 2, November 2011). Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10. What is the probability that 2 of the expectant mothers will have a Caesarean delivery?

0.01 47

B. 0.0606 C. 0.2090 D. 0.3088 The probability of two successes in seven Bernoulli trials is

. This ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of zero and one Caesarean deliveries as well as

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

67.

Refer to Exhibit 5-10. What is the probability that at least 1 of the expectant mothers will have a Caesarean delivery?

0.06 06

B. 0.2090 C. 0.9394 D. 0.9742 The probability of zero successes in seven Bernoulli trials is

probability of at least one success is . This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of exactly zero and one Caesarean deliveries.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

68.

Refer to Exhibit 5-10. The expected number of mothers who will not have a Caesarean delivery is ______.

A. 1.2 4 B. 2.31 C. 3.50 D. 4.69 The probability that a randomly selected mother will not have a Caesarean delivery is 0.67. The expected number of mothers who will not have a ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Caesarean delivery is (0.67)(7) = 4.69. Distractors: Wrong answers include the expected number of mothers who will have a Caesarean delivery.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

69.

Refer to Exhibit 5-10. What is the standard deviation of the number of mothers who will have a Caesarean delivery?

A. 1.2 4 B. 1.54 C. 2.31 D. 4.69 The variance of the probability distribution is (7) (0.33)(0.67) = 1.54. The standard deviation is

Distractors: Wrong answers include the variance,

the expected number of mothers who will have a Caesarean delivery, and the expected number of mothers who will not have a Caesarean delivery.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

70.

Exhibit 5-11. For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11. What is the probability that three of the customers redeem the coupon?

0.04 86

B. 0.1912 C. 0.3513 D. 0.4015 The probability of three successes in six Bernoulli trials is

T his result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability

of exactly 1 success and exactly 0 successes.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

71.

Refer to Exhibit 5-11. What is the probability that no more than one of the customers redeems the coupon?

0.24 72

B. 0.3513 C. 0.4015 D. 0.7528 The probability of no more than one success in six Bernoulli trials is

. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability

of exactly one success, exactly zero successes, and more than one success.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

72.

0.24 72

B. 0.3513 C. 0.4015 D. 0.7528 The probability of at least two successes in six Bernoulli trials is . Where,

. Therefore, ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of exactly one success, exactly zero successes, and no more than one success.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

73.

A. 0.8 1 B. 0.96 C. 3.42 D. 5.04 The expected number of coupons is (0.16)(6) = 0.96. Distractors: Wrong answers include the expected number of coupons that will not be redeemed and the variance of the probability distribution. ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

74.

Refer to Exhibit 5-12. What is the probability that exactly one of the residents was unemployed?

0.04 19

B. 0.1678 C. 0.2936 D. 0.3355 The probability of one success in eight Bernoulli trials is

This result can also be found using Excel's BINOM.DIST function. (See the text for details. Distractors: Wrong answers include the probability of zero and two unemployed workers as well as

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium

Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

75.

Exhibit 5-12. According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics, May, 2011). Eight working-age residents were chosen at random. Refer to Exhibit 5-12. What is the probability that at least two of the residents were unemployed?

0.16 78

B. 0.3355 C. 0.4967 D. 0.5033 The probability of zero successes in eight Bernoulli trials and one success in eight trials are

d The probability of at least two successes is

This result can also be found using Excel's BINOM.DIST function. (See the text for details. Distractors: Wrong answers include the probability of exactly zero, one, and two people unemployed.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard

Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

76.

0.00 13

B. 0.0091 C. 0.0459 D. 0.1468 The probability of four successes in eight Bernoulli trials is

. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of exactly three and five people unemployed.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

77.

Exhibit 5-12. According to a Department of Labor report, the city of Detroit had a 20% ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

unemployment rate in May of 2011 (Bureau of Labor Statistics, May, 2011). Eight working-age residents were chosen at random. Refer to Exhibit 5-12. What was the expected number of unemployed residents, when eight working-age residents were randomly selected?

A. 1.0 B. 1.6 C. 2.0 D. 6.4 The Expected value is

Distractors: Wrong answers include the correct answer rounded up, rounded down, and q times eight.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

78.

Exhibit 5-13. Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw percentage of 89.4%. Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13. What is the probability that Billups makes all six free throws?

0.10 70

B. 0.3632 C. 0.5105 D. 0.6530 The probability of six successes in six Bernoulli trials is

. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of exactly five and four successful free throws.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

79.

0.36 32

B. 0.5105 C. 0.8737 D. 0.8940 The probability of five or more successes in six Bernoulli trials is ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

. This result can also be found using Excel's BINOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of exactly five successes and exactly six successes.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

80.

Exhibit 5-13. Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw percentage of 89.4%. Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13. What is the expected number of free throws that Billups will make?

0.63 6

B. 5.364 C. 5.686 D. 6.000 The expected number of coupons is (0.894)(6) = 5.364. Distractors: Wrong answers include the expected number of free throws that will not be made, and the variance of the probability distribution off one ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

decimal place.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

81.

Exhibit 5-13. Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw percentage of 89.4%. Suppose he shoots six free throws in tonight's game.

Refer to Exhibit 5-13. What is the standard deviation of the number of free throws that Billups will make?

0.53 64

B. 0.5686 C. 0.7540 D. 5.6860 The variance of the probability distribution is (6) (0.894)(1 - 0.894) = 0.5686. The standard deviation is

Distractors: Wrong answers include the variance, the expected value off a decimal place, and the variance off a decimal place.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

82.

Which of the following statements is most

accurate about a Poisson random variable?

It counts the number of successes in a given number of trials.

B. It counts the number of successes in a specified time or space in C. It is a continuous random variable. D. It has a bell-shaped distribution. AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

83.

Exhibit 5-14. The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston, up from an average of one per week in 2005.

Refer to Exhibit 5-14. What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?

0.16 80

B. 0.1954 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

C. 0.2240 D. 0.8153 The probability that exactly four auctions occur is . This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that two auctions occur, and the probability that no more than four auctions occur.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

84.

Refer to Exhibit 5-14. What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?

0.04 98

B. 0.1494 C. 0.8009 D. 0.9502 The probability that at least one success occurs is

This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that exactly zero auctions occur, exactly one auction occurs, and more than one auction occurs.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

85.

Refer to Exhibit 5-14. What is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?

0.19

91 B. 0.2240 C. 0.4232 D. 0.5768 The probability of no more than two successes is . Using the Poisson probability distribution function,

. This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that no more than one auction occurs, that two auctions occur, and that more than two auctions occur.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

86.

Refer to Exhibit 5-14. What is the probability that exactly 10 foreclosure auctions occurred during a ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

randomly selected five-day week in 2011 in Boston?

0.00 08

B. 0.0486 C. 0.1185 D. 0.9514 The mean over a four-day period is

The probability that exactly 10 successes occur over a four-day period is This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that at most 10 successes occur, and the probability that 10 successes occur with mean 3.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

87.

Exhibit 5-15. A bank manager estimates that an average of two customers enter the tellers' queue every five minutes. Assume that the number of customers that enter the tellers' queue is Poissondistributed.

Refer to Exhibit 5-15. What is the probability that exactly three customers enter the queue in a ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

randomly selected five-minute period?

0.09 02

B. 0.1804 C. 0.2240 D. 0.2707 The probability that exactly three customers enter the queue is

. This

result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that exactly two customers enter the queue and exactly four customers enter the queue.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

88.

Refer to Exhibit 5-15. What is the probability that less than two customers enter the queue in a randomly selected five-minute period?

0.13 53

B. 0.2707 C. 0.4060 D. 0.6767 The probability that less than two customers enter the queue is

This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that exactly zero customers enter the queue, exactly one customer enters the queue, and no more than two customers enter the queue.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

89.

Refer to Exhibit 5-15. What is the probability that at least two customers enter the queue in a randomly selected five-minute period?

0.13

53 B. 0.2707 C. 0.4060 D. 0.5940 The probability that at least two customers enter the queue is

. This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that exactly zero customers enter the queue, exactly one customer enters the queue, and no more than one customer enters the queue.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

90.

Refer to Exhibit 5-15. What is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period?

0.00 34

B. 0.1033 C. 0.1377 D. 0.1606 Over a 15-minute period,

. The

probability that exactly seven customers enter the queue is

. This result

can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that exactly six customers enter the queue, the probability that exactly eight customers enter the queue, and the probability of seven customers enter the queue with an unadjusted mean of two.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

91.

Cars arrive randomly at a tollbooth at a rate of 20 cars per 10 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?

0.03 78

B. 0.0500 C. 0.1251 D. 0.5000 Over a five-minute period,

. The

probability that exactly five cars arrive over a fiveminute interval is

This result can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

92.

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel?

0.00 02

B. 0.1353 C. 0.1804 D. 0.8647 The probability of no defects in 10 feet of steel is

. This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that one defect and at least one defect is found in 10 feet of steel.

AACSB: Analytic Blooms: Apply

Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

93.

Exhibit 5-16. According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years.

Refer to Exhibit 5-16. What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years?

0.00 67

B. 0.0337 C. 0.1353 D. 0.2707 The mean number of successes in 40 years is

equal to

. Using the Poisson

probability distribution function, . This result can also be found using Excel's POISSON.DIST function. (See the text for details.) Distractors: Wrong answers include the probability of one earthquake and the probability of no earthquakes given the mean number of earthquakes was equal to five.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

94.

Exhibit 5-16. According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16. What is the probability that more than two earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next 40 years?

0.13 53

B. 0.2706 C. 0.3233 D. 0.8754 The probability of more than two earthquakes occurring is

. Using the Poisson probability distribution function,

. This result can also be found using Excel's POISSON.DIST function. (See text for details.) Distractors: Wrong answers include the probability that 2 earthquakes occur, the probability that more

than two earthquakes occur given the mean number of successes was five, and the probability of no earthquakes.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

95.

Exhibit 5-16. According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years.

Refer to Exhibit 5-16. What is the probability that one or more earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next year?

0.04 88

B. 0.1353 C. 0.4878 D. 0.9512 The mean number of earthquakes in one year is equal to

. Using the Poisson

probability distribution function,

. This result can also be found using Excel's ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

POISSON.DIST function. (See text for details.) Distractors: Wrong answers include the probability of no earthquakes in the next year.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution hamad alkhaldi bowling green ky

96.

Exhibit 5-16. According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16. What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?

A. 1.41 4 B. 2.000 C. 2.236 D. 5.000 The mean number of earthquakes in 40 years is equal to

. The standard deviation is

equal to the square root of the mean number of successes:

Distractors: Wrong answers include the variance, the variance if the mean number of successes is ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

equal to five, and the standard deviation if the mean number of successes is equal to five.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

97.

Which of the following is true about the hypergeometric distribution?

The trials are independ probability of success to trial.

B. The trials are independent and the probability of success does n

C. The trials are not independent and the probability of success ma

D. The trials are not independent and the probability of success doe trial. The hypergeometric probability distribution is appropriate in applications where we cannot assume the trials are independent. The probability of success or the probability of failure change from trial to trial.

AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-08 Describe the hypergeometric distribution and compute relevant probabilities. Topic: The Hypergeometric Probability Distribution hamad alkhaldi bowling green ky

98.

An urn contains 12 balls, 5 of which are red. The selection of a red ball is desired and is therefore considered to be a success. If a person draws ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

three balls from the urn, what is the probability of two successes?

0.15 91

B. 0.3182 C. 0.6810 D. 0.8409 To use the formula for the hypergeometric distribution, we need the following:

N = 12 total balls in the urn, S = 5 possible successes in the urn, N - S possible failures in the urn, n = 3 balls chosen, x = 2 successes sought, failure sought:

This result can also be found using Excel's HYPGEOM.DIST function. (See text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-08 Describe the hypergeometric distribution and compute relevant probabilities. Topic: The Hypergeometric Probability Distribution hamad alkhaldi bowling green ky

99.

An urn contains 12 balls, 5 of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

selected, what is the expected value of the distribution of the number of selected red balls?

0.41 67

B. 0.8333 C. 0.5833 D. 1.2500

N = 12 total balls in the urn, S = 5 possible successes in the urn,

possible failures

in the urn, n = 3 balls chosen:

. This result can also be found using Excel's HYPGEOM.DIST function. (See text for details.)

100.

Exhibit 5-17. Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of those 14 players, assume that 3 have recently taken a performance-enhancing drug. Suppose the league decides to randomly test five members of the team.

Refer to Exhibit 5-17. What is the probability that exactly two of the tested players are found to have taken a performance-enhancing drug? hamad alkhaldi bowling green ky ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

0.23 08

B. 0.2473 C. 0.4945 D. 0.7692

N = 14, S = 3,

, n = 5, x = 2

This result can also be found using Excel's HYPGEOM.DIST function. (See text for details.) Distractors: Wrong answers include the probability that exactly zero, one, and at least one player has taken a performance-enhancing drug.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-08 Describe the hypergeometric distribution and compute relevant probabilities. Topic: The Hypergeometric Probability Distribution

101.

Refer to Exhibit 5-17. What is the probability that at least one of the tested players is found to have ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

taken a performance-enhancing drug? hamad alkhaldi bowling green ky A.

0.23 08

B. 0.2473 C. 0.4945 D. 0.7692 Given N = 14, S = 3,

, n = 5, the

probability of at least one player testing positive is , where

Therefore,

Distractors: Wrong answers include the probability that exactly zero, one, and two players test positive. This result can also be found using Excel's HYPGEOM.DIST function. (See the text for details.)

102.

Exhibit 5-18. There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in the last year. Joe, a member of the staff, randomly selects six of the pit bulls for his group.

Refer to Exhibit 5-18. What is the probability that exactly one of the pit bulls in Joe's group attacked another dog last year?

0.16 18

B. 0.3235 C. 0.4314 D. 0.4853 Given N = 18, S = 4,

, n = 6, the

probability that exactly one pit bull attacked another dog is

. This result can also be found using Excel's HYPGEOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that exactly zero, two, and less than two pit bulls attacked another dog.

103.

group. hamad alkhaldi bowling green ky Refer to Exhibit 5-18. What is the probability that at least one of the pit bulls in Joe's group attacked another dog last year?

0.16 18

B. 0.4314 C. 0.5686 D. 0.8382 The probability that at least one pit bull attacked another dog is

, where

. Therefore,

. This

result can also be found using Excel's HYPGEOM.DIST function. (See the text for details.) Distractors: Wrong answers include the probability that one, zero, and the complement of the probability that one pit bull attacked another dog.

Essay Questions

104.

A six-sided, unfair (weighted) die has the following probability distribution.

Find the probability of rolling a 3 or less.

0.6667

Feedback: The probability of rolling a 3 or less is the sum of the probabilities of rolling a 1, 2, and 3. Therefore, the answer is P(X = 1) + P(X = 2) + P(X = 3) = 1/4 + 1/12 + 1/3 = 8/12 = 0.6667.

105.

Does the following table describe a discrete probability distribution?

No, the sum of probabilities is 0.9 rather than 1.

Feedback: The two properties that must be met are:

• The probability of each outcome is a number between 0 and 1, or equivalently, . • The sum of the probabilities over all mutually exclusive and exhaustive values of X equals 1. In other words,

where the

represent an exhaustive list of all distinct

outcomes of X.

106.

An analyst estimates that a stock has the following probabilities of year-end prices.

a. Calculate the expected price at year-end. b. Calculate the variance and the standard deviation.

E(X) = 88, Var(X) = 21, and SD(X) = 4.58

Feedback:

= -80(0.1) + 85(0.4) + 1(0.3) + 2(0.2) = 88 © 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

= (80 - 88) (0.1) + (80 - 88) (0.4) + (80 - 88) (0.3) 2

+ (80 - 88) (0.2) = 21.

107.

You have inherited a lottery ticket that may be a $5,000 winner. You have a 35% chance of winning the $5,000 and a 65% chance of winning $0. You have an opportunity to sell the lottery for $1500. What should you do if are risk neutral?

E(X) = $1750. Therefore, keep the ticket, since the expected value is greater than the sale price ($1500).

Feedback: A risk neutral consumer completely ignores risk and always accepts a prospect that offers a positive expected gain. Using the expected value formula, we find

= 5000(0.35) + 0(0.65) = $1750.

The expected value ($1750) is greater than the sale price of the lottery ($1500); therefore, you expect to gain more by keeping the lottery ticket.

108.

You have inherited a lottery ticket worth $10,000. You have a 0.25 chance of winning the $10,000 and a 0.75 chance of winning $0. You have an opportunity to sell the lottery ticket for

$2,500. What should you do if you are risk averse?

Sell the lottery ticket.

Feedback: A risk averse consumer may decline a risky prospect even if it offers a positive expected gain; he/she will definitely decline a risky prospect if there is no positive expected gain. Using the expected value formula, we find

= 10,000(0.25)

+ 0(0.75) = $2500. Here, the expected value of $2500 is the same as the sale price of $2,500 of the lottery. Since the risky prospect does not offer a positive expected gain, a risk averse person would sell the ticket rather than hold out to have a chance of winning $10,000.

109.

An investor has a $120,000 portfolio of which $50,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are as follows:

a. Calculate the correlation coefficient. b. Calculate the expected return of the portfolio. c. Calculate the standard deviation of the portfolio.

a. ρAB= 0.2485; b.

; c.

Feedback: a.

= 38.20/(15.93 × 9.65) = 0.2485; b. First find the portfolio

weights, and then use the formula

to find the expected

return on the portfolio: wA = 50,000/120,000 = 0.4167 and wB = 70,000/120,000 = 0.5833, so

) = 0.4167(11.2%) + 0.5833(8.6%) = 9.6833%; c. 2

= (0.4167) (15.93) + (0.5833) (9.65) + 2(0.4167) (0.5833)(38.20) = 94.32; so SD(Rp) =

= 9.71.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns. Topic: Portfolio Returns

110.

An investor has an $80,000 portfolio of which $60,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are as follows:

a. Calculate the correlation coefficient. b. Calculate the expected return of the portfolio. c. Calculate the standard deviation of the portfolio.

; b.

; c.

© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Feedback:

= -11.20/(23.82 Ă&#x2014; 7.54) = -0.06; b. First find the portfolio weights,

and then use the formula

to find the expected return on the

portfolio: wA = 60,000/80,000 = 0.75 and wB = 20,000/80,000 = 0.25, so

) = 0.75(-2.3%) + 0.25(5.1%) = -0.45%; c. 2

(0.75) (23.82) + (0.25) (7.54) + 2(0.75)(0.25)(-11.20) = 318.51; so SD(Rp) =

17.84.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute summary measures to evaluate portfolio returns. Topic: Portfolio Returns

111.

Suppose your firm is buying five new computers. The manufacturer offers a warranty to replace any computer that breaks down within three years. Suppose there is a 25% chance that any given computer breaks down within three years. a. What is the probability that exactly one of the computers breaks down within five years? b. What is the probability that at least one of the computers breaks down within five years? c. Suppose the warranty for five computers costs $700, while a new computer costs $600. Is the warranty less expensive than the expected cost of replacing the broken computers?

; b.

; c. Yes.

Feedback: a. The probability of one success in five trials is

c. The expected number of computers that will break down is

np = (5)(0.25) = 1.25.

Since to replace a broken computer, the firm must pay $600, the expected cost of replacing the broken computers is (1.25)($600) = $750. The warranty, which costs $700, is less expensive. These results can also be found using Excel's BINOM.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

112 Lisa is in a free-throw shooting contest where each contestant attempts 10 free throws. On .

average, Lisa makes 77% of the free throws she attempts. a. What is the probability that she makes exactly eight free throws? b. What is the probability she makes at least nine free throws? c. What is the probability she makes less than nine free throws? d. Lisa is competing against Bill to see who can make the most free throws in 10 attempts. Suppose Bill goes first and makes seven. Should we expect Lisa to make at least as many as Bill? Explain.

; b.

; c.

;

d. Yes, on average we expect Lisa to make as many free throws as Bill since 7.7 > 7.

Feedback: a.

;

, where

and

. Therefore,

c. The probability of less than nine successes is know that

From part b, we

Therefore,

Results a-c can also be found using Excel's BINOM.DIST function. (See the text for details.) d. The expected value of a binomial probability distribution is

The expected

number of free throws that Lisa can expect to make is (0.77)(10) = 7.7. Since this is greater than seven, Lisa will, on average, make seven or more free throws.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

11 George buys six lottery tickets for $2 each. In addition to the grand prize, there is a 20% chance 3. that each lottery ticket gives a prize of $4. Assume that these tickets are not grand prize winners.

a. What is the probability that the tickets pay out more than George spent on them? b. What is the probability that none of the tickets are winners? c. What is the probability that at least one of the tickets is a winner?

; b.

; c.

Feedback: a. The tickets cost $12 total. In order for George to make more than $12, more than three of them need to be winners.

, where

and

. Therefore, .

b. The probability that none of the tickets are winners is

c. The probability that at least one of the tickets is a winner is

These results can also be found using Excel's BINOM.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

114.

A car salesman has a 5% chance of landing a sale with a random customer on his lot. Suppose 10 people come on the lot today. a. What is the probability that he sells exactly three cars today? b. What is the probability he sells less than two cars today? c. What is the expected number of cars he is going to sell today?

a. 0.0105; b. 0.9139; c. 0.5

Feedback: a. The probability that he sells exactly three cars today is

;

b. The probability he sells less than two cars is equal to

Results a and b can also be found using Excel's BINOM.DIST function. (See the text for details.) c. The expected number of cars he is going to sell is np = (10)(0.05) = 0.5.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

115.

A company is going to release four quarterly reports this year. Suppose the company has a 32% chance of beating analyst expectations each quarter. a. What is the probability that the company beats analyst expectations every quarter of this year? b. What is the probability the company beats analyst expectations more than half the time this year? c. What is the probability of the expected number of times the company will beat analyst expectations this year?

; b.

; c. 1.28

Feedback: a. The probability of beating analyst expectations every quarter is

. b. The probability of beating analyst expectations more than half the time is equal to

Results a and b can also be found using Excel's BINOM.DIST function. (See the text for details.) c. The expected number of times the company will beat analyst expectations is equal to np = (4)(0.32) = 1.28.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Describe the binomial distribution and compute relevant probabilities. Topic: The Binomial Probability Distribution

116.

Assume that the mean success rate of a Poisson process is six successes per hour. a. Find the expected number of successes in a 40-minute period. b. Find the expected number of successes in a three-hour period. c. Find the probability of at least two successes in a 30-minute period.

a. 4; b. 18; c. 0.8008

Feedback: a. Since there are six successes expected in an hour, and 40 minutes is two-thirds of an hour, there will be 6 × (2/3) = 4 expected successes in 40 minutes. b. Since there are six successes expected in an hour, the expected number of successes in three hours is 3 × 6 = 18. c. Since we are looking at a half-hour period, the mean number of successes is 3 per this

period. P(X ≥ 2) = 1 -[P(X = 0) + P(X = 1)] =

= 1 - 0.0498 - 0.1494 =

0.8008. This result can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply

Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

117.

Sam is a trucker and believes that for every 60 miles he drives on the freeway in Indiana, there is an average of 2 state troopers checking his speed with a radar gun. a. What is the probability that at least one trooper is checking his speed on a randomly selected 60-mile stretch? b. What is the probability that exactly three troopers are checking his speed on a randomly selected 60-mile stretch? c. Sam drives 240 miles a day. What is the average number of state troopers that check his speed on a given day? d. Sam drives 240 miles a day. What is the probability that exactly five troopers check Sam's speed on a randomly selected day?

; b.

; c. Eight troopers; d.

Feedback: a. The probability that at least one trooper is checking his speed is . b. The probability that exactly three troopers are checking his speed is . c. Since two troopers, on average, check his speed every 60 miles, eight troopers, on average, will check his speed every 240 miles; d. The probability that exactly five troopers check his speed over 240 miles is These results can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic

Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

118.

Due to turnover and promotion, a bank manager knows that, on average, she hires four new tellers per year. Suppose the number of tellers she hires is Poisson-distributed. a. What is the probability that in a given year, the manager hires exactly five new tellers? b. What is the average number of tellers the manager hires in a six-month period? c. What is the probability that the manager hires at least one new teller in a given six-month period?

; b. Two tellers; c.

Feedback: a. The probability that the manager must hire five tellers is

. b. In a given six-month period, the manager hires an average of 2 (4/2) new tellers. c. The probability that the manager hires at least one teller is

These results can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

1 A telemarketer knows that, on average, he is able to make three sales in a 30-minute period. 1 Suppose the number of sales he can make in a given time period is Poisson-distributed. 9.

a. What is the probability that he makes exactly four sales in a 30-minute period? ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

b. What is the probability that he makes at least two sales in a 30-minute period? c. What is the probability that he makes five sales in an hour-long period?

; b.

; c.

Feedback: a. The probability that the telemarketer makes exactly four sales is . b. The probability that he makes at least two sales is

where

and

Therefore, ; c. The probability that he makes five sales in one

hour is These results can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

120.

A construction company found that on average its workers get into four car accidents per week. a. What is the probability of exactly six car accidents in a random week? b. What is the probability that there are less than two car accidents in a random week? c. What is the probability that there are exactly eight car accidents over the course of three weeks?

a. 0.1042; b. 0.0916; c. 0.0655 ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Feedback: a. The probability of exactly six car accidents in a week is equal to

. b. The probability of less than two accidents in a week is equal to

. c. The mean number of accidents over the course of three weeks is equal to 4 Ă&#x2014; 3 = 12. The probability of exactly eight accidents over the course of three weeks is equal to . These results can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

121.

During an hour of class, a professor anticipates six questions on average. a. What is the probability that in a given hour of class, exactly six questions are asked? b. What is the expected number of questions asked in a 20-minute period? c. What is the probability that no questions are asked over a 20-minute period?

a. 0.1606; b. 2; c. 0.1353

Feedback: a. The probability that in a given hour of class, exactly six questions are asked is

equal to

b. In a 20-minute period, the expected number of questions asked is equal to the number of ÂŠ 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

questions per hour divided by 3: 6/3 = 2. c. The probability that no questions are asked over a 20-minute period is equal to

. These results can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

122.

A plane taking off from an airport in New York can expect to run into a flock of birds once out of every 1,250 take-offs. a. What is the expected number of bird strikes for 10,000 take-offs? b. What is the standard deviation of the number of bird strikes for 10,000 take-offs? c. What is the probability of running into seven flocks of birds in 10,000 take-offs?

a. 8; b. 2.8284; c. 0.1396

Feedback: a. The expected number of bird strikes for 10,000 take-offs is equal to the expected number of bird strikes per take-off times 10,000

b. The standard deviation of the number of bird strikes for 10,000 take-offs is equal to the square root of the expected value

c. The probability of striking seven flocks of birds in 10,000 take-offs is equal to . This result can also be found using Excel's POISSON.DIST function. (See the text for details.)

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Describe the Poisson distribution and compute relevant probabilities. Topic: The Poisson Probability Distribution

12 You are attending a baseball game with two family members when it is announced that four fans in 3. your section (which holds 20 spectators total) will win a free autographed baseball. a. What is the probability that at least one member in your family (including yourself) wins an autographed baseball? b. What is the probability that exactly two members of your family win an autographed baseball? c. What is the probability that all three of you win an autographed baseball?

; b.

; c.

Feedback: For this problem: N = 20, S = 4,

, n = 3.

a. The probability that at least one family member wins is

where

Therefore,

b. The probability that exactly two family members win is

c. The probability that all three win is These results can also be found using Excel's HYPGEOM.DIST function. (See the text for details.)

124.

Four of your students submitted an entry to a writing contest. There were a total of 24 entries submitted. Six of the entries will move on to the next round. a. What is the probability that all four of your students will move on to the next round? b. How many of your students are expected to move to the next round? c. What is the probability that fewer of your students than expected make it to the next round than expected?

a. 0.0014; b. 1; c. 0.2880

Feedback: For this problem: N = 24, S = 6,

,n=4

a. The probability that all four of your students make to the next round is where

. b. The expected number of students that will move on to the next round is

. c. Since the expected value is equal to one, fewer students than expected will make it to the

next round if zero students make it;

These results can also be found using Excel's HYPGEOM.DIST function. (See the text for details.)

125.

In a particular game of cards, success is measured by the number of aces drawn by each player. Eight cards are drawn by the first player. Given that the player is drawing from a full poker deck of 52 cards, find the probability that this player will draw two aces from the deck.

0.0978 Feedback: For this problem: N = 52, S = 4,

, n = 8.

. This result can also be found using Excel's HYPGEOM.DIST function. (See the text for details.)

126.

An urn is filled with three different colors of balls: red, blue, and white. There are three red balls, seven blue balls, and five white balls. If four balls are drawn, what is the probability of drawing two blue balls?

0.4308 Feedback: For this problem: N = 15, S = 7,

, n = 4.

. This result can also be found using Excel's HYPGEOM.DIST function. (See the text for details.)