Ch05 – Ch 7. prep questions

Analytical Methods for Business (University of Arizona)

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ch05

*Student:*

1. A random variable is a function that assigns numerical values to the outcomes of a random experiment.

True False

2. A discrete random variable *X* may assume an (infinitely) uncountable number of distinct values. True False

3. A continuous random variable *X* assumes an (infinitely) uncountable number of distinct values. True False

4. A probability distribution of a continuous random variable *X* gives the probability that *X* takes on a particular value *x*, *P*(*X* = *x*).

True False

5. A cumulative probability distribution of a random variable *X* is the probability *P*(*X* = *x*), where *X* is equal to a particular value *x*.

True False

6. The expected value of a random variable *X* can be referred to as the population mean. True False

7. The variance of a random variable *X* provides us with a measure of central location of the distribution of

*X*.

True False

8. The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance.

True False

9. A risk-averse consumer may decline a risky prospect even if it offers a positive expected value. True False

10. A risk averse consumer ignores risk and makes his/her decisions solely on the basis of expected value.

True False

11. Given two random variables *X* and *Y*, the expected value of their sum, , is equal to the sum of

their individual expected values, . True False

12. A Bernoulli process consists of a series of *n* independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

True False

13. A binomial random variable is defined as the number of successes achieved in *n* trials of a Bernoulli process.

True False

14. A Poisson random variable counts the number of successes (occurrences of a certain event) over a given interval of time or space.

True False

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15. We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size *N* is significantly larger than the sample size *n*.

True False

16. Which of the following can be represented by a discrete random variable?

A. The number of obtained spots when rolling a six-sided die

B. The height of college students

C. The average outside temperature taken every day for two weeks

D. The finishing time of participants in a cross-country meet

17. Which of the following can be represented by a discrete random variable?

A. The circumference of a randomly generated circle

B. The time of a flight between Chicago and New York

C. The number of defective light bulbs in a sample of five

D. The average distance achieved in a series of long jumps

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

A. 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-hour period

D. The score of a randomly selected student on a five-question multiple-choice quiz

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

A. The average temperature in Tampa, Florida, during a month of July

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

C. The number of students who will get financial assistance in a group of 50 randomly selected students

D. The number of customers who visit a department store between 10:00 am and 11:00 am on Mondays

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

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

B. For every possible value *x*, the probability is between 0 and 1.

C. Describes all possible values *x* with the associated probabilities .

D. All of the above.

21. What are the two key properties of a discrete probability distribution?

A.

and

B.

and

C.

and

D.

and

22. **EXHIBIT** **5-1. **Consider the following discrete probability distribution.

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

A. 0.10

B. 0.35

C. 0.55

D. 0.65

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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. 0.10

B. 0.35

C. 0.55

D. 0.65

24. **EXHIBIT** **5-1. **Consider the following discrete probability distribution.

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

A. 0.00

B. 0.10

C. 0.15

D. 0.35

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. 0.10

B. 0.15

C. 0.35

D. 0.45

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. 0.14

B. 0.30

C. 0.44

D. 0.56

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. 0.14

B. 0.30

C. 0.44

D. 0.56

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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. 0.14

B. 0.30

C. 0.44

D. 0.56

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

A. The long-run average of the random variable values generated over 100 independent repetitions

B. The long-run average of the random variable values generated over 1000 independent repetitions

C. The long-run average of the random variable values generated over infinitely many independent repetitions

D. The long-run average of the random variable values generated over a finite number of independent repetitions

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

31. **EXHIBIT** **5-3. **Consider the following probability distribution.

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

A. 0.9

B. 1.5

C. 1.9

D. 2.5

32. **EXHIBIT** **5-3. **Consider the following probability distribution.

Refer to Exhibit 5-3. The variance is .

A. 0.89

B. 0.94

C. 1.65

D. 1.90

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33. **EXHIBIT** **5-3.** Consider the following probability distribution.

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

A. 0.89

B. 0.94

C. 1.65

D. 1.90

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

35. **EXHIBIT** **5-4. **Consider the following probability distribution.

Refer to Exhibit 5-4. The variance is .

A. 1.14

B. 1.29

C. 1.65

D. 1.94

36. **EXHIBIT** **5-4. **Consider the following probability distribution.

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

A. 1.14

B. 1.29

C. 1.65

D. 1.94

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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:

A. Option A

B. Option B

C. Option C

D. Option D

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%

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 .

A. $87.50

B. $88.50

C. $89.00

D. $90.00

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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. 0.20

B. 0.40

C. 0.60

D. 0.80

41. **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 sells no more than one house during a month?

A. 0.20

B. 0.40

C. 0.60

D. 0.80

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

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. 0.56

B. 0.75

C. 1

D. 1.2

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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. 0.20

B. 0.40

C. 0.60

D. 0.80

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. 0.20

B. 0.40

C. 0.60

D. 0.80

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

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. 0.56

B. 0.75

C. 0.80

D. 1

48. A consumer who is risk averse is *best* characterized as .

A. A consumer who may accept a risky prospect even if the expected gain is negative

B. A consumer who demands a positive expected gain as compensation for taking risk

C. A consumer who completely ignores risk and makes his/her decisions based solely on expected values

D. None of the above

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49. A consumer who is risk neutral is *best* characterized as .

A. A consumer who may accept a risky prospect even if the expected gain is negative

B. A consumer who demands a positive expected gain as compensation for taking risk

C. A consumer who completely ignores risk and makes his/her decisions based solely on expected values

D. None of the above

50. How would you characterize a consumer who is risk loving?

A. A consumer who may accept a risky prospect even if the expected gain is negative.

B. A consumer who demands a positive expected gain as compensation for taking risk.

C. A consumer who completely ignores risk and makes his/her decisions solely on the basis of expected values.

D. None of the above.

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. -0.17

B. 0.20

C. 0.80

D. 4.97

52. **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 expected return of the portfolio is .

A. 2.60%

B. 5.04%

C. 7.64%

D. 14.90%

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53. **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 portfolio variance is .

A. 8.17%

B. 13.80%

C. 66.78 (%)2

D. 190.70 (%)2

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 .

A. 6.30%

B. 6.75%

C. 7.38%

D. 13.50%

55. **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 standard deviation of the portfolio is .

A. 9.39 (%)

B. 14.19 (%)

C. 88.23 (%)2

D. 201.41 (%)2

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

A. -0.212

B. -0.167

C. 0.167

D. 0.212

57. Which of the following statements is *most accurate* about a binomial random variable?

A. It has a bell-shaped 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 region.

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?

A. 0.00729

B. 0.0081

C. 0.081

D. 0.03

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?

A. 0.0010

B. 0.2916

C. 0.3439

D. 0.6561

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?

A. 0.0010

B. 0.2916

C. 0.3439

D. 0.6561

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?

A. 0.027

B. 0.300

C. 0.343

D. 0.900

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?

A. 0.300

B. 0.343

C. 0.657

D. 0.900

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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?

A. 0.0105

B. 0.0746

C. 0.3151

D. 0.5987

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?

A. 0.0105

B. 0.0746

C. 0.3151

D. 0.5987

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?

A. 0.475 and 0.475

B. 0.475 and 0.6892

C. 0.50 and 0.475

D. 0.50 and 0.6892

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?

A. 0.0147

B. 0.0606

C. 0.2090

D. 0.3088

67. **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 at least 1 of the expectant mothers will have a Caesarean delivery?

A. 0.0606

B. 0.2090

C. 0.9394

D. 0.9742

68. **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. The expected number of mothers who will not have a Caesarean delivery is

.

A. 1.24

B. 2.31

C. 3.50

D. 4.69

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69. **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 standard deviation of the number of mothers who will have a Caesarean delivery?

A. 1.24

B. 1.54

C. 2.31

D. 4.69

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?

A. 0.0486

B. 0.1912

C. 0.3513

D. 0.4015

71. **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 no more than one of the customers redeems the coupon?

A. 0.2472

B. 0.3513

C. 0.4015

D. 0.7528

72. **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 at least two of the customers redeem the coupon?

A. 0.2472

B. 0.3513

C. 0.4015

D. 0.7528

73. **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 expected number of coupons that will be redeemed?

A. 0.81

B. 0.96

C. 3.42

D. 5.04

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74. **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 exactly one of the residents was unemployed?

A. 0.0419

B. 0.1678

C. 0.2936

D. 0.3355

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?

A. 0.1678

B. 0.3355

C. 0.4967

D. 0.5033

76. **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 exactly four residents were unemployed?

A. 0.0013

B. 0.0091

C. 0.0459

D. 0.1468

77. **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 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

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?

A. 0.1070

B. 0.3632

C. 0.5105

D. 0.6530

79. **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 five or more of his free throws?

A. 0.3632

B. 0.5105

C. 0.8737

D. 0.8940

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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?

A. 0.636

B. 5.364

C. 5.686

D. 6.000

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?

A. 0.5364

B. 0.5686

C. 0.7540

D. 5.6860

82. Which of the following statements is *most accurate* about a Poisson random variable?

A. 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 interval.

C. It is a continuous random variable.

D. It has a bell-shaped 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?

A. 0.1680

B. 0.1954

C. 0.2240

D. 0.8153

84. **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 at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?

A. 0.0498

B. 0.1494

C. 0.8009

D. 0.9502

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85. **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 no more than two foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?

A. 0.1991

B. 0.2240

C. 0.4232

D. 0.5768

86. **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 10 foreclosure auctions occurred during a randomly selected five-day week in 2011 in Boston?

A. 0.0008

B. 0.0486

C. 0.1185

D. 0.9514

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 Poisson-distributed.

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

A. 0.0902

B. 0.1804

C. 0.2240

D. 0.2707

88. **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 Poisson-distributed.

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

A. 0.1353

B. 0.2707

C. 0.4060

D. 0.6767

89. **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 Poisson-distributed.

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

A. 0.1353

B. 0.2707

C. 0.4060

D. 0.5940

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90. **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 Poisson-distributed.

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

A. 0.0034

B. 0.1033

C. 0.1377

D. 0.1606

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?

A. 0.0378

B. 0.0500

C. 0.1251

D. 0.5000

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?

A. 0.0002

B. 0.1353

C. 0.1804

D. 0.8647

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?

A. 0.0067

B. 0.0337

C. 0.1353

D. 0.2707

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?

A. 0.1353

B. 0.2706

C. 0.3233

D. 0.8754

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?

A. 0.0488

B. 0.1353

C. 0.4878

D. 0.9512

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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. 1.414

B. 2.000

C. 2.236

D. 5.000

97. Which of the following is true about the hypergeometric distribution?

A. The trials are independent and the probability of success may change from trial to trial.

B. The trials are independent and the probability of success does not change from trial to trial.

C. The trials are not independent and the probability of success may change from trial to trial.

D. The trials are not independent and the probability of success does not change from trial to trial.

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

A. 0.1591

B. 0.3182

C. 0.6810

D. 0.8409

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

A. 0.4167

B. 0.8333

C. 0.5833

D. 1.2500

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?

A. 0.2308

B. 0.2473

C. 0.4945

D. 0.7692

101.**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 at least one of the tested players is found to have taken a performance-enhancing drug?

A. 0.2308

B. 0.2473

C. 0.4945

D. 0.7692

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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?

A. 0.1618

B. 0.3235

C. 0.4314

D. 0.4853

103.**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 at least one of the pit bulls in Joe’s group attacked another dog last year?

A. 0.1618

B. 0.4314

C. 0.5686

D. 0.8382

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

Find the probability of rolling a 3 or less.

105.Does the following table describe a discrete probability distribution?

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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.

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?

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?

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.

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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.

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?

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.

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113.George buys six lottery tickets for $2 each. In addition to the grand prize, there is a 20% chance 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?

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?

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?

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.

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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?

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?

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

a. What is the probability that he makes exactly four sales in a 30-minute period?

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?

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?

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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?

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?

123.You are attending a baseball game with two family members when it is announced that four fans in 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?

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?

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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.

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?