chapter 5: discrete probability distributions · 2019-12-19 · discrete probability distributions...

Discrete Probability Distributions 5-1

CHAPTER 5: DISCRETE PROBABILITY DISTRIBUTIONS

1. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

a) 5 days b) 45 days c) 65 days d) 81 days

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, mean

2. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4

students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?

a) 0.0256 b) 0.0625 c) 0.16 d) 1.00

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution 3. A probability distribution is an equation that

a) associates a particular probability of occurrence with each outcome. b) measures outcomes and assigns values of X to the simple events. c) assigns a value to the variability of the set of events. d) assigns a value to the center of the set of events.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: probability distribution 4. The connotation "expected value" or "expected gain" from playing roulette at a casino means

a) the amount you expect to "gain" on a single play. b) the amount you expect to "gain" in the long run over many plays. c) the amount you need to "break even" over many plays. d) the amount you should expect to gain if you are lucky.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: expected value

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5-2 Discrete Probability Distributions

5. Which of the following about the binomial distribution is not a true statement? a) The probability of the event of interest must be constant from trial to trial. b) Each outcome is independent of the other. c) Each outcome may be classified as either "event of interest" or "not event of interest." d) The variable of interest is continuous.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties

6. In a binomial distribution

a) the variable X is continuous. b) the probability of event of interest π is stable from trial to trial. c) the number of trials n must be at least 30. d) the results of one trial are dependent on the results of the other trials.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 7. Whenever π = 0.5, the binomial distribution will

a) always be symmetric. b) be symmetric only if n is large. c) be right-skewed. d) be left-skewed.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 8. Whenever π = 0.1 and n is small, the binomial distribution will be

a) symmetric. b) right-skewed. c) left-skewed. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties

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9. If n = 10 and π = 0.70, then the mean of the binomial distribution is a) 0.07 b) 1.45. c) 7.00 d) 14.29

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, mean 10. If n = 10 and π = 0.70, then the standard deviation of the binomial distribution is

a) 0.07 b) 1.45 c) 7.00 d) 14.29

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, standard deviation

11. If the outcomes of a variable follow a Poisson distribution, then their

a) mean equals the standard deviation. b) median equals the standard deviation. c) mean equals the variance. d) median equals the variance.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Poisson distribution, mean, standard deviation, properties 12. What type of probability distribution will the consulting firm most likely employ to analyze the

insurance claims in the following problem? An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample 100 of the company’s insurance claims. They believe the number of these 100 that are false will yield the information the company desires. a) binomial distribution. b) Poisson distribution. c) hypergeometric distribution. d) none of the above.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution, properties



13. The covariance a) must be between -1 and +1. b) must be positive. c) can be positive or negative. d) must be less than +1.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: covariance, properties 14. What type of probability distribution will most likely be used to analyze warranty repair needs on

new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold. a) binomial distribution. b) Poisson distribution. c) hypergeometric distribution. d) none of the above.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution, properties 15. What type of probability distribution will most likely be used to analyze the number of blue

chocolate chips per bag in the following problem? The quality control manager of a candy plant is inspecting a batch of chocolate chip bags. When the production process is in control, the mean number of blue chocolate chips per bag is 6.0. The manager is interested in analyzing the probability that any particular bag being inspected has fewer than 5.0 blue chocolate chips. a) binomial distribution. b) Poisson distribution. c) hypergeometric distribution. d) none of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties



16. What type of probability distribution will most likely be used to analyze the number of cars with defective radios in the following problem?

From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. The sales manager of one dealership wants to predict the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios. a) binomial distribution. b) Poisson distribution. c) hypergeometric distribution. d) none of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution, properties 17. A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the

list whose prices are expected to rise by more than 20% after 30 days. In reality, the prices of only 5 stocks would rise by more than 20% after 30 days. If he randomly selected 3 stocks from the list, he would use what type of probability distribution to compute the probability that all of the chosen stocks would appreciate more than 20% after 30 days?

a) binomial distribution. b) Poisson distribution. c) hypergeometric distribution. d) none of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution, properties 18. A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.

To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?





19. A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probability distribution?


ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties

20. The portfolio expected return of two investments

a) will be higher when the covariance is zero. b) will be higher when the covariance is negative. c) will be higher when the covariance is positive. d) does not depend on the covariance.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: portfolio, mean 21. A financial analyst is presented with information on the past records of 60 start-up companies

and told that in fact only 3 of them have managed to become highly successful. He selected 3 companies from this group as the candidates for success. To analyze his ability to spot the companies that will eventually become highly successful, he will use what type of probability distribution?


ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution, properties



22. On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?



23. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who

has not studied for the test decides to answer all questions randomly. What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?


ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 24. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab

conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.

a) Most of the weeks resulted in rat costs of $13.00. b) The median cost for the distribution of rat costs is $13.00. c) The expected or mean cost for all weekly rat purchases is $13.00. d) The rat cost that occurs more often than any other is $13.00.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean (expected value), probability distribution



25. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year’s rat orders be, assuming this distribution does not change?

a) $520 b) $637 c) $650 d) $780

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean (expected value), probability distribution

26. The local police department must write, on average, 5 tickets a day to keep department revenues

at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

a) The number of tickets that is written most often is 6.5 tickets per day. b) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5

tickets written. c) If we sampled all days, the arithmetic average or expected number of tickets written

would be 6.5 tickets per day. d) The mean has no interpretation since 0.5 ticket can never be written.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean (expected value), Poisson distribution

27. True or False: The Poisson distribution can be used to model a continuous random variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties 28. True or False: Another name for the mean of a probability distribution is its expected value.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mean (expected value)



29. True or False: The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties 30. True or False: The number of customers arriving at a department store in a 5-minute period has a

Poisson distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties

31. True or False: The number of males selected in a sample of 5 students taken without replacement

from a class of 9 females and 18 males has a binomial distribution.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: hypergeometric distribution, properties

32. True or False: The number of males selected in a sample of 5 students taken without replacement

from a class of 9 females and 18 males has a hypergeometric distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: hypergeometric distribution, properties

33. True or False: The diameters of 10 randomly selected bolts have a binomial distribution.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 34. True or False: The largest value that a Poisson random variable X can have is n.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties



35. True or False: In a Poisson distribution, the mean and standard deviation are equal.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties

36. True or False: In a Poisson distribution, the mean and variance are equal.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 37. True or False: If π remains constant in a binomial distribution, an increase in n will increase the

variance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties

38. True or False: If π remains constant in a binomial distribution, an increase in n will not change

the mean.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties

39. True or False: Suppose that a judge’s decisions follow a binomial distribution and that his verdict

is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: binomial distribution, probability 40. True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson

process. The mean number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.05041.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, probability



41. True or False: The covariance between two investments is equal to the sum of the variances of the investments.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: covariance, variance

42. True or False: If the covariance between two investments is zero, the variance of the sum of the

two investments will be equal to the sum of the variances of the investments.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: covariance, variance

43. True or False: The expected return of the sum of two investments will be equal to the sum of the

expected returns of the two investments plus twice the covariance between the investments.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value)

44. True or False: The variance of the sum of two investments will be equal to the sum of the

variances of the two investments plus twice the covariance between the investments.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: covariance, variance

45. True or False: The variance of the sum of two investments will be equal to the sum of the

variances of the two investments when the covariance between the investments is zero.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: covariance, variance

46. True or False: The expected return of a two-asset portfolio is equal to the product of the weight

assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: portfolio, mean (expected value)



SCENARIO 5-1 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.

47. Referring to Scenario 5-1, the probability that both sound an alarm in the presence of smoke is

________.

ANSWER: 0.64 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution

48. Referring to Scenario 5-1, the probability that neither sound an alarm in the presence of smoke is

________.


49. Referring to Scenario 5-1, the probability that at least one sounds an alarm in the presence of

smoke is ________.

ANSWER: 0.96 TYPE: FI DIFFICULTY: Difficult KEYWORDS: binomial distribution

SCENARIO 5-2

A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).

50. Referring to Scenario 5-2, the probability that all 3 businesses succeed is ________.

ANSWER: 0.216 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 51. Referring to Scenario 5-2, the probability that all 3 businesses fail is ________.




52. Referring to Scenario 5-2, the probability that at least 1 business succeeds is ________.

ANSWER: 0.936 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 53. Referring to Scenario 5-2, the probability that exactly 1 business succeeds is ________.

ANSWER: 0.288 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 54. If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .

ANSWER: 0.4116 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution

55. If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ .


56. If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .


57. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5

students is to be selected. The probability that exactly 1 prefers brand C is ________.



students is to be selected. The probability that at least 1 prefers brand C is ________.




59. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 3 prefer brand C is ________.

ANSWER: 0.3456 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution 60. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5

students is to be selected. The probability that exactly 4 prefer brand C is ________.



students is to be selected. The probability that 2 or fewer prefer brand C is ________.



students is to be selected. The probability that more than 3 prefer brand C is ________.



students is to be selected. The probability that fewer than 2 prefer brand C is ________.



students is to be selected. The mean number that you would expect to prefer brand C is ________.

ANSWER: 3 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, mean



65. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The variance of the number that prefer brand C is ________.

ANSWER: 1.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, variance SCENARIO 5-3

The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.

X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05

66. Referring to Scenario 5-3, the probability of no retransmissions is ________.

ANSWER: 0.35 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution

67. Referring to Scenario 5-3, the probability of at least one retransmission is ________.


68. Referring to Scenario 5-3, the mean or expected value for the number of retransmissions is

________.

ANSWER: 1.0 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, mean (expected value), 69. Referring to Scenario 5-3, the variance for the number of retransmissions is ________.

ANSWER: 0.80 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, variance

70. Referring to Scenario 5-3, the standard deviation of the number of retransmissions is ________.

ANSWER: 0.894 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, standard deviation



71. In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she does not get audited is ________.

ANSWER: 0.2373 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 72. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,

11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited once is ________.


73. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,

11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited at least once is ________.

ANSWER: 0.7627 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 74. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,

11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited no more than 2 times is ________.



11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The expected number of times she will be audited is ________.

ANSWER: 1.25 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, mean (expected value),



76. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The variance of the number of times she will be audited is ________.

ANSWER: 0.9375 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution, variance


11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The standard deviation of the number of times she will be audited is ________.

ANSWER: 0.968 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution, standard deviation SCENARIO 5-4

The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.

X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05

78. Referring to Scenario 5-4, the probability of 3 accidents is ________.


79. Referring to Scenario 5-4, the probability of at least 1 accident is ________.

ANSWER: 0.90 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution 80. Referring to Scenario 5-4, the mean or expected value of the number of accidents is ________.

ANSWER: 2.0 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, mean,



81. Referring to Scenario 5-4, the variance of the number of accidents is ________.

ANSWER: 1.4 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, variance

82. Referring to Scenario 5-4, the standard deviation of the number of accidents is ________.

ANSWER: 1.18 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, standard deviation

83. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of

6 outages per year. The probability that there will be exactly 3 power outages in a year is ____________.

ANSWER: 0.0892 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution 84. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of

6 outages per year. The probability that there will be at least 3 power outages in a year is ____________.

ANSWER: 0.9380 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Poisson distribution


6 outages per year. The probability that there will be at least 1 power outage in a year is ____________.

ANSWER: 0.9975 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Poisson distribution


6 outages per year. The probability that there will be no more than 1 power outage in a year is ____________.




87. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be between 1 and 3 inclusive power outages in a year is ____________.

ANSWER: 0.1487 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Poisson distribution


6 outages per year. The variance of the number of power outages is ____________.

ANSWER: 6 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution

89. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.

The probability of seven 911 calls in a day is ____________.

ANSWER: 0.0901 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution 90. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.

The probability of seven or eight 911 calls in a day is ____________.

ANSWER: 0.2027 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Poisson distribution 91. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.

The probability of 2 or more 911 calls in a day is ____________.


92. The number of 911 calls in a small city has a Poisson distribution with a mean of 10.0 calls a

day. The standard deviation of the number of 911 calls in a day is ____________.

ANSWER: 3.16 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution



93. An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?

ANSWER: 0.1213 TYPE: FI DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 94. An Undergraduate Study Committee of 6 members at a major university is to be formed from a

pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that all of the members will be men?

ANSWER: 0.1379 TYPE: FI DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 95. A debate team of 4 members for a high school will be chosen randomly from a potential group of

15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that none of the members chosen for the team have any competition experience?

ANSWER: 0.1538 TYPE: FI DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 96. A debate team of 4 members for a high school will be chosen randomly from a potential group of

15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that at least 1 of the members chosen for the team have some prior competition experience?

ANSWER: 0.8462 TYPE: FI DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution 97. A debate team of 4 members for a high school will be chosen randomly from a potential group of

15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that no more than 1 of the members chosen for the team have some prior competition experience?

ANSWER: 0.5934 TYPE: FI DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution



98. A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that exactly half of the members chosen for the team have some prior competition experience?

ANSWER: 0.3297 TYPE: FI DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 99. The Department of Commerce in a particular state has determined that the number of small

businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.

ANSWER: 0.8811 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution

100. The Department of Commerce in a particular state has determined that the number of small

businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that exactly 5 bankruptcies occur next month.

ANSWER: 0.1487 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution

101. Current estimates suggest that 75% of the home-based computers in a foreign country have

access to on-line services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that fewer than 10 of those sampled currently have access to on-line services.

ANSWER: 0.0039 TYPE: PR DIFFICULTY: Moderate KEYWORDS: binomial distribution 102. Current estimates suggest that 75% of the home-based computers in a foreign country have

access to on-line services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that more than 9 of those sampled currently do not have access to on-line services.

ANSWER: 0.0139 TYPE: PR DIFFICULTY: Difficult KEYWORDS: binomial distribution



103. A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability all of the hotels in the sample offered hairdryers in the bathrooms.

ANSWER: 0.0008 TYPE: PR DIFFICULTY: Moderate KEYWORDS: binomial distribution

104. A national trend predicts that women will account for half of all business travelers in the next 3

years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

ANSWER: 0.2264 TYPE: PR DIFFICULTY: Moderate KEYWORDS: binomial distribution

105. A national trend predicts that women will account for half of all business travelers in the next 3

years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.

ANSWER: 0.1133 TYPE: PR DIFFICULTY: Difficult KEYWORDS: binomial distribution 106. The local police department must write, on average, 5 tickets a day to keep department

revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. Find the probability that less than 6 tickets are written on a randomly selected day from this population.

ANSWER: 0.3837 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution



107. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. Find the probability that exactly 6 tickets are written on a randomly selected day from this population.

ANSWER: 0.1586 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution SCENARIO 5-5 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. 108. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, no more than 2 of the cars have defective radios? ANSWER: 0.6863 TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution 109. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, exactly half of the cars have defective radios? ANSWER: 0.0773 TYPE: PR DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 110. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, none of the cars have defective radios? ANSWER: 0.0802 TYPE: PR DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 111. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, at least half of the cars have defective radios? ANSWER: 0.09388 TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution



112. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, no more than half of the cars have defective radios?

ANSWER: 0.9834 TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution 113. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, no more than 2 of the cars have defective radios? ANSWER: 0.6863 TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution 114. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, exactly two of the cars have non-defective radios? ANSWER: 0.001543 TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution 115. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, at most three of the cars have non-defective radios? ANSWER: 0.01661 TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution 116. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,

when each is tested, no more than half of the cars have non-defective radios? ANSWER: 0.09388 TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution



SCENARIO 5-6 The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per shift is 6.0. 117. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has

produced 4.0 bad bulbs. ANSWER: 0.1339 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 118. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has

produced fewer than 5.0 bad bulbs. ANSWER: 0.2851 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 119. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has

produced at least 6.0 bad bulbs. ANSWER: 0.5543 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 120. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has

produced between 5.0 and 8.0 inclusive bad bulbs. ANSWER: 0.5622 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 121. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has

less than 5.0 or more than 8.0 bad bulbs. ANSWER: 0.4378 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Poisson distribution



SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighborhood A Neighborhood B

.25 −$22,500 $30,500

.40 $10,000 $25,000

.35 $40,500 $10,500 122. Referring to Scenario 5-7, what is the expected value gain for the house in neighborhood A? ANSWER: $ 12,550 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, mean (expected value), 123. Referring to Scenario 5-7, what is the expected value gain for the house in neighborhood B? ANSWER: $ 21,300 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, mean (expected value), 124. Referring to Scenario 5-7, what is the variance of the gain in value for the house in

neighborhood A? ANSWER: 583,147,500 dollars2 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, variance 125. Referring to Scenario 5-7, what is the variance of the gain in value for the house in

neighborhood B? ANSWER: 67,460,000 dollars2 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, variance 126. Referring to Scenario 5-7, what is the standard deviation of the value gain for the house in

neighborhood A? ANSWER: $24,148.45 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, standard deviation



127. Referring to Scenario 5-7, what is the standard deviation of the value gain for the house in neighborhood B?

ANSWER: $8,213.40 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, standard deviation 128. Referring to Scenario 5-7, what is the covariance of the two houses? ANSWER: −190,040,000 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, covariance 129. Referring to Scenario 5-7, what is the expected value gain if you invest in both houses? ANSWER: $ 33,850 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean of the sum 130. Referring to Scenario 5-7, what is the total variance of value gain if you invest in both houses? ANSWER: 270,527,500 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, variance of the sum 131. Referring to Scenario 5-7, what is the total standard deviation of value gain if you invest in

both houses? ANSWER: $ 16,447.72 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation of the sum 132. Referring to Scenario 5-7, if you can invest half of your money on the house in neighborhood

A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?

ANSWER: $ 16,925 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value)



133. Referring to Scenario 5-7, if you can invest half of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

ANSWER: $ 8,223.86 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation, risk 134. Referring to Scenario 5-7, if you can invest 10% of your money on the house in neighborhood


ANSWER: $ 20,425 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value) 135. Referring to Scenario 5-7, if you can invest 10% of your money on the house in neighborhood

A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?





ANSWER: $ 2,392.04 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation, risk



138. Referring to Scenario 5-7, if you can invest 70% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?







ANSWER: $ 20,947.96 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation, risk 142. Referring to Scenario 5-7, if your investment preference is to maximize your expected return

while exposing yourself to the minimal amount of risk, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

ANSWER: 30% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value), standard deviation, risk, coefficient of variation



143. Referring to Scenario 5-7, if your investment preference is to maximize your expected return and not worry at all about the risk that you have to take, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

ANSWER: 10% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value) 144. Referring to Scenario 5-7, if your investment preference is to minimize the amount of risk that

you have to take and do not care at all about the expected return, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

ANSWER: 30% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation, risk SCENARIO 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270

145. Referring to Scenario 5-8, the table above is called the ______________ for the two designs. ANSWER: probability distribution TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution 146. Referring to Scenario 5-8, what is your expected profit when Design A is chosen? ANSWER: $256 thousands or $256,000 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, mean (expected value)



147. Referring to Scenario 5-8, what is your expected profit when Design B is chosen? ANSWER: $340 thousands or $340,000 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, mean (expected value) 148. Referring to Scenario 5-8, what is the variance of your profit when Design A is chosen? ANSWER:

24,144 1,000× or 4,144,000,000 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, variance 149. Referring to Scenario 5-8, what is the variance of your profit when Design B is chosen? ANSWER:

28, 400 1,000× or 8,400,000,000 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, variance 150. Referring to Scenario 5-8, what is the standard deviation of your profit when Design A is

chosen? ANSWER: $64.37391 thousands or $64,373.91 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, standard deviation 151. Referring to Scenario 5-8, what is the standard deviation of your profit when Design B is

chosen? ANSWER: $91.65151 thousands or $91,651.51 TYPE: PR DIFFICULTY: Easy KEYWORDS: portfolio, standard deviation 152. Referring to Scenario 5-8, what is the covariance of the profits from the two different designs? ANSWER:

24,320 1,000− × or −4,320,000,000 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, covariance



153. Referring to Scenario 5-8, what is the expected profit if you increase the shift of your production lines and choose to produce both designs?

ANSWER: $596 thousands or $596,000 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean of the sum 154. Referring to Scenario 5-8, what is the total variance of the profit if you increase the shift of

your production lines and choose to produce both designs? ANSWER:

23,904 1,000× or 3,904,000,000 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, variance of the sum 155. Referring to Scenario 5-8, what is the total standard deviation of the profit if you increase the

shift of your production lines and choose to produce both designs? ANSWER: $62.48200 thousands or $62,482.00 TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation of the sum 156. Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and

Design B for the other half, what is your expected profit? ANSWER: $ 298 thousands or $298,000 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, mean (expected value) 157. Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and

Design B for the other half, what is the risk of your investment? ANSWER: $31.241 thousands or $31,241 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, standard deviation, risk 158. Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and

Design B for the other half, what is the coefficient of variation of your investment? ANSWER: 10.48% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, coefficient of variation



159. Referring to Scenario 5-8, if you decide to choose Design A for 10% of the production lines and Design B for the remaining production lines, what is the expected profit?

ANSWER: $ 331.6 thousands or $331,600 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, mean (expected value) 160. Referring to Scenario 5-8, if you decide to choose Design A for 10% of the production lines

and Design B for the remaining production lines, what is the risk of your investment? ANSWER: $77.89634 thousands or $77,896.34 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, standard deviation, risk 161. Referring to Scenario 5-8, if you decide to choose Design A for 10% of the production lines

and Design B for the remaining production lines, what is the coefficient of variation of your investment?

ANSWER: 23.49% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, coefficient of variation 162. Referring to Scenario 5-8, if you decide to choose Design A for 30% of the production lines

and Design B for the remaining production lines, what is the expected profit? ANSWER: $314.8 thousands or $314,800 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, mean (expected value) 163. Referring to Scenario 5-8, if you decide to choose Design A for 30% of the production lines

and Design B for the remaining production lines, what is the risk of your investment? ANSWER: $51.71615 thousands or $51,716.15 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, standard deviation, risk 164. Referring to Scenario 5-8, if you decide to choose Design A for 30% of the production lines


ANSWER: 16.42% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, coefficient of variation



165. Referring to Scenario 5-8, if you decide to choose Design A for 70% of the production lines and Design B for the remaining production lines, what is the expected profit?

ANSWER: $281.2 thousands or $281,200 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, mean (expected value) 166. Referring to Scenario 5-8 if you decide to choose Design A for 70% of the production lines and

Design B for the remaining production lines, what is the risk of your investment? ANSWER: $31.17948 thousands or $31,179.48 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, standard deviation, risk 167. Referring to Scenario 5-8, if you decide to choose Design A for 70% of the production lines


ANSWER: 11.09% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, coefficient of variation 168. Referring to Scenario 5-8, if you decide to choose Design A for 90% of the production lines

and Design B for the remaining production lines, what is the expected profit? ANSWER: $264.4 thousands or $264,400 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, mean (expected value) 169. Referring to Scenario 5-8 if you decide to choose Design A for 90% of the production lines and

Design B for the remaining production lines, what is the risk of your investment? ANSWER: $51.60465 thousands or $ 51,604.65 TYPE: PR DIFFICULTY: Difficult KEYWORDS: portfolio, standard deviation, risk 170. Referring to Scenario 5-8, if you decide to choose Design A for 90% of the production lines


ANSWER: 19.52% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, coefficient of variation



171. Referring to Scenario 5-8, if your investment preference is to maximize your expected profit while exposing yourself to the minimal amount of risk, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

ANSWER: 50% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value), standard deviation, risk, coefficient of variation NOTE: 50% yields the lowest coefficient of variation 172. Referring to Scenario 5-8, if your investment preference is to maximize your expected profit

and not worry at all about the risk that you have to take, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

ANSWER: 10% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, mean (expected value) 173. Referring to Scenario 5-8, if your investment preference is to minimize the amount of risk that

you have to take and do not care at all about the expected profit, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

ANSWER: 70% TYPE: PR DIFFICULTY: Moderate KEYWORDS: portfolio, standard deviation, risk SCENARIO 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. 174. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have no mishandled bags? ANSWER: 0.0172 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution



175. Referring to Scenario 5-9, what is the probability that in the next 1,000 custoers, the chain will have at least one mishandled bags?

ANSWER: 0.9828 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 176. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have at least two mishandled bags? ANSWER: 0.9127 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 177. Referring to Scenario 5-9, what is the probability that in the next 1,000 customer, the hotel

chain will have no more than three mishandled bags? ANSWER: 0.4218 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 178. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have no more than four mishandled bags? ANSWER: 0.6171 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 179. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have fewer than six mishandled bags? ANSWER: 0.7757 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 180. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have fewer than eight mishandled bags? ANSWER: 0.9452 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution



181. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than eight mishandled bags?

ANSWER: 0.02320 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 182. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have more than ten mishandled bags? ANSWER: 0.003172 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 183. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have between two and four inclusive mishandled bags? ANSWER: 0.5298 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 184. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have more than five but less than eight mishandled bags? ANSWER: 0.1695 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 185. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have less than two or more than eight mishandled bags? ANSWER: 0.1105 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 186. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have no more than two or at least eight mishandled bags? ANSWER: 0.2842 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution



187. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have less than two and more than eight mishandled bags?

ANSWER: 0 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Poisson distribution 188. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel

chain will have no more than two and at least eight mishandled bags? ANSWER: 0 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Poisson distribution SCENARIO 5-10 An accounting firm in a college town usually recruits employees from two of the universities in town. This year, there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. 189. Referring to Scenario 5-10, what is the probability that two of the new employees will be from

University A? ANSWER: 0.0135 or 1.35% TYPE: PR DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 190. Referring to Scenario 5-10, what is the probability that all six of the new employees will be

from University A? ANSWER: 0.1291 or 12.91% TYPE: PR DIFFICULTY: Easy KEYWORDS: hypergeometric distribution 191. Referring to Scenario 5-10, what is the probability that none of the new employees will be

from University B? ANSWER: 0.1291 or 12.91% TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution



192. Referring to Scenario 5-10, what is the probability that none of the new employees will be from University A?

ANSWER: 0 or “it can never happen” TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution 193. Referring to Scenario 5-10, what is the probability that all of the new employees will be from

University B? ANSWER: 0 or “it can never happen” TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution 194. Referring to Scenario 5-10, what is the probability that at least one of the new employees will

be from University A? ANSWER: 1.0 or 100% TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution 195. Referring to Scenario 5-10, what is the probability that no more than four of the new

employees will be from University A? ANSWER: 0.4835 or 48.35% TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution 196. Referring to Scenario 5-10, what is the probability that at least two of the new employees will

be from University B? ANSWER: 0.4835 or 48.35% TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution 197. Referring to Scenario 5-10, what is the probability that more than four of the new employees

will be from University A? ANSWER: 0.5165 or 51.65% TYPE: PR DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution



198. Referring to Scenario 5-10, what is the probability that no more than two of the new employees will be from University B?

ANSWER: 0.5165 or 51.65% TYPE: PR DIFFICULTY: Difficult KEYWORDS: hypergeometric distribution SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month. Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. 199. Referring to Scenario 5-11, what is mean number of transactions per month for this subscriber? ANSWER: 5 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 200. Referring to Scenario 5-11, what is variance of the number of transactions per month for this

subscriber? ANSWER: 5 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 201. Referring to Scenario 5-11, what is probability that exactly ten security transactions will be

conducted in one month? ANSWER: 0.0181 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 202. Referring to Scenario 5-11, what is probability that at least five security transactions will be

conducted in one month? ANSWER: 0.5595 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution



203. Referring to Scenario 5-11, what is probability that no more than five security transactions will be conducted in one month?

ANSWER: 0.6160 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 204. Referring to Scenario 5-11, what is probability that no security transaction will be conducted in

one month? ANSWER: 0.0067 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 205. Referring to Scenario 5-11, what is probability that more than two security transactions will be

conducted in one month? ANSWER: 0.8753 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 206. Referring to Scenario 5-11, what is probability that fewer than two security transactions will be

conducted in one month? ANSWER: 0.0404 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution


chapter 5: discrete probability distributions · 2019-12-19 · discrete probability distributions...

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