File: ch05 Chapter 5: Discrete Distributions

True/False

1. Variables which take on values only at certain points over a given interval are called continuous random variables

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

2. A variable that can take on values at any point over a given interval is called a discrete random variable

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

3. The number of visitors to a website each day is an example of a discrete random variable

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

4. The amount of time a patient waits in a doctor’s office is an example of a continuous random variable

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

5. The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Easy

Learning Objective: 5.2: Determine the mean variance and standard deviation of a discrete distribution.

6. To compute the variance of a discrete distribution it is not necessary to know the mean of the distribution.

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Medium

Learning Objective: 5.2: Determine the mean variance and standard deviation of a discrete distribution.

7. The variance of a discrete distribution increases if we add a positive constant to each one of its value.

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Medium

Learning Objective: 5.2: Determine the mean variance and standard deviation of a discrete distribution.

8. In a binomial experiment any single trial contains only two possible outcomes and successive trials are independent.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

9. In a binomial distribution p the probability of getting a successful outcome on any single trial increases proportionately with every success.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

10. The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20th of the population size.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

11. For a binomial distribution in which the probability of success is p = 0.5 the variance is twice the mean.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Hard

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

12. The Poisson distribution is a continuous distribution which is very useful in solving waiting time problems

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

13. Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

14. The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

15. For the Poisson distribution the mean represents twice the value of the standard deviation..

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

16. A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Mexico.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

17. For the Poisson distribution the mean and the variance are the same.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

18. Poisson distribution describes the occurrence of discrete events that may occur over a continuous interval of time or space.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Hard

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

19. A Poisson distribution is characterized by one parameter.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

20. A hypergeometric distribution applies to experiments in which the trials represent sampling with replacement.

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Easy

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

21. As in a binomial distribution each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes i.e. either a success or a failure.

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Medium

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

22. The number of successes in a hypergeometric distribution is unknown

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Hard

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

23. In a hypergeometric distribution the population N is finite and known.

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Hard

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Multiple Choice

24. The volume of liquid in an unopened 1-gallon can of paint is an example of _________.

a) the binomial distribution

b) both discrete and continuous variable

c) a continuous random variable

d) a discrete random variable

e) a constant

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Medium

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

25. The number of finance majors within the School of Business is an example of _______.

a) a discrete random variable

b) a continuous random variable

c) the Poisson distribution

d) the normal distribution

e) a constant

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

26. The speed at which a jet plane can fly is an example of _________.

a) neither discrete nor continuous random variable

b) both discrete and continuous random variable

c) a continuous random variable

d) a discrete random variable

e) a constant

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Medium

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

27. In American Roulette there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets 1 unit on red his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (or winning -1) is 20/38. Let x be the player profit per game. The mean (average) value of x is approximately_______________.

a) 0.0526

b) -0.0526

c) 1

d) -1

e) 0

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Easy

Learning Objective: 5.2: Determine the mean variance and standard deviation of a discrete distribution.

28. A recent analysis of the number of rainy days per month found the following outcomes and probabilities.

Number of Raining Days (x)

P(x)

3

.40

4

.20

5

.40

The mean of this distribution is _____________.

a) 2

b) 3

c) 4

d) 5

e) 0.5

b) p = 1.0

c) p = 0

d) p 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

39. The following graph is a binomial distribution with n = 6.

This graph reveals that ____________.

a) p = 0.5

b) p = 1.0

c) p = 0

d) p 0) is _______________.

a) 0.8171

b) 0.1074

c) 0.8926

d) 0.3020

e) 1.0000

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

49. Pinky Bauer Chief Financial Officer of Harrison Haulers Inc. suspects irregularities in the payroll system and orders an inspection of a random sample of vouchers issued since January 1 2006. A sample of ten vouchers is randomly selected without replacement from the population of 2000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors the mean value of x is __________.

a) 400

b) 2

c) 200

d) 5

e) 1

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

50. Pinky Bauer Chief Financial Officer of Harrison Haulers Inc. suspects irregularities in the payroll system and orders an inspection of a random sample of vouchers issued since January 1 2006. A sample of ten vouchers is randomly selected without replacement from the population of 2000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors the standard deviation of x is ______.

a) 1.26

b) 1.60

c) 14.14

d) 3.16

e) 0.00

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

51. Dorothy Little purchased a mailing list of 2000 names and addresses for her mail order business but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic and x is the number of non-authentic names in her sample P(x=0) is ______________.

a) 0.8154

b) 0.0467

c) 0.0778

d) 0.4000

e) 0.5000

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

52. Dorothy Little purchased a mailing list of 2000 names and addresses for her mail order business but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic and x is the number of non-authentic names in her sample P(x0) is ______________.

a) 0.2172

b) 0.9533

c) 0.1846

d) 0.9222

e) 1.0000

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

54. Dorothy Little purchased a mailing list of 2000 names and addresses for her mail order business but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic and x is the number on non-authentic names in her sample the expected (average) value of x is ______________.

a) 2.50

b) 2.00

c) 1.50

d) 1.25

e) 1.35

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

55. A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices 10% receive the discount. In a company audit 10 invoices are sampled at random. The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

a) 0.1937

b) 0.057

c) 0.001

d) 0.3486

e) 0.9298

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Hard

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

56. A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices 10% receive the discount. In a company audit 15 invoices are sampled at random. The mean (average) value of the number of the 15 sampled invoices that receive discount is _______

a) 1

b) 3

c) 1.5

d) 2

e) 10

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

57. In a certain communications system there is an average of 1 transmission error per 10 seconds. Assume that the distribution of transmission errors is Poisson. The probability of 1 error in a period of one-half minute is approximately ________

a) 0.1493

b) 0.3333

c) 0.3678

d) 0.1336

e) 0.03

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Hard

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

58. It is known that screws produced by a certain company will be defective with probability .01 independently of each other. The company sells the screws in packages of 25 and offers a money-back guarantee that at most 1 of the 25 screws is defective. Using Poisson approximation for binomial distribution the probability that the company must replace a package is approximately _________

a) 0.01

b) 0.1947

c) 0.7788

d) 0.0264

e) 0.2211

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Hard

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

59. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is _______.

a) 0.0940

b) 0.0417

c) 0.1500

d) 0.1008

e) 0.2890

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

60. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 3 cars arriving over a five-minute interval is _______.

a) 0.2700

b) 0.0498

c) 0.2240

d) 0.0001

e) 0.0020

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

61. Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes. The number of occurrences per hour follows a Poisson distribution with equal to _________

a) 5

b) 60

c) 30

d) 10

e) 20

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Hard

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

62. On Monday mornings customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval. Using the Poisson distribution the probability that five cars will arrive during the next fifteen-minute interval is _____________.

a) 0.1008

b) 0.0361

c) 0.1339

d) 0.1606

e) 0.5000

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

63. On Monday mornings customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen minute interval. Using the Poisson distribution the probability that five cars will arrive during the next five minute interval is _____________.

a) 0.1008

b) 0.0361

c) 0.1339

d) 0.1606

e) 0.3610

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Hard

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

64. The Poisson distribution is being used to approximate a binomial distribution. If n=30 and p=0.03 what value of lambda would be used?

a) 0.09

b) 9.0

c) 0.90

d) 90

e) 30

Ans: Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

65. The Poisson distribution is being used to approximate a binomial distribution. If n=60 and p=0.02 what value of lambda would be used?

a) 0.02

b) 12

c) 0.12

d) 1.2

e) 120

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

66. The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled with the _________.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

67. The number of defects per 1000 feet of extruded plastic pipe is best modeled with the ________________.

a) Poisson distribution

b) Pascal distribution

c) binomial distribution

d) hypergeometric distribution

e) exponential distribution

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

68. Which of the following conditions is not a condition for the hypergeometric distribution?

a) the probability of success is the same on each trial

b) sampling is done without replacement

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