University of North Carolina, Greensboro

ECO 25

Chapter 5

DISCRETE PROBABILITY DISTRIBUTIONS 

MULTIPLE CHOICE QUESTIONS

1)A numerical description of the outcome of an experiment is called a

1. 1. descriptive statistic
   2. probability function
   3. variance
   4. random variable

2. A random variable that can assume only a finite number of values is referred to as a(n)
   1. infinite sequence
   2. finite sequence
   3. discrete random variable
   4. discrete probability function

3. A continuous random variable may assume
   1. any value in an interval or collection of intervals
   2. only integer values in an interval or collection of intervals
   3. only fractional values in an interval or collection of intervals
   4. only the positive integer values in an interval

6. An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is the number of sales made.

This random variable is a

6. 1. discrete random variable
   2. continuous random variable
7. complex random variable

8. None of the answers is correct.

5. The number of customers that enter a store during one day is an example of
   1. a continuous random variable
   2. a discrete random variable
   3. either a continuous or a discrete random variable, depending on the number of the customers
   4. either a continuous or a discrete random variable, depending on the gender of the customers

8. An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a
   1. discrete random variable
   2. continuous random variable
   3. complex random variable
   4. None of the answers is correct.

7. The weight of an object, measured in grams, is an example of
   1. a continuous random variable
   2. a discrete random variable
   3. either a continuous or a discrete random variable, depending on the weight of the object
   4. either a continuous or a discrete random variable depending on the units of measurement

8. The weight of an object, measured to the nearest gram, is an example of
   1. a continuous random variable
   2. a discrete random variable
   3. either a continuous or a discrete random variable, depending on the weight of the object

1. 4. either a continuous or a discrete random variable depending on the units of measurement

8. A description of how the probabilities are distributed over the values the random variable can assume is called a
   1. probability distribution
   2. probability function
   3. random variable
   4. expected value

10. Which of the following is(are) required condition(s) for a discrete probability function?

a.         ?f(x) = 0

2. f(x) ? 1 for all values of x
3. f(x) < 0
4. None of the answers is correct.

11. Which of the following is not a required condition for a discrete probability function?
    1. f(x) ? 0 for all values of x

b.         ?f(x) = 1

c.         ?f(x) = 0

d.         All of the answers are correct.

13. Which of the following statements about a discrete random variable and its probability distribution are true?
    1. Values of the random variable can never be negative.
    2. Negative values of f(x) are allowed as long as ?f(x) = 1.
    3. Values of f(x) must be greater than or equal to zero.
    4. The values of f(x) increase to a maximum point and then decrease.

13. A measure of the average value of a random variable is called a(n)
    1. variance
    2. standard deviation
    3. expected value
    4. None of the answers is correct.

14. A weighted average of the value of a random variable, where the probability function provides weights is known as

1. 1. a probability function
   2. a random variable
   3. the expected value
   4. None of the answers is correct

15. The expected value of a random variable is the
    1. value of the random variable that should be observed on the next repeat of the experiment
    2. value of the random variable that occurs most frequently
    3. square root of the variance
    4. None of the is correct.

16. The expected value of a discrete random variable
    1. is the most likely or highest probability value for the random variable
    2. will always be one of the values x can take on, although it may not be the highest probability value for the random variable

1. 3. is the average value for the random variable over many repeats of the experiment
   4. All of the answers are correct.

13. Excel’s                     function can be used to compute the expected value of a discrete random variable.
    1. SUMPRODUCT
    2. AVERAGE
    3. MEDIAN
    4. VAR

18. Variance is
    1. a measure of the average, or central value of a random variable
    2. a measure of the dispersion of a random variable
    3. the square root of the standard deviation
    4. the sum of the deviation of data elements from the mean

19. The variance is a weighted average of the
    1. square root of the deviations from the mean
    2. square root of the deviations from the median
    3. squared deviations from the median
    4. squared deviations from the mean

13. Excel’s                     function can be used to compute the variance of a discrete random variable.
    1. SUMPRODUCT
    2. AVERAGE
    3. MEDIAN
    4. VAR

21. The standard deviation is the
    1. variance squared
    2. square root of the sum of the deviations from the mean
    3. same as the expected value
    4. positive square root of the variance

22. X is a random variable with the probability function: f(x) = x/6   for x = 1,2 or 3. The expected value of x is

Exhibit 5-1

The following represents the probability distribution for the daily demand of microcomputers at a local store.

13.       Refer to Exhibit 5-1. The probability of having a demand for at least two microcomputers is

Exhibit 5-2

The probability distribution for the daily sales at Michael's Co. is given below.

25. Refer to Exhibit 5-2. The expected daily sales are

26. Refer to Exhibit 5-2. The probability of having sales of at least $50,000 is

Exhibit 5-3

The probability distribution for the number of goals the Lions soccer team makes per game is given below.

27. Refer to Exhibit 5-3. The expected number of goals per game is

13.       Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score at least 1 goal?

13.       Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score less than 3 goals?

a.         0.85

b.         0.55

c.         0.45

d.         0.80

13.       Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score no goals?

a.         0.95

b.         0.85

c.         0.75

d.         None of the answers is correct.

Exhibit 5-4

A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.

31. Refer to Exhibit 5-4. The expected number of machine breakdowns per month is

a.         2

b.         1.70

3. one
4. None of the alternative answers is correct.

32. Refer to Exhibit 5-4. The probability of at least 3 breakdowns in a month is a.  0.5

b.         0.10

c.         0.30

d.         None of the alternative answers is correct.

33. Refer to Exhibit 5-4. The probability of no breakdowns in a month is a. 0.88

b.         0.00

c.         0.50

d.         None of the alternative answers is correct.

Exhibit 5-5

AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.

34. Refer to Exhibit 5-5. The expected number of new clients per month is

35. Refer to Exhibit 5-5. The variance is

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

13.       The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.

The mean and the standard deviation for the number of electrical outages (respectively) are

a.         2.6 and 5.77

b.         0.26 and 0.577

3. 3 and 0.01
4. 0 and 0.8

Exhibit 5-6

Probability Distribution

38. Refer to Exhibit 5-6. The expected value of x equals

a.         24

b.         25

c.         30

d.         100

39. Refer to Exhibit 5-6. The variance of x equals

Exhibit 5-7

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information.

40. Refer to Exhibit 5-7. The expected number of cups of coffee is

41. Refer to Exhibit 5-7. The variance of the number of cups of coffee is

42. Which of the following is a characteristic of a binomial experiment?
    1. at least 2 outcomes are possible
    2. the probability of success changes from trial to trial
    3. the trials are independent
    4. All of these answers are correct.

43. In a binomial experiment, the
    1. probability of success does not change from trial to trial
    2. probability of success does change from trial to trial
    3. probability of success could change from trial to trial, depending on the situation under consideration
    4. All of these answers are correct.

44. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
    1. the experiment has a sequence of n identical trials
    2. exactly two outcomes are possible on each trial
    3. the trials are dependent
    4. the probabilities of the outcomes do not change from one trial to another

45. Which of the following is not a property of a binomial experiment?
    1. the experiment consists of a sequence of n identical trials
    2. each outcome can be referred to as a success or a failure
    3. the probabilities of the two outcomes can change from one trial to the next
    4. the trials are independent

46. A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a
    1. uniform probability distribution
    2. binomial probability distribution
    3. hypergeometric probability distribution
    4. normal probability distribution

47. The binomial probability distribution is used with
    1. a continuous random variable
    2. a discrete random variable
    3. any distribution, as long as it is not normal
    4. All of these answers are correct.

48. If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of 4 successes in 15 trials, the correct probability function to use is the
    1. standard normal probability density function
    2. normal probability density function
    3. Poisson probability function
    4. binomial probability function

49. In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

50. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

51. A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

52. Excel’s BINOMDIST function can be used to compute
    1. bin width for histograms
    2. binomial probabilities
    3. cumulative binomial probabilities
    4. Both binomial probabilities and cumulative binomial probabilities are correct.

53. Excel’s BINOMDIST function has how many arguments?
    1. 2
    2. 3
    3. 4
    4. 5

54. When using Excel’s BINOMDIST function, one should choose TRUE for the fourth argument if
    1. a probability is desired
    2. a cumulative probability is desired
    3. the expected value is desired
    4. the correct answer is desired

55. The expected value for a binomial probability distribution is
    1. E(x) = pn(1 - n)

b.         E(x) = p(1 - p)

3. E(x) = np
4. E(x) = np(1 - p)

56. The variance for the binomial probability distribution is
    1. Var(x) = p(1 - p)
    2. Var(x) = np
    3. Var(x) = n(1 - p)
    4. Var(x) = np(1 - p)

57. The standard deviation of a binomial distribution is
    1. E(x) = pn(1 - n)
    2. E(x) = np(1 - p)
    3. E(x) = np
    4. None of the alternative answers is correct.

58. Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is

a.         0.50

b.         0.30

c.         50

d.         Not enough information is given to answer this question.    

59. Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is

a.         20

b.         12

c.         3.46

d.         Not enough information is given to answer this question.

60. Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

Exhibit 5-8

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.

61. Refer to Exhibit 5-8. What is the random variable in this experiment?
    1. the 60% of female students
    2. the random sample of 8 students
    3. the number of female students out of 8
    4. the student body size

62. Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?

63. Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 7 are female?

a.         0.1064

b.         0.0896

c.         0.0168

d.         0.8936      

64. Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 6 are male?

Exhibit 5-9

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.

65. Refer to Exhibit 5-9. What is the random variable in this experiment?
    1. the 40% of female registered voters
    2. the random sample of 5 voters
    3. the number of female voters out of 5
    4. the number of registered voters in the nation

66. Refer to Exhibit 5-9. The probability that the sample contains 2 female voters is

67. Refer to Exhibit 5-9. The probability that there are no females in the sample is

Exhibit 5-10

The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.

68. Refer to Exhibit 5-10. What is the random variable in this experiment?
    1. the 0.8 probability of catching fish
    2. the 3 days
    3. the number of days out of 3 that Pete catches fish
    4. the number of fish in the body of water

69. Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is

70. Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is

71. Refer to Exhibit 5-10. The expected number of days Pete will catch fish is

72. Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is

73. The Poisson probability distribution is a
    1. continuous probability distribution
    2. discrete probability distribution
    3. uniform probability distribution
    4. normal probability distribution

74. The Poisson probability distribution is used with
    1. a continuous random variable
    2. a discrete random variable
    3. either a continuous or discrete random variable
    4. any random variable

75. When dealing with the number of occurrences of an event over a specified interval of time or space and when the occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval, the appropriate probability distribution is a
    1. binomial distribution
    2. Poisson distribution
    3. normal distribution

1. 4. hypergeometric probability distribution

76. Excel’s POISSON function can be used to compute
    1. bin width for histograms
    2. Poisson probabilities
    3. cumulative Poisson probabilities
    4. Both Poisson probabilities and cumulative Poisson probabilities are correct.

77. Excel’s POISSON function has how many arguments?

78. When using Excel’s POISSON function, one should choose TRUE for the third argument if
    1. a probability is desired
    2. a cumulative probability is desired
    3. the expected value is desired
    4. the correct answer is desired

79. In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the
    1. normal distribution
    2. binomial distribution
    3. Poisson distribution
    4. uniform distribution

Exhibit 5-11

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

80. Refer to Exhibit 5-11. The random variable x satisfies which of the following probability distributions?
    1. normal
    2. Poisson
    3. binomial
    4. Not enough information is given to answer this question.

81. Refer to Exhibit 5-11. The appropriate probability distribution for the random variable is
    1. discrete
    2. continuous
    3. either a or b depending on how the interval is defined
    4. not enough information is given

82. Refer to Exhibit 5-11. The expected value of the random variable x is
    1. 2

b.         5.3

c.         10

d.         2.30    

83. Refer to Exhibit 5-11. The probability that there are 8 occurrences in ten minutes is

84. Refer to Exhibit 5-11. The probability that there are less than 3 occurrences is a      0659

b.......... 0948

c.......... 1016

d.         .1239

85. When sampling without replacement, the probability of obtaining a certain sample is best given by a
    1. hypergeometric distribution
    2. binomial distribution
    3. Poisson distribution
    4. normal distribution

86. The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution the
    1. probability of success must be less than 0.5
    2. probability of success changes from trial to trial
    3. trials are independent of each other
    4. random variable is continuous

87. Excel’s HYPGEOMDIST function can be used to compute
    1. bin width for histograms
    2. hypergeometric probabilities
    3. cumulative hypergeometric probabilities
    4. Both hypergeometric probabilities and cumulative hypergeometric probabilities are correct.

88. Excel’s HYPGEOMDIST function has how many arguments?
    1. 2
    2. 3
    3. 4
    4. 5