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Multiple Choice

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

a. descriptive statistic

b. probability function

c. variance

d. random variable

ANSWER: d

2. A random variable that can assume only a finite number of values is referred to as a(n)

a. infinite sequence

b. finite sequence

c. discrete random variable

d. discrete probability function

ANSWER: c

3. 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

a. uniform probability distribution

b. binomial probability distribution

c. hypergeometric probability distribution

d. normal probability distribution

ANSWER: b

4. Variance is

a. a measure of the average, or central value of a random variable

b. a measure of the dispersion of a random variable

c. the square root of the standard deviation

d. the sum of the squared deviation of data elements from the mean

ANSWER: b

5. A continuous random variable may assume

a. any value in an interval or collection of intervals

b. only integer values in an interval or collection of intervals

c. only fractional values in an interval or collection of intervals

d. only the positive integer values in an interval

ANSWER: a

6. A description of the distribution of the values of a random variable and their associated probabilities is called a

a. probability distribution

b. random variance

c. random variable

d. expected value

ANSWER: a

7. Which of the following is a required condition for a discrete probability function?

a. f(x) = 0 for all values of x

b. f(x) 1 for all values of x

c. f(x) < 0 for all values of x
d. f(x) = 1 for all values of x
ANSWER: d
8. A measure of the average value of a random variable is called a(n)
a. variance
b. standard deviation
c. expected value
d. coefficient of variation
ANSWER: c
9. Which of the following is not a required condition for a discrete probability function?
a. f(x) 0 for all values of x
b. f(x) = 1 for all values of x
c. f(x) = 0 for all values of x
d. f(x) 1 for all values of x
ANSWER: c
10. The standard deviation is the
a. variance squared
b. square root of the sum of the deviations from the mean
c. same as the expected value
d. positive square root of the variance
ANSWER: d
11. The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the
a. square root of the deviations from the mean
b. square root of the deviations from the median
c. squared deviations from the median
d. squared deviations from the mean
ANSWER: d
12. A weighted average of the value of a random variable, where the probability function provides weights is known as
a. a probability function
b. a random variable
c. the expected value
d. random function
ANSWER: c
13. An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a
a. discrete random variable
b. continuous random variable
c. complex random variable
d. simplex random variable
ANSWER: a
14. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a
a. discrete random variable
b. continuous random variable
c. complex random variable
d. simplex random variable
ANSWER: b
15. 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.
x f(x)
0 0.80
1 0.15
2 0.04
3 0.01
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
c. 3 and 0.01
d. 0 and 0.8
ANSWER: b
16. The number of customers that enter a store during one day is an example of
a. a continuous random variable
b. a discrete random variable
c. either a continuous or a discrete random variable, depending on the number of the customers
d. either a continuous or a discrete random variable, depending on the gender of the customers
ANSWER: b
17. The weight of an object is an example of
a. a continuous random variable
b. a discrete random variable
c. either a continuous or a discrete random variable, depending on the weight of the object
d. either a continuous or a discrete random variable depending on the units of measurement
ANSWER: a
18. 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?
a. 0.2592
b. 0.0142
c. 0.9588
d. 0.7408
ANSWER: b
19. When sampling without replacement, the probability of obtaining a certain sample is best given by a
a. hypergeometric distribution
b. binomial distribution
c. Poisson distribution
d. normal distribution
ANSWER: a
20. 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
a. 20
b. 16
c. 4
d. 2
ANSWER: c
21. If you are conducting an experiment where the probability of a success is 0.2 per day and you are interested in finding the probability of 4 successes in in three days, the correct probability function to use is
a. the standard normal probability density function
b. the normal probability density function
c. the Poisson probability function
d. any probability as long as the tables are available
ANSWER: c
22. Which of the following statements about a discrete random variable and its probability distribution are true?
a. Values of the random variable can never be negative.
b. Some negative values of f(x) are allowed as long as f(x) = 1.
c. Values of f(x) must be greater than or equal to zero.
d. The values of f(x) increase to a maximum point and then decrease.
ANSWER: c
23. 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
a. normal distribution
b. binomial distribution
c. Poisson distribution
d. uniform distribution
ANSWER: c
24. The Poisson probability distribution is a
a. continuous probability distribution
b. discrete probability distribution
c. uniform probability distribution
d. normal probability distribution
ANSWER: b
25. The binomial probability distribution is used with
a. a continuous random variable
b. a discrete random variable
c. any distribution, as long as it is not normal
d. None of these alternatives is correct.
ANSWER: b
26. The expected value of a discrete random variable
a. is the most likely or highest probability value for the random variable
b. will always be one of the values x can take on, although it may not be the highest probability value for the random variable
c. is the average value for the random variable over many repeats of the experiment
d. None of these alternatives is correct.
ANSWER: c
27. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
a. the experiment has a sequence of n identical trials
b. exactly two outcomes are possible on each trial
c. the trials are dependent
d. the probabilities of the outcomes do not change from one trial to another
ANSWER: c
28. Which of the following is a characteristic of a binomial experiment?
a. at least 2 outcomes are possible
b. the probability changes from trial to trial
c. the trials are independent
d. None of these alternatives is correct.
ANSWER: c
29. Assume that you have a binomial experiment with p = 0.3 and a sample size of 100. The value of the variance is
a. 30
b. 33.33
c. 100
d. 210
ANSWER: d
30. The expected value of a random variable is
a. the value of the random variable that should be observed on the next repeat of the experiment
b. the value of the random variable that occurs most frequently
c. the square root of the variance
d. None of these alternatives is correct.
ANSWER: d
31. In a binomial experiment
a. the probability does not change from trial to trial
b. the probability does change from trial to trial
c. the probability could change from trial to trial, depending on the situation under consideration
d. None of these alternatives is correct.
ANSWER: a
32. 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. 100
d. 50
ANSWER: d
33. Which of the following is not a property of a binomial experiment?
a. the experiment consists of a sequence of n identical trials
b. each outcome can be referred to as a success or a failure
c. the probabilities of the two outcomes can change from one trial to the next
d. the trials are independent
ANSWER: c
34. The Poisson probability distribution is used with
a. a continuous random variable
b. a discrete random variable
c. either a continuous or discrete random variable
d. any random variable
ANSWER: b
35. The standard deviation of a binomial distribution is a. (x) = P(1 - P)
b. (x) = nP
c. (x) = nP(1 - P)
d. None of these alternatives is correct.
ANSWER: d
36. The expected value for a binomial probability distribution is
a. E(x) = Pn(1 - n) b. E(x) = P(1 - P)
c. E(x) = nP
d. E(x) = nP(1 - P)
ANSWER: c
37. The variance for the binomial probability distribution is
a. var(x) = P(1 - P)
b. var(x) = nP
c. var(x) = n(1 - P)
d. var(x) = nP(1 - P)
ANSWER: d
38. 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?
a. 0.0004
b. 0.0038
c. 0.10
d. 0.02
ANSWER: b
39. When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a
a. binomial distribution
b. Poisson distribution
c. normal distribution
d. hypergeometric probability distribution
ANSWER: b
40. The hypergeometric probability distribution is identical to
a. the Poisson probability distribution
b. the binomial probability distribution
c. the normal distribution
d. None of these alternatives is correct.
ANSWER: d
41. Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The value of the standard deviation is
a. 50
b. 2
c. 25
d. 5
ANSWER: d
42. The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution
a. the probability of success must be less than 0.5
b. the probability of success changes from trial to trial
c. the trials are independent of each other
d. the random variable is continuous
ANSWER: b
43. 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. 144
ANSWER: b
44. In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials? a. 0.0036
b. 0.0600
c. 0.0555
d. 0.2800
ANSWER: c
45. 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 a. 0.333
b. 0.500
c. 2.000
d. 2.333
ANSWER: d
46. A random variable that may take on any value in an interval or collection of intervals is known as a
a. continuous random variable
b. discrete random variable
c. continuous probability function
d. finite probability function
ANSWER: a
Exhibit 5-1
The following represents the probability distribution for the daily demand of computers at a local store.
Demand Probability
0 0.1
1 0.2
2 0.3
3 0.2
4 0.2
47. Refer to Exhibit 5-1. The expected daily demand is
a. 1.0
b. 2.2
c. 2, since it has the highest probability
d. of course 4, since it is the largest demand level
ANSWER: b
48. Refer to Exhibit 5-1. The probability of having a demand for at least two computers is a. 0.7
b. 0.3
c. 0.4
d. 1.0
ANSWER: a
Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
49. Refer to Exhibit 5-2. What is the probability that among the students in the sample exactly two are female? a. 0.0896
b. 0.2936
c. 0.0413
d. 0.0007
ANSWER: c
50. Refer to Exhibit 5-2. 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
ANSWER: a
51. Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 6 are male? a. 0.0413
b. 0.0079
c. 0.0007
d. 0.0499
ANSWER: d
Exhibit 5-3
Roth 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.
Number of New Clients
Probability
0 0.05
1 0.10
2 0.15
3 0.35
4 0.20
5 0.10
6 0.05
52. Refer to Exhibit 5-3. The expected number of new clients per month is
a. 6
b. 0
c. 3.05
d. 21
ANSWER: c
53. Refer to Exhibit 5-3. The variance is a. 1.431
b. 2.047
c. 3.05
d. 21
ANSWER: b
54. Refer to Exhibit 5-3. The standard deviation is a. 1.431
b. 2.047
c. 3.05
d. 21
ANSWER: a
Exhibit 5-4
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
55. Refer to Exhibit 5-4. The probability that the sample contains 2 female voters is a. 0.0778
b. 0.7780
c. 0.5000
d. 0.3456
ANSWER: d
56. Refer to Exhibit 5-4. The probability that there are no females in the sample is a. 0.0778
b. 0.7780
c. 0.5000
d. 0.3456
ANSWER: a
Exhibit 5-5
Probability Distribution
x f(x)
10 .2
20 .3
30 .4
40 .1
57. Refer to Exhibit 5-5. The expected value of x equals
a. 24
b. 25
c. 30 d. 100
ANSWER: a
58. Refer to Exhibit 5-5. The variance of x equals a. 9.165
b. 84
c. 85
d. 93.33
ANSWER: b
Exhibit 5-6
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.
Cups of Coffee Frequency
0 700
1 900
2 600
3 300
2,500
59. Refer to Exhibit 5-6. The expected number of cups of coffee is
a. 1 b. 1.2 c. 1.5 d. 1.7
ANSWER: b
60. Refer to Exhibit 5-6. The variance of the number of cups of coffee is a. .96
b. .9798
c. 1 d. 2.4
ANSWER: a
Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
61. Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is a. .008
b. .096
c. .104
d. .8
ANSWER: b
62. Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is a. .008
b. .096
c. .104
d. .8
ANSWER: c
63. Refer to Exhibit 5-7. The expected number of days Pete will catch fish is
a. .6
b. .8 c. 2.4
d. 3
ANSWER: c
64. Refer to Exhibit 5-7. The variance of the number of days Pete will catch fish is a. .16
b. .48
c. .8 d. 2.4
ANSWER: b
Exhibit 5-8
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.
65. Refer to Exhibit 5-8. The random variable x satisfies which of the following Discrete Probability Distributions?
a. normal
b. Poisson
c. binomial
d. Not enough information is given to answer this question.
ANSWER: b
66. Refer to Exhibit 5-8. The appropriate probability distribution for the random variable is
a. discrete
b. continuous
c. either discrete or continuous depending on how the interval is defined
d. None of these alternatives is correct.
ANSWER: a
67. Refer to Exhibit 5-8. The expected value of the random variable x is
a. 2 b. 5.3
c. 10 d. 2.30
ANSWER: b
68. Refer to Exhibit 5-8. The probability that there are 8 occurrences in ten minutes is a. .0241
b. .0771
c. .1126
d. .9107
ANSWER: b
69. Refer to Exhibit 5-8. The probability that there are less than 3 occurrences is a. .0659
b. .0948
c. .1016
d. .1239
ANSWER: c
Exhibit 5-9
The probability distribution for the daily sales at Michael's Co. is given below.
Daily Sales (In $1,000s)
Probability
40 0.1
50 0.4
60 0.3
70 0.2
70. Refer to Exhibit 5-9. The expected daily sales are
a. $55,000 b. $56,000 c. $50,000 d. $70,000
ANSWER: b
71. Refer to Exhibit 5-9. The probability of having sales of at least $50,000 is a. 0.5
b. 0.10
c. 0.30
d. 0.90
ANSWER: d
Exhibit 5-10
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
Number Of Goals
Probability
0 0.05
1 0.15
2 0.35
3 0.30
4 0.15
72. Refer to Exhibit 5-10. The expected number of goals per game is
a. 0
b. 1
c. 2, since it has the highest probability d. 2.35
ANSWER: d
73. Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score at least 1 goal? a. 0.20
b. 0.55
c. 1.0
d. 0.95
ANSWER: d
74. Refer to Exhibit 5-10. 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
ANSWER: b
75. Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score no goals? a. 0.95
b. 0.05
c. 0.75
d. 0.60
ANSWER: b
Exhibit 5-11
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below:
Number of Breakdowns
Probability
0 0.12
1 0.38
2 0.25
3 0.18
4 0.07
76. Refer to Exhibit 5-11. The expected number of machine breakdowns per month is
a. 2
b. 1.70
c. one, since it has the highest probability
d. at least 4
ANSWER: b
77. Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is a. 0.93
b. 0.88
c. 0.75
d. 0.25
ANSWER: d
78. Refer to Exhibit 5-11. The probability of no breakdowns in a month is a. 0.88
b. 0.00
c. 0.50
d. 0.12
ANSWER: d
Exhibit 5-12
The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents.
Number of Fatal Accidents
Number of Days
0 45
1 75
2 120
3 45
4 15
79. Refer to Exhibit 5-12. What is the probability that in a given day there will be less than 3 accidents?
a. 0.2
b. 120
c. 0.5
d. 0.8
ANSWER: d
80. Refer to Exhibit 5-12. What is the probability that in a given day there will be at least 1 accident? a. 0.15
b. 0.85
c. at least 1 d. 0.5
ANSWER: b
81. Refer to Exhibit 5-12. What is the probability that in a given day there will be no accidents? a. 0.00
b. 1.00
c. 0.85
d. 0.15
ANSWER: d
Exhibit 5-13
Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.
Production Per Month x
Probability f(x)
1 0.01
2 0.04
3 0.10
4 0.80
5 0.05
82. Refer to Exhibit 5-13. the expected monthly production level is
a. 1.00
b. 4.00
c. 3.00
d. 3.84
ANSWER: d
83. Refer to Exhibit 5-13. The standard deviation for the production is a. 4.32
b. 3.74
c. 0.374
d. 0.612
ANSWER: d
Subjective Short Answer
84. Thirty-two percent of the students in a management class are graduate students. A random sample of 5 students is selected. Using the binomial probability function, determine the probability that the sample contains exactly 2 graduate students?
ANSWER: 0.322 (rounded)
85. Seventy percent of the students applying to a university are accepted. Using the binomial probability tables, what is the probability that among the next 18 applicants
a. At least 6 will be accepted?
b. Exactly 10 will be accepted?
c. Exactly 5 will be rejected?
d. Fifteen or more will be accepted?
e. Determine the expected number of acceptances.
f. Compute the standard deviation.
ANSWER:
a. 0.9986
b. 0.0811
c. 0.2017
d. 0.1646
e. 12.6
f. 1.9442
86. General Hospital has noted that they admit an average of 8 patients per hour.
a. What is the probability that during the next hour less then 3 patients will be admitted?
b. What is the probability that during the next two hours exactly 8 patients will be admitted?
ANSWER:
a. 0.0137
b. 0.0120
87. The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM company's monthly demand.
x
Unit Demand f(x) Probability
0 0.10
1,000 0.10
2,000 0.30
3,000 0.40
4,000 0.10
a. Determine the expected number of units demanded per month.
b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2000 units?
ANSWER:
a. 2300
b. Profit = $1600
88. Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected.
a. What is the probability that the sample contains exactly 4 minorities?
b. What is the probability that the sample contains fewer than 2 minorities?
c. What is the probability that the sample contains exactly 1 non-minority?
d. What is the expected number of minorities in the sample?
e. What is the variance of the minorities?
ANSWER:
a. 0.0577
b. 0.4450
c. 0.0013
d. 1.75
e. 1.3125
89. A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10.
a. What is the probability the salesperson will make exactly two sales in a day?
b. What is the probability the salesperson will make at least two sales in a day?
c. What percentage of days will the salesperson not make a sale?
d. What is the expected number of sales per day?
ANSWER:
a. 0.1488
b. 0.1869
c. 43.05%
d. 0.8
90. A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch.
a. What is the probability that during the next week exactly seven claims will be filed?
b. What is the probability that during the next week no claims will be filed?
c. What is the probability that during the next week fewer than four claims will be filed?
d. What is the probability that during the next week at least seventeen claims will be filed?
ANSWER:
a. 0.1490
b. 0.0009
c. 0.0817
d. 0.0009
91. When a particular machine is functioning properly, 80% of the items produced are non-defective. If three items are examined, what is the probability that one is defective? Use the binomial probability function to answer this question.
ANSWER: 0.384
92. Ten percent of the items produced by a machine are defective. Out of 15 items chosen at random,
a. what is the probability that exactly 3 items will be defective?
b. what is the probability that less than 3 items will be defective?
c. what is the probability that exactly 11 items will be non-defective?
ANSWER:
a. 0.1285
b. 0.816
c. 0.0428
93. The student body of a large university consists of 30% Business majors. A random sample of 20 students is selected.
a. What is the probability that among the students in the sample at least 10 are Business majors?
b. What is the probability that at least 16 are not Business majors?
c. What is the probability that exactly 10 are Business majors?
d. What is the probability that exactly 12 are not Business majors?
ANSWER:
a. 0.0479
b. 0.2374
c. 0.0308
d. 0.1144
94. Shoppers enter Hamilton Place Mall at an average of 120 per hour.
a. What is the probability that exactly 5 shoppers will enter the mall between noon and 12:05 p.m.?
b. What is the probability that at least 35 shoppers will enter the mall between 5:00 and 5:10 p.m.?
ANSWER:
a. 0.0378
b. 0.0015
95. A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected.
a. What is the probability that the sample will contain 7 non-defective parts?
b. What is the probability that the sample will contain at least 4 defective parts?
c. What is the probability that the sample will contain less than 5 non-defective parts?
d. What is the probability that the sample will contain no defective parts?
ANSWER:
a. 0.0574
b. 0.0128
c. 0.0001
d. 0.3487
96. Fifty-five percent of the applications received for a particular credit card are accepted. Among the next twelve applications,
a. what is the probability that all will be rejected?
b. what is the probability that all will be accepted?
c. what is the probability that exactly 4 will be accepted?
d. what is the probability that fewer than 3 will be accepted?
e. Determine the expected number and the variance of the accepted applications.
ANSWER:
a. 0.0001
b. 0.0008
c. 0.0762
d. 0.0079
e. 6.60; 2.9700
97. The probability distribution of the daily demand for a product is shown below.
Demand Probability
0 0.05
1 0.10
2 0.15
3 0.35
4 0.20
5 0.10
6 0.05
a. What is the expected number of units demanded per day?
b. Determine the variance and the standard deviation.
ANSWER:
a. 3.05
b. variance = 2.0475 std. dev. = 1.431
98. In a large corporation, 65% of the employees are male. A random sample of five employees is selected. Use the Binomial probability tables to answer the following questions.
a. What is the probability that the sample contains exactly three male employees?
b. What is the probability that the sample contains no male employees?
c. What is the probability that the sample contains more than three female employees?
d. What is the expected number of female employees in the sample?
ANSWER:
a. 0.3364
b. 0.0053
c. 0.0541
d. 1.75
99. For the following probability distribution:
x f(x)
0 0.01
1 0.02
2 0.10
3 0.35
4 0.20
5 0.11
6 0.08
7 0.05
8 0.04
9 0.03
10 0.01
a. Determine E(x).
b. Determine the variance and the standard deviation.
ANSWER:
a. 4.14
b. variance = 3.7 std. dev. = 1.924
100. A random variable x has the following probability distribution:
x f(x)
0 0.08
1 0.17
2 0.45
3 0.25
4 0.05
a. Determine the expected value of x.
b. Determine the variance.
ANSWER:
a. 2.02
b. 0.9396
101. A company sells its products to wholesalers in batches of 1,000 units only. The daily demand for its product and the respective probabilities are given below.
Demand (Units) Probability
0 0.2
1000 0.2
2000 0.3
3000 0.2
4000 0.1
a. Determine the expected daily demand.
b. Assume that the company sells its product at $3.75 per unit. What is the expected daily revenue?
ANSWER:
a. 1800
b. $6,750
102. The records of a department store show that 20% of its customers who make a purchase return the merchandise in order to exchange it. In the next six purchases,
a. what is the probability that three customers will return the merchandise for exchange?
b. what is the probability that four customers will return the merchandise for exchange?
c. what is the probability that none of the customers will return the merchandise for exchange?
ANSWER:
a. 0.0819
b. 0.0154
c. 0.2621
103. In a large university, 15% of the students are female. If a random sample of twenty students is selected,
a. what is the probability that the sample contains exactly four female students?
b. what is the probability that the sample will contain no female students?
c. what is the probability that the sample will contain exactly twenty female students?
d. what is the probability that the sample will contain more than nine female students?
e. what is the probability that the sample will contain fewer than five female students?
f. what is the expected number of female students?
ANSWER:
a. 0.1821
b. 0.0388
c. 0.0000
d. 0.0002
e. 0.8298
f. 3
104. In a southern state, it was revealed that 5% of all automobiles in the state did not pass inspection. Of the next ten automobiles entering the inspection station,
a. what is the probability that none will pass inspection?
b. what is the probability that all will pass inspection?
c. what is the probability that exactly two will not pass inspection?
d. what is the probability that more than three will not pass inspection?
e. what is the probability that fewer than two will not pass inspection?
f. Find the expected number of automobiles not passing inspection.
g. Determine the standard deviation for the number of cars not passing inspection.
ANSWER:
a. 0.0000
b. 0.5987
c. 0.0746
d. 0.0011
e. 0.9138
f. 0.5
g. 0.6892
105. The random variable x has the following probability distribution:
x f(x)
0 .25
1 .20
2 .15
3 .30
4 .10
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.
ANSWER:
a. yes f(x) 0 and f(x) = 1 b. 1.8
c. 1.86
d. 1.364
106. The probability function for the number of insurance policies John will sell to a customer is given by f(X) = .5 - (X/6) for X = 0, 1, or 2
a. Is this a valid probability function? Explain your answer.
b. What is the probability that John will sell exactly 2 policies to a customer?
c. What is the probability that John will sell at least 2 policies to a customer?
d. What is the expected number of policies John will sell?
e. What is the variance of the number of policies John will sell?
ANSWER:
a. yes f(x) 0 and f(x) = 1
b. 0.167
c. 0.167
d. 0.667
e. 0.556
107. The probability distribution for the rate of return on an investment is
Rate of Return (In Percent)
Probability
9.5 .1
9.8 .2
10.0 .3
10.2 .3
10.6 .1
a. What is the probability that the rate of return will be at least 10%?
b. What is the expected rate of return?
c. What is the variance of the rate of return?
ANSWER:
a. 0.7
b. 10.03
c. 0.0801
108. In a large university, 75% of students live in dormitories. A random sample of 5 students is selected. Use the binomial probability tables to answer the following questions.
a. What is the probability that the sample contains exactly three students who live in the dormitories?
b. What is the probability that the sample contains no students who lives in the dormitories?
c. What is the probability that the sample contains more than three students who do not live in the dormitories?
d. What is the expected number of students (in the sample) who do not live in the dormitories?
ANSWER:
a. 0.2637
b. 0.001
c. 0.0156
d. 1.25
109. A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is .1. Define a random variable X to be the number of machines that will break down in a day.
a. What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution.
b. Compute the probability that 4 machines will break down.
c. Compute the probability that at least 4 machines will break down.
d. What is the expected number of machines that will break down in a day?
e. What is the variance of the number of machines that will break down in a day?
ANSWER:
a. binomial
b. 0.00045
c. 0.00046
d. 0.5
e. 0.45
110. On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour.
a. What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution.
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour.
ANSWER:
a. Poisson; it shows the probability of x occurrences of the event over a time period. b. 0.1385
c. 0.3406
111. Twenty-five percent of all resumes received by a corporation for a management position are from females. Fifteen resumes will be received tomorrow.
a. What is the probability that exactly 5 of the resumes will be from females?
b. What is the probability that fewer than 3 of the resumes will be from females?
c. What is the expected number of resumes from women?
d. What is the variance of the number of resumes from women?
ANSWER:
a. 0.1651
b. 0.2361
c. 3.75
d. 2.8125
112. The average number of calls received by a switchboard in a 30-minute period is 15.
a. What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 10 calls?
b. What is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 15 calls?
c. What is the probability that between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?
ANSWER:
a. 0.0486
b. 0.3958
c. 0.0075
113. Two percent of the parts produced by a machine are defective. Twenty parts are selected at random. Use the binomial probability tables to answer the following questions.
a. What is the probability that exactly 3 parts will be defective?
b. What is the probability that the number of defective parts will be more than 2 but fewer than 6?
c. What is the probability that fewer than 4 parts will be defective?
d. What is the expected number of defective parts?
e. What is the variance for the number of defective parts?
ANSWER:
a. 0.0065
b. 0.0071
c. 0.9974
d. 0.4
e. 0.392
114. Compute the hypergeometric probabilities for the following values of n and x. Assume N = 8 and r = 5.
a. n = 5, x = 2 b. n = 6, x = 4 c. n = 3, x = 0 d. n = 3, x = 3
ANSWER:
a. 0.1786
b. 0.5357
c. 0.01786
d. 0.1786
115. Seven students have applied for merit scholarships. This year 3 merit scholarships were awarded. If a random sample of 3 applications (from the population of 7) is selected,
a. what is the probability that 2 students were recipients of scholarships?
b. what is the probability that no students were the recipients of scholarship?
ANSWER:
a. 0.2143
b. 0.1143
116. Determine the probability of being dealt 4 kings in a 5-card poker hand.
ANSWER: 120/6,497,400 = 0.00001847
117. Twenty percent of the applications received for a particular position are rejected. What is the probability that among the next fourteen applications,
a. none will be rejected?
b. all will be rejected?
c. less than 2 will be rejected?
d. more than four will be rejected?
e. Determine the expected number of rejected applications and its variance.
ANSWER:
a. 0.0440
b. 0.0000
c. 0.1979
d. 0.1297
e. 2.8, 2.24
118. An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch.
What is the probability that during the next week
a. exactly seven claims will be filed?
b. no claims will be filed?
c. less than four claims will be filed?
d. at least eighteen claims will be filed?
ANSWER:
a. 0.1171
b. 0.0001
c. 0.0212
d. 0.0053
119. A local university reports that 10% of their students take their general education courses on a pass/fail basis. Assume that fifteen students are registered for a general education course.
a. What is the expected number of students who have registered on a pass/fail basis?
b. What is the probability that exactly five are registered on a pass/fail basis?
c. What is the probability that more than four are registered on a pass/fail basis?
d. What is the probability that less than two are registered on a pass/fail basis?
ANSWER:
a. 1.5
b. 0.01050
c. 0.0127
d. 0.5491
120. Only 0.02% of credit card holders of a company report the loss or theft of their credit cards each month. The company has 15,000 credit cards in the city of Memphis. Use the Poisson probability tables to answer the following questions. What is the probability that during the next month in the city of Memphis
a. no one reports the loss or theft of his or her credit cards?
b. every credit card is lost or stolen?
c. six people report the loss or theft of their cards?
d. at least nine people report the loss or theft of their cards?
e. Determine the expected number of reported lost or stolen credit cards.
f. Determine the standard deviation for the number of reported lost or stolen cards.
ANSWER:
a. 0.0498
b. 0.0000
c. 0.0504
d. 0.0038
e. 3
f. 1.73
121. A production process produces 2% defective parts. A sample of 5 parts from the production is selected. What is the probability that the sample contains exactly two defective parts? Use the binomial probability function and show your computations to answer this question.
ANSWER: 0.0037648
122. A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment. The retailer sold two VCRs to two customers.
a. Can a binomial formula be used for the solution of the above problem?
b. What kind of probability distribution does the above satisfy, and is there a function for solving such problems?
c. What is the probability that both customers received damaged VCRs?
d. What is the probability that one of the two customers received a defective VCR?
ANSWER:
a. No, in a binomial experiment, trials are independent of each other.
b. Hypergeometric probability distribution c. 0.2
d. 0.6
123. The management of a grocery store has kept a record of bad checks received per day for a period of 200 days. The data are shown below.
Number of Bad Checks Received
Number of Days
0 8
1 12
2 20
3 60
4 40
5 30
6 20
7 10
a. Develop a probability distribution for the above data.
b. Is the probability distribution that you found in Part a a proper probability distribution? Explain.
c. Determine the cumulative probability distribution F(x).
d. What is the probability that in a given day the store receives four or less bad checks?
e. What is the probability that in a given day the store receives more than 3 bad checks?
ANSWER:
a.
c.
Number Bad Checks
0 Probability
.04 F(x)
.04
1 .06 .10
2 .10 .20
3 .30 .50
4 .20 .70
5 .15 .85
6 .10 .95
7 .05 1.00
b. Yes, the sum of the probabilities is equal to 1. d. 0.7
e. 0.5
124. The following probability distribution represents the number of grievances filed per month with the MNM. Corporation.
x f(x)
0 0.04
1 0.36
2 0.50
3 0.08
4 0.02
a. Determine the expected value of the number of grievances in a month.
b. Determine the variance.
c. Compute the standard deviation.
ANSWER: a. 1.68
b. 0.5776
c. 0.76
125. The number of bad checks received per day by a store and the respective probabilities are shown below.
Number of Bad Checks Received Per Day
Probability
0 0.04
1 0.06
2 0.10
3 0.30
4 0.20
5 0.15
6 0.10
7 0.05
a. What is the expected number of bad checks received per day?
b. Determine the variance in the number of bad checks received per day.
c. What is the standard deviation?
ANSWER: a. 3.66
b. 2.7644
c. 1.6626
126. A cosmetics salesperson, who calls potential customers to sell her products, has determined that 30% of her telephone calls result in a sale. Determine the probability distribution for her next three calls. Note that the next three calls could result in 0, 1, 2, or 3 sales.
ANSWER:
x
p
0 0.3430
1 0.4410
2 0.1890
3 0.0270
127. The following table shows part of the probability distribution for a random variable x.
x f(x)
0 0.2
1 ?
2 0.15
3 ?
4 0.15
a. The mean of the above distribution is known to be 1.8 (i.e., E(x) = 1.8). Determine f(1) and f(3).
b. Compute the variance and the standard deviation for the above probability distribution.
ANSWER: a. 0.3 and 0.2
b. Variance = 1.86, Standard deviation = 1.364 (rounded)
128. The following table shows part of the probability distribution for the number of boats sold daily at Boats Unlimited. It is known that the average number of boats sold daily is 1.57.
x f(x)
0 0.20
1 0.30
2 0.32
3 ?
4 0.05
5 0.02
Compute the variance and the standard deviation for this probability distribution.
ANSWER: Variance = 1.4051, Standard deviation = 1.1854 (rounded)

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