Deck 5: Discrete Probability Distributions

Question 1

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 1

A

Question 2

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 2

B

Question 3

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 3

A

Question 4

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

Question 5

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

A) ?fx) = 0 for all values of x
B) fx) $\geq$ 1 for all values of x
C) fx) < 0 for all values of x
D) ?fx) = 1 for all values of x

Question 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

Question 7

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

Question 8

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

Question 9

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

Question 10

A measure of the average value of a random variable is called an)

A) variance
B) standard deviation
C) expected value
D) coefficient of variation

Question 11

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

Question 12

A random variable that can assume only a finite number of values is referred to as an)

A) infinite sequence
B) finite sequence
C) discrete random variable
D) discrete probability function

Question 13

Which of the following is not a required condition for a discrete probability function?

A) fx) ≥ 0 for all values of x
B) ∑fx) = 1 for all values of x
C) ∑fx) = 0 for all values of x
D) ∑fx) ≥ 1 for all values of x

Question 14

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. $\begin{array}{ll}x&fx)\\0 & 0.80 \\1 & 0.15 \\2 & 0.04 \\3 & 001\end{array}$ 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

Question 15

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

A) descriptive statistic
B) probability function
C) variance
D) random variable

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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

Question 23

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

Question 24

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.

Question 25

The standard deviation of a binomial distribution is

A) σx) = P1 - P)
B) σx) = nP
C) σx) = nP1 - P)
D) None of these alternatives is correct.

Question 26

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

Question 27

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

Question 28

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.

Question 29

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

Question 30

The expected value for a binomial probability distribution is

A) Ex) = Pn1 - n)
B) Ex) = P1 - P)
C) Ex) = nP
D) Ex) = nP1 - P)

Question 31

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

Question 32

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 fx) are allowed as long as ∑fx) = 1.
C) Values of fx) must be greater than or equal to zero.
D) The values of fx) increase to a maximum point and then decrease.

Question 33

The variance for the binomial probability distribution is

A) varx) = P1 - P)
B) varx) = nP
C) varx) = n1 - P)
D) varx) = nP1 - P)

Question 34

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.

Question 35

The Poisson probability distribution is a

A) continuous probability distribution
B) discrete probability distribution
C) uniform probability distribution
D) normal probability distribution

Question 36

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.

Question 37

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.

Question 38

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

Question 39

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.

Question 40

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

Question 41

Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
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

Question 42

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.
$$\begin{array} { c c } \text { Number of } & \\\text { New Clients } & \text { Prabability } \\0 & 0.05 \\1 & 0.10 \\2 & 0.15 \\3 & 0.35 \\4 & 0.20 \\5 & 0.10 \\6 & 0.05\end{array}$$

-Refer to Exhibit 5-3. The expected number of new clients per month is

A) 6
B) 0
C) 3.05
D) 21

Question 43

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

Question 44

X is a random variable with the probability function: fX) = 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

Question 45

Exhibit 5-1
The following represents the probability distribution for the daily demand of computers at a local store.
$$\begin{array} { c c } \text { Demand } & \text { Probability } \\0 & 0.1 \\1 & 0.2 \\2 & 0.3 \\3 & 0.2 \\4 & 0 ?\end{array}$$

-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

Question 46

Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
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

Question 47

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.
$\begin{array}{ll}\text { Cups of Coffee }&\text { Frequency }\\0 & 700 \\1 & 900 \\2 & 600 \\3 & 300\\&2,500\end{array}$

-Refer to Exhibit 5-6. The variance of the number of cups of coffee is

A) .96
B) .9798
C) 1
D) 2.4

Question 48

Exhibit 5-1
The following represents the probability distribution for the daily demand of computers at a local store.
$$\begin{array} { c c } \text { Demand } & \text { Probability } \\0 & 0.1 \\1 & 0.2 \\2 & 0.3 \\3 & 0.2 \\4 & 0 ?\end{array}$$

-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

Question 49

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.
$$\begin{array} { c c } \text { Number of } & \\\text { New Clients } & \text { Prabability } \\0 & 0.05 \\1 & 0.10 \\2 & 0.15 \\3 & 0.35 \\4 & 0.20 \\5 & 0.10 \\6 & 0.05\end{array}$$

-Refer to Exhibit 5-3. The variance is

A) 1.431
B) 2.047
C) 3.05
D) 21

Question 50

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.
$\begin{array}{ll}\text { Cups of Coffee }&\text { Frequency }\\0 & 700 \\1 & 900 \\2 & 600 \\3 & 300\\&2,500\end{array}$

-Refer to Exhibit 5-6. The expected number of cups of coffee is

A) 1
B) 1.2
C) 1.5
D) 1.7

Question 51

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

Question 52

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

Question 53

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.
$$\begin{array} { c c } \text { Number of } & \\\text { New Clients } & \text { Prabability } \\0 & 0.05 \\1 & 0.10 \\2 & 0.15 \\3 & 0.35 \\4 & 0.20 \\5 & 0.10 \\6 & 0.05\end{array}$$

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

A) 1.431
B) 2.047
C) 3.05
D) 21

Question 54

Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
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

Question 55

Exhibit 5-4
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
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

Question 56

Exhibit 5-4
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
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

Question 57

Exhibit 5-5
Probability Distribution
$\begin{array}{ll}x&fx)\\10 & .2 \\20 & .3 \\30 & .4 \\40 & .1\end{array}$

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

A) 9.165
B) 84
C) 85
D) 93.33

Question 58

Exhibit 5-5
Probability Distribution
$\begin{array}{ll}x&fx)\\10 & .2 \\20 & .3 \\30 & .4 \\40 & .1\end{array}$

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

A) 24
B) 25
C) 30
D) 100

Question 59

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

Question 60

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

Question 61

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.
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

Question 62

Exhibit 5-10
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
$$\begin{array} { c c } \text { Number } & \\\text { Of Goals } & \text { Prabability } \\0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 015\end{array}$$

-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

Question 63

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.
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.

Question 64

Exhibit 5-12
The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents.
$\begin{array}{cc}\text { Number of Fatal }\\\text { Accidents }&\text { Number of Day }\\0 & 45 \\1 & 75 \\2 & 120 \\3 & 45 \\4 & 15\end{array}$

-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

Question 65

Exhibit 5-10
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
$$\begin{array} { c c } \text { Number } & \\\text { Of Goals } & \text { Prabability } \\0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 015\end{array}$$

-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

Question 66

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.
Refer to Exhibit 5-8. The probability that there are less than 3 occurrences is

A) .0659
B) .0948
C) .1016
D) .1239

Question 67

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.
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.

Question 68

Exhibit 5-9
The probability distribution for the daily sales at Michael's Co. is given below.
$\begin{array}{cc}\text { Daily Sales }\\\text { In } \$ 1,000 \text { s) }&\text { Probability }\\40 & 0.1 \\50 & 0.4 \\60 & 0.3 \\70 & 0 ?\end{array}$

-Refer to Exhibit 5-9. The expected daily sales are

A) $55,000
B) $56,000
C) $50,000
D) $70,000

Question 69

Exhibit 5-11
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below:
$\begin{array}{ll}\text { Number of } & \\\text { Breakdowns } & \text { Prabability } \\0 & 0.12 \\1 & 0.38 \\2 & 0.25 \\3 & 0.18 \\4 & 0.07\end{array}$

-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

Question 70

Exhibit 5-10
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
$$\begin{array} { c c } \text { Number } & \\\text { Of Goals } & \text { Prabability } \\0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 015\end{array}$$

-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

Question 71

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.
Refer to Exhibit 5-7. The expected number of days Pete will catch fish is

A) .6
B) .8
C) 2.4
D) 3

Question 72

Exhibit 5-12
The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents.
$\begin{array}{cc}\text { Number of Fatal }\\\text { Accidents }&\text { Number of Day }\\0 & 45 \\1 & 75 \\2 & 120 \\3 & 45 \\4 & 15\end{array}$

-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

Question 73

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.
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

Question 74

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.
Refer to Exhibit 5-8. The expected value of the random variable x is

A) 2
B) 5.3
C) 10
D) 2.30

Question 75

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

A) .0241
B) .0771
C) .1126
D) .9107

Question 76

Exhibit 5-10
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
$$\begin{array} { c c } \text { Number } & \\\text { Of Goals } & \text { Prabability } \\0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 015\end{array}$$

-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

Question 77

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.
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

Question 78

Exhibit 5-11
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below:
$\begin{array}{ll}\text { Number of } & \\\text { Breakdowns } & \text { Prabability } \\0 & 0.12 \\1 & 0.38 \\2 & 0.25 \\3 & 0.18 \\4 & 0.07\end{array}$

-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

Question 79

Exhibit 5-11
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below:
$\begin{array}{ll}\text { Number of } & \\\text { Breakdowns } & \text { Prabability } \\0 & 0.12 \\1 & 0.38 \\2 & 0.25 \\3 & 0.18 \\4 & 0.07\end{array}$

-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

Question 80

Exhibit 5-9
The probability distribution for the daily sales at Michael's Co. is given below.
$\begin{array}{cc}\text { Daily Sales }\\\text { In } \$ 1,000 \text { s) }&\text { Probability }\\40 & 0.1 \\50 & 0.4 \\60 & 0.3 \\70 & 0 ?\end{array}$

-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