Deck 5: Discrete Probability Distributions

Question 1

The variance 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 1

D

Question 2

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)All of the answers are correct.

Answer 2

C

Question 3

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)Negative values of f(x) are allowed as long as $\Sigma$ 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 3

Values of f(x) must be greater than or equal to zero.

Question 4

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

A)discrete random variable
B)continuous random variable
C)complex random variable
D)None of the answers is correct.

Question 5

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

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

Question 6

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 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 deviation of data elements from the mean

Question 8

The weight of an object, measured to the nearest gram, 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 9

The expected value of a random variable is the

A)value of the random variable that should be observed on the next repeat of the experiment
B)value of the random variable that occurs most frequently
C)square root of the variance
D)None of the answers is correct.

Question 10

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

Question 11

The weight of an object, measured in grams, 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 12

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

A)f(x) $\ge$ 0 for all values of x
B) $\Sigma$ f(x) = 1
C) $\Sigma$ f(x) = 0
D)All of the answers are correct.

Question 13

Excel's __________ function can be used to compute the expected value of a discrete random variable.

A)SUMPRODUCT
B)AVERAGE
C)MEDIAN
D)VAR

Question 14

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

A)discrete random variable
B)continuous random variable
C)complex random variable
D)None of the answers is correct.

Question 15

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

A)variance
B)standard deviation
C)expected value
D)None of the answers is correct.

Question 16

A description of how the probabilities are distributed over the values the random variable can assume is called a

A)probability distribution
B)probability function
C)random variable
D)expected value

Question 17

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

A) $\Sigma$ f(x) = 0
B)f(x) $\ge$ 1 for all values of x
C)f(x) < 0
D)None of the answers is correct.

Question 18

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

Question 19

Excel's __________ function can be used to compute the variance of a discrete random variable.

A)SUMPRODUCT
B)AVERAGE
C)MEDIAN
D)VAR

Question 20

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)None of the answers is correct

Question 21

Exhibit 5-2
The probability distribution for the daily sales at Michael's Co. is given below.
Refer to Exhibit 5-2. The probability of having sales of at least $50,000 is

A)0.5
B)0.10
C)0.30
D)0.90

Question 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

A)0.333
B)0.500
C)2.000
D)2.333

Question 23

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.
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
C)3 and 0.01
D)0 and 0.8

Question 24

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

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

Question 25

Exhibit 5-1
The following represents the probability distribution for the daily demand of microcomputers at a local store.
Refer to Exhibit 5-1. The expected daily demand is

A)1.0
B)2.2
C)2
D)4

Question 26

Exhibit 5-2
The probability distribution for the daily sales at Michael's Co. is given below.
Refer to Exhibit 5-2. The expected daily sales are

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

Question 27

Exhibit 5-1
The following represents the probability distribution for the daily demand of microcomputers at a local store.
Refer to Exhibit 5-1. The probability of having a demand for at least two microcomputers is

A)0.7
B)0.3
C)0.4
D)1.0

Question 28

Exhibit 5-4
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.
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.

Question 29

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.
Refer to Exhibit 5-5. The variance is

A)1.431
B)2.0475
C)3.05
D)21

Question 30

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

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

Question 31

Exhibit 5-4
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.
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.

Question 32

Exhibit 5-3
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
Refer to Exhibit 5-3. The expected number of goals per game is

A)0
B)1
C)2
D)2.35

Question 33

Exhibit 5-4
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.
Refer to Exhibit 5-4. The expected number of machine breakdowns per month is

A)2
B)1.70
C)one
D)None of the alternative answers is correct.

Question 34

Exhibit 5-3
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
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

Question 35

Exhibit 5-3
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
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.

Question 36

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 37

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

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

Question 38

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

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

Question 39

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

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

Question 40

Exhibit 5-3
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
Refer to Exhibit 5-3. 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 41

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)

Question 42

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.
Which of the following is a characteristic of a binomial experiment?

A)at least 2 outcomes are possible
B)the probability of success changes from trial to trial
C)the trials are independent
D)All of these answers are correct.

Question 43

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.
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

A)standard normal probability density function
B)normal probability density function
C)Poisson probability function
D)binomial probability function

Question 44

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.

Question 45

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)

Question 46

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 47

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.
In a binomial experiment, the

A)probability of success does not change from trial to trial
B)probability of success does change from trial to trial
C)probability of success could change from trial to trial, depending on the situation under consideration
D)All of these answers are correct.

Question 48

The standard deviation of a binomial distribution is

A)E(x) = np(1 - n)
B)E(x) = np(1 - p)
C)E(x) = np
D)None of the alternative answers is correct.

Question 49

Excel's BINOM.DIST function can be used to compute

A)bin width for histograms
B)binomial probabilities
C)cumulative binomial probabilities
D)both binomial probabilities and cumulative binomial probabilities are correct.

Question 50

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.
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 51

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.
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)0.06
C)0.0554
D)0.28

Question 52

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 53

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 54

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.
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 55

When using Excel's BINOM.DIST function, one should choose TRUE for the fourth input if

A)a probability is desired
B)a cumulative probability is desired
C)the expected value is desired
D)the correct answer is desired

Question 56

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.

Question 57

Excel's BINOM.DIST function has how many inputs?

A)2
B)3
C)4
D)5

Question 58

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

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

Question 59

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.
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 60

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.
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)All of these answers are correct.

Question 61

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.
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 62

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

A).008
B).096
C).104
D).8

Question 63

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.
Excel's POISSON.DIST function has how many inputs?

A)2
B)3
C)4
D)5

Question 64

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

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

Question 65

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

A).008
B).096
C).104
D).8

Question 66

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.
The Poisson probability distribution is a

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

Question 67

Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
Refer to Exhibit 5-9. The probability that there are no females in the sample is

A)0.0778
B)0.7780
C)0.5000
D)0.3456

Question 68

Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
Refer to Exhibit 5-9. The probability that the sample contains 2 female voters is

A)0.0778
B)0.7780
C)0.5000
D)0.3456

Question 69

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

A).16
B).48
C).8
D)2.4

Question 70

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.
Excel's POISSON.DIST function can be used to compute

A)bin width for histograms
B)Poisson probabilities
C)cumulative Poisson probabilities
D)Both Poisson probabilities and cumulative Poisson probabilities are correct.

Question 71

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.
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

A)binomial distribution
B)Poisson distribution
C)normal distribution
D)hypergeometric probability distribution

Question 72

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
Refer to Exhibit 5-8. 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 73

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.
Refer to Exhibit 5-11. The random variable x satisfies which of the following probability distributions?

A)normal
B)Poisson
C)binomial
D)Not enough information is given to answer this question.

Question 74

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.
When using Excel's POISSON.DIST function, one should choose TRUE for the third input if

A)a probability is desired
B)a cumulative probability is desired
C)the expected value is desired
D)the correct answer is desired

Question 75

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
Refer to Exhibit 5-8. What is the random variable in this experiment?

A)the 60% of female students
B)the random sample of 8 students
C)the number of female students out of 8
D)the student body size

Question 76

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
Refer to Exhibit 5-8. 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 77

Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
Refer to Exhibit 5-9. What is the random variable in this experiment?

A)the 40% of female registered voters
B)the random sample of 5 voters
C)the number of female voters out of 5
D)the number of registered voters in the nation

Question 78

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.
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 79

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

Question 80

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.
Refer to Exhibit 5-10. What is the random variable in this experiment?

A)the 0.8 probability of catching fish
B)the 3 days
C)the number of days out of 3 that Pete catches fish
D)the number of fish in the body of water