Deck 5: Discrete Probability Distributions

Question 1

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 nature of the object.
D) either a continuous or a discrete random variable, depending on the unit of measurement.

Answer 1

a continuous random variable.

Question 2

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 2

binomial probability distribution.

Question 3

The Poisson probability distribution is a

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

Answer 3

discrete probability distribution.

Question 4

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

A) $\Sigma$ f(x) = 0 for all values of x
B) f(x) $\geq$ 1 for all values of x
C) f(x) < 0 for all values of x
D) $\Sigma$ f(x) = 1 for all values of x

Question 5

The binomial probability distribution is used with

A) a continuous random variable.
B) a discrete random variable.
C) a uniform random variable.
D) an intermittent random variable.

Question 6

A continuous random variable may assume

A) any numerical value in an interval or collection of intervals.
B) finite number of values in a collection of intervals.
C) an infinite sequence of values.
D) only the positive integer values in an interval.

Question 7

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

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

Question 8

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) is the value it is expected to assume in the next trial.

Question 9

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 whether odd or even number of the customers enter.
D) either a continuous or a discrete random variable, depending on the gender of the customers.

Question 10

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) mixed type random variable.
D) multivariate random variable.

Question 11

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

A) the probable value.
B) the median value.
C) the expected value.
D) the variance.

Question 12

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 13

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 14

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 15

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 16

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

A) probability distribution.
B) empirical discrete distribution.
C) bivariate distribution.
D) table of binomial probability.

Question 17

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

A) f(x) $\leq$ 0 for all values of x
B) $\Sigma$ f(x) = 1 for all values of x
C) $\Sigma$ f(x) = 0 for all values of x
D) $\Sigma$ f(x) $\geq$ 1 for all values of x

Question 18

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?

A) The experiment has at least two possible outcomes
B) Exactly two outcomes are possible on each trial
C) The trials are dependent on each other
D) The probabilities of the outcomes changes from one trial

Question 19

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.

Question 20

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 21

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) mixed type random variable.
D) multivariate random variable.

Question 22

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 23

The variance Var(x) for the binomial distribution is given by equation

A) np(n - 1).
B) np(1 - np).
C) n(1 - p).
D) np(1 - p).

Question 24

The expected value for a binomial distribution is given by equation

A) (n - 1)(1 - p).
B) n(1 - p).
C) np.
D) (n - 1)p.

Question 25

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 26

The student body of a large university consists of 60% female students.A random sample of 8 students is selected.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 27

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 28

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. $$\begin{array}{l}\text { Number of }\\\begin{array} { c c } \text { New Clients } & \text { Probability } \\\hline 0 & 0.05 \\1 & 0.10 \\2 & 0.15 \\3 & 0.35 \\4 & 0.20 \\5 & 0.10 \\6 & 0.05\end{array}\end{array}$$
The standard deviation is

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

Question 29

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 30

In a binomial experiment

A) the probability does not change from trial to trial.
B) the probability changes from trial to trial.
C) the probability could change from trial to trial, depending on the situation under consideration.
D) the probability could change depending on the number of outcomes.

Question 31

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 32

The following represents the probability distribution for the daily demand of computers at a local store. $$\begin{array} { c c } \text { Demand } & \text { Probability } \\0 & 0.1 \\1 & 0.2 \\2 & 0.3 \\3 & 0.2 \\4 & 0.2\end{array}$$ 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 33

The student body of a large university consists of 60% female students.A random sample of 8 students is selected.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 34

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 35

Random variable x has 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 36

The student body of a large university consists of 60% female students.A random sample of 8 students is selected.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 37

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 38

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

A) 1.0
B) 2.2
C) 2.0
D) 4.0

Question 39

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. $$\begin{array}{l}\text { Number of }\\\begin{array} { c c } \text { New Clients } & \text { Probability } \\\hline 0 & 0.05 \\1 & 0.10 \\2 & 0.15 \\3 & 0.35 \\4 & 0.20 \\5 & 0.10 \\6 & 0.05\end{array}\end{array}$$ The variance is

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

Question 40

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. $$\begin{array}{l}\text { Number of }\\\begin{array} { c c } \text { New Clients } & \text { Probability } \\\hline 0 & 0.05 \\1 & 0.10 \\2 & 0.15 \\3 & 0.35 \\4 & 0.20 \\5 & 0.10 \\6 & 0.05\end{array}\end{array}$$ The expected number of new clients per month is

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

Question 41

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.The variance of the number of days Pete will catch fish is

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

Question 42

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. $$\begin{array} { c c } \text { Cups of Coffee } & \text { Frequency } \\0 & 700 \\1 & 900 \\2 & 600 \\3 & 300 \\& 2,500\end{array}$$ The variance of the number of cups of coffee is

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

Question 43

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.The probability that there are less than 3 occurrences is

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

Question 44

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. $\begin{array}{cc}\text { Production } & \\\text { Per Month } & \text { Probability } \\1 & 0.01 \\2 & 0.04 \\3 & 0.10 \\4 & 0.80 \\5 & 0.05\end{array}$ The standard deviation for the production is

A) 4.32
B) 3.74
C) 0.374
D) 0.612

Question 45

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.The expected value of the random variable x is

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

Question 46

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.The probability that Pete will catch fish on one day or less is

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

Question 47

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

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

Question 48

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.The probability that Pete will catch fish on exactly one day is​

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

Question 49

The probability distribution for the number of goals the Lions soccer team makes per game is given below.
$\begin{array}{cc}\text { Number } & \\\text { Of Goals } & \text { Probability } \\0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 0.15\end{array}$
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 50

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.Which of the following discrete probability distributions' properties are satisfied by random variable x?

A) Normal
B) Poisson
C) Binomial
D) Hypergeometric

Question 51

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.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) binomial.

Question 52

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

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

Question 53

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.The expected number of days Pete will catch fish is

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

Question 54

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. $$\begin{array} { c c } \text { Cups of Coffee } & \text { Frequency } \\0 & 700 \\1 & 900 \\2 & 600 \\3 & 300 \\& 2,500\end{array}$$ The expected number of cups of coffee is?

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

Question 55

The probability distribution for the daily sales at Michael's Co.is given below. $\begin{array}{cc}\text { Daily Sales } & \\\text { (In } \$ 1,000 \text { s) } & \text { Probability } \\40 & 0.1 \\50 & 0.4 \\60 & 0.3 \\70 & 0.2\end{array}$
The probability of having sales of no more than $60,000 is

A) 0.7
B) 0.2
C) 0.8
D) 0.5

Question 56

Consider the probability distribution below. $$\begin{array} { c c } x & f ( x ) \\10 & .2 \\20 & .3 \\30 & .4 \\40 & .1\end{array}$$ The variance of x equals

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

Question 57

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.The probability that there are 8 occurrences in ten minutes is

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

Question 58

Consider the probability distribution below. x
F(x)
10
)2
20
)3
30
)4
40
)1
​
The expected value of x equals

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

Question 59

The probability distribution for the daily sales at Michael's Co.is given below. $\begin{array}{cc}\text { Daily Sales } & \\\text { (In } \$ 1,000 \text { s) } & \text { Probability } \\40 & 0.1 \\50 & 0.4 \\60 & 0.3 \\70 & 0.2\end{array}$
The probability of having sales of at least $50,000 is

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

Question 60

Random variable x has 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 61

The probability distribution for the number of goals the Lions soccer team makes per game is given below. $$\begin{array} { c c } \text { Number of Goals } & \text { Probability } \\\hline 0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 0.15\end{array}$$
What is the probability that in a given game the Lions will score less than 3 goals?

A) .85
B) .55
C) .45
D) .80

Question 62

A name closely associated with the binomial probability distribution is​

A) ​Bernoulli.
B) ​de Moivre.
C) ​Pareto.
D) ​Poisson.

Question 63

The probability distribution for the daily sales at Michael's Co.is given below. $$\begin{array} { c c } \text { Daily Sales } ( \$ 1,000 s ) & \text { Probability } \\40 & 0.1 \\50 & 0.4 \\60 & 0.3 \\70 & 0.2\end{array}$$
The expected daily sales are

A) $50,000
B) $55,000
C) $56,000
D) $60,000

Question 64

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use th​e

A) ​binomial probability distribution.
B) ​Poisson probability distribution.
C) ​hypergeometric probability distribution.
D) ​exponential probability distribution.

Question 65

The _____ probability function is based in part on the counting rule for combinations.​

A) ​binomial
B) ​Poisson
C) ​hypergeometric
D) ​exponential

Question 66

A binomial probability distribution with p = .3 is​

A) ​negatively skewed.
B) ​symmetric.
C) ​positively skewed.
D) ​multi-modal.

Question 67

If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the​

A) ​binomial probability distribution.
B) ​Poisson probability distribution.
C) ​hypergeometric probability distribution.
D) ​exponential probability distribution.

Question 68

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 69

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) 2.83

Question 70

The use of the relative frequency method to develop discrete probability distributions leads to what is called a​

A) ​binomial discrete distribution.
B) ​empirical discrete distribution.
C) ​non-uniform discrete distribution.
D) ​uniform discrete distribution.

Question 71

Experiments with repeated independent trials will be described by the binomial distribution if​

A) ​the trials are continuous.
B) ​each trial result influences the next.
C) ​the time between trials is constant.
D) ​each trial has exactly two outcomes whose probabilities do not change.

Question 72

The binomial probability distribution is most symmetric when​

A) ​n is 30 or greater.
B) ​n equals p.
C) ​p approaches 1.
D) ​p equals 0.5.

Question 73

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 74

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.
$$\begin{array} { c c } x & f ( x ) \\\hline 0 & 0.80 \\1 & 0.15 \\2 & 0.04 \\3 & 0.01\end{array}$$
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 75

?In a Poisson probability problem, the rate of defects is one every two hours.To find the probability of three defects in four hours,

A) = 1, x = 4
B) 11ef1cb7_756f_355c_98f1_c34873e26645_TB1213_11 = 2, x = 3
C) 11ef1cb7_756f_355c_98f1_c34873e26645_TB1213_11= 3, x = 4
D) 11ef1cb7_756f_355c_98f1_c34873e26645_TB1213_11 = 4, x = 3

Question 76

Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.​

A) ​discrete
B) ​continuous
C) ​uniform
D) ​intermittent

Question 77

In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is​

A) ​2
B) ​5
C) ​6
D) ​10

Question 78

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) ​a nominal random variable.
D) ​a mixed type random variable.

Question 79

Which of the following properties of a binomial experiment is called the stationarity assumption? ​

A) ​The experiment consists of n identical trials
B) ​Two outcomes are possible on each trial
C) ​The probability of success is the same for each trial
D) ​The trials are independent

Question 80

The probability distribution for the number of goals the Lions soccer team makes per game is given below. $$\begin{array} { c c } \text { Number of Goals } & \text { Probability } \\\hline 0 & 0.05 \\1 & 0.15 \\2 & 0.35 \\3 & 0.30 \\4 & 0.15\end{array}$$ The expected number of goals per game is?

A) 2
B) 2.35
C) 2.5
D) 3