Deck 5: Discrete Probability Distributions

Question 1

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

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

Answer 1

expected value.

Question 2

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 _____ distribution

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

Answer 2

Poisson

Question 3

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 3

The trials are dependent.

Question 4

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 5

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 6

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

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

Question 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

Question 8

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 9

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

Question 10

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 11

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 12

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.

Question 13

The binomial probability distribution is used with a(n) _____ random variable.

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

Question 14

Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is

A) 20.
B) 64.
C) 8.
D) 40.

Question 15

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 16

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 17

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 _____ random variable.

A) discrete
B) continuous
C) mixed type
D) multivariate

Question 18

Three 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) 0.0003
B) 0.0082
C) 0.0077
D) 0.0008

Question 19

The Poisson probability distribution is a _____ probability distribution.

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

Question 20

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 21

The following represents the probability distribution for the daily demand of computers at a local store. ​ The expected daily demand is

A) 1.0.
B) 1.75.
C) 2.0.
D) 1.09.

Question 22

The following represents the probability distribution for the daily demand of computers at a local store. ​ The probability of having a demand for at least two computers is

A) 0.75.
B) 0.35.
C) 0.60.
D) 1.00.

Question 23

In a binomial experiment the probability of success is 0.05. What is the probability of two successes in seven trials?

A) 0.0036
B) 0.0000
C) 0.0406
D) 0.3667

Question 24

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 female?

A) 0.3154
B) 0.6846
C) 0.0168
D) 0.8936

Question 25

A production process produces 2.5% 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) 0.2637
B) 0.0058
C) 0.0000
D) 0.0250

Question 26

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. ​ The variance is

A) 1.45.
B) 2.09.
C) 3.1.
D) 9.61.

Question 27

The Poisson probability distribution is used with _____ random variable.

A) a continuous
B) a discrete
C) either a continuous or discrete
D) any

Question 28

In a binomial experiment, the probability

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

Question 29

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 male?

A) 0.0896
B) 0.2090
C) 0.0413
D) 0.0007

Question 30

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 31

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a _____ distribution.

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

Question 32

The key difference between the binomial and hypergeometric distribution is that, with the hypergeometric distribution the

A) probability of success must be less than 0.5.
B) probability of success changes from trial to trial.
C) trials are independent of each other.
D) random variable is continuous.

Question 33

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 34

The student body of a large university consists of 65% 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) 0.0036
B) 0.1691
C) 0.4278
D) 0.0253

Question 35

A random variable that may take on any value in an interval or collection of intervals is known as a _____ random variable.

A) continuous
B) discrete
C) mixed type
D) multivariate

Question 36

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. ​ The expected number of new clients per month is

A) 6.
B) 0.
C) 3.1.
D) 3.

Question 37

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. ​ ​
The standard deviation is

A) 1.45.
B) 2.09.
C) 3.1.
D) 9.61.

Question 38

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 39

Assume that you have a binomial experiment with p = 0.4 and a sample size of 150. The variance of this distribution is

A) 36.
B) 6.
C) 2.9.
D) 216.

Question 40

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 41

Consider the probability distribution below. ​ The expected value of x equals

A) 23.
B) 25.
C) 30.
D) 100.

Question 42

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 43

The probability distribution for the number of goals the Lions soccer team makes per game is given below. ​ 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 44

The probability that Pete will catch fish when he goes fishing is .88. 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) 0.56.
B) 0.88.
C) 2.64.
D) 0.3168.

Question 45

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. The standard deviation for the production is

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

Question 46

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 47

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 48

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 49

The probability distribution for the daily sales at Michael's Co. is given below. ​ The probability of having sales of at least $50,000 is

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

Question 50

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. The expected monthly production level is

A) 1.00.
B) 4.00.
C) 3.00.
D) 3.84.

Question 51

The probability that Pete will catch fish when he goes fishing is .88. 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) 0.56.
B) 0.88.
C) 2.64.
D) 0.3168.

Question 52

Forty-four 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) 0.0551.
B) 0.9450.
C) 0.4400.
D) 0.1649.

Question 53

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 54

Forty-four 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) 0.6600.
B) 0.6114.
C) 0.5000.
D) 0.3400.

Question 55

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 expected number of cups of coffee is

A) 1.
B) 1.24.
C) 1.5.
D) 1.03.

Question 56

The probability distribution for the daily sales at Michael's Co. is given below. ​ 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 57

Consider the probability distribution below. ​ The variance of x equals

A) 9.
B) 23.
C) 81.
D) 610.

Question 58

The probability that Pete will catch fish when he goes fishing is .88. 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) 0.880.
B) 0.038.
C) 0.040.
D) 0.960.

Question 59

The probability that Pete will catch fish when he goes fishing is .88. 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) 0.880.
B) 0.038.
C) 0.040.
D) 0.960.

Question 60

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 variance of the number of cups of coffee is

A) 1.06.
B) 1.03.
C) 2.25.
D) 1.24.

Question 61

A production process produces 3% 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) 0.9918
B) 0.0082
C) 0.0003
D) 0.9997

Question 62

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

A) binomial
B) empirical
C) non-uniform
D) uniform

Question 63

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. ​
Compute the variance and the standard deviation for this probability distribution.

Question 64

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.

Question 65

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

A) 2.
B) 2.33.
C) 2.5.
D) 1.1.

Question 66

In a binomial experiment the probability of success is 0.16. What is the probability of two successes in seven trials?

A) 0.7752
B) 0.0866
C) 0.2248
D) 0.9134

Question 67

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 68

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 69

The mean number of pages per day written by an author is 27. What is the probability this author writes 33 pages on a particular day? Assume a Poisson distribution for this scenario.

A) 0.0372.
B) 0.9628.
C) 0.4277.
D) 0.9572.

Question 70

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 71

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

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

Question 72

The probability distribution for the number of goals the Lions soccer team makes per game is given below. ​ ​
What is the probability that in a given game the Lions will score less than 2 goals?

A) .20
B) .50
C) .15
D) .80

Question 73

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

A) $53,000.
B) $55,000.
C) $50,000.
D) $60,000.

Question 74

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 75

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the _____ probability distribution.

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

Question 76

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 77

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 78

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

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

Question 79

A name closely associated with the binomial probability distribution is​

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

Question 80

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.