Deck 5: Discrete Probability Distributions

Question 1

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.

Answer 1

the expected value

Question 2

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 2

any value in an interval or collection of intervals

Question 3

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

Answer 3

a discrete random variable

Question 4

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
C) ∑f(x) = 0
D) All of the answers are correct.

Question 5

Which of the following statements about a discrete random variable and its probability distribution is true?

A) Values of the random variable can never be negative.
B) Negative values of f(x) are allowed if ∑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.

Question 6

Highway patrol officers measure the speed of automobiles on a highway using 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 7

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 8

The number of customers who 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 9

A marketing manager instructs his team to make 80 telephone calls to attempt to sell an 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 10

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

Question 11

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 12

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

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

Question 13

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

A) ∑f(x) = 0
B) f(x) ≥ 1 for all values of x
C) f(x) < 0
D) None of the answers is correct.

Question 14

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

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

Question 15

A description of how the probabilities are distributed over the values the random variable can assume is called a(n) _____.

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

Question 16

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 17

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 18

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 19

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.

Question 20

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 21

The standard deviation of a binomial distribution is _____.

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

Question 22

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 the answers are correct.

Question 23

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 24

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 25

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 26

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

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

Question 27

In a binomial experiment, the probability of success is .06. What is the probability of two successes in seven trials?

A) .0036
B) .06
C) .0554
D) .28

Question 28

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 29

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 30

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 31

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 32

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

Question 33

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 34

If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two 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 35

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 the answers are correct.

Question 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)

Question 37

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) .2592
B) .0142
C) .9588
D) .7408

Question 38

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

A) At least two outcomes are possible.
B) The probability of success changes from trial to trial.
C) The trials are independent.
D) All of the answers are correct.

Question 39

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) .0004
B) .0038
C) .10
D) .02

Question 40

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 .577
C) 3 and .01
D) 0 and .8

Question 41

The key difference between binomial and hypergeometric distributions is that with the hypergeometric distribution the _____.

A) probability of success must be less than .5
B) probability of success changes from trial to trial
C) trials are independent of each other
D) random variable is continuous

Question 42

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 43

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 44

When using Excel's HYPGEOM.DIST function, one should choose TRUE for the fifth input if _____.

A) a probability is desired
B) a cumulative probability is desired
C) the expected value is desired
D) None of the answers is correct.

Question 45

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

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

Question 46

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 47

If one wanted to find the probability of 10 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 48

Excel's HYPGEOM.DIST function can be used to compute _____.

A) bin width for histograms
B) hypergeometric probabilities
C) cumulative hypergeometric probabilities
D) both hypergeometric probabilities and cumulative hypergeometric probabilities

Question 49

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 50

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 51

The Poisson probability distribution is a _____.

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

Question 52

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

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

Question 53

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

Question 54

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 55

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

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

Question 56

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 57

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

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 58

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 59

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 60

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

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

Question 61

To compute a binomial probability. we must know all of the following except the _____.

A) probability of success
B) number of elements in the population
C) number of trials
D) value of the random variable

Question 62

A binomial probability distribution with p = 0.3 is _____.

A) negatively skewed
B) symmetrical
C) positively skewed
D) bimodal

Question 63

The function used to compute the probability of x successes in n trials, when the trials are dependent, is the _____.

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

Question 64

An example of a bivariate experiment is _____.

A) tossing a coin once
B) rolling a pair of dice
C) winning or losing a football game
D) passing or failing a course

Question 65

Bivariate probabilities are often called _____.

A) union probabilities
B) conditional probabilities
C) marginal probabilities
D) joint probabilities

Question 66

A property of the Poisson distribution is that the mean equals the _____.

A) mode
B) median
C) variance
D) standard deviation

Question 67

The expected value of a random variable is the _____.

A) most probable value
B) simple average of all the possible values
C) median value
D) mean value

Question 68

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