Deck 5: Discrete Distributions

Question 1

The Poisson distribution is a continuous distribution which is very useful in solving waiting time problems

Answer 1

False

Question 2

Variables which take on values only at certain points over a given interval are called continuous random variables

Answer 2

False

Question 3

The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

Answer 3

True

Question 4

For the Poisson distribution the mean represents twice the value of the standard deviation.

Question 5

The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20^th of the population size.

Question 6

A Poisson distribution is characterized by one parameter.

Question 7

The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

Question 8

In a binomial experiment, any single trial contains only two possible outcomes and successive trials are independent.

Question 9

For a binomial distribution in which the probability of success is p = 0.5, the variance is twice the mean.

Question 10

A hypergeometric distribution applies to experiments in which the trials represent sampling with replacement.

Question 11

The amount of time a patient waits in a doctor's office is an example of a continuous random variable

Question 12

A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Mexico.

Question 13

For the Poisson distribution the mean and the variance are the same.

Question 14

Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials.

Question 15

Poisson distribution describes the occurrence of discrete events that may occur over a continuous interval of time or space.

Question 16

To compute the variance of a discrete distribution, it is not necessary to know the mean of the distribution.

Question 17

A variable that can take on values at any point over a given interval is called a discrete random variable

Question 18

The number of visitors to a website each day is an example of a discrete random variable

Question 19

In a binomial distribution, p, the probability of getting a successful outcome on any single trial, increases proportionately with every success.

Question 20

The variance of a discrete distribution increases if we add a positive constant to each one of its values.

Question 21

If the owner of a deli wanted to see all the outcomes of the time between arrivals at the deli counter during 2-hour lunch periods with the probabilities of each outcome, this would be __________.

A)a discrete random variable
B)a continuous random variable
C)the continuous distribution
D)the normal distribution
E)a discrete distribution

Question 22

A manufacturer of cans of soda pop weights every 10^th can to determine if the production line is working properly.The number of cans weighed in an hour would be an example of ___________.

A)a discrete random variable
B)a continuous random variable
C)the continuous distribution
D)the normal distribution
E)a discrete distribution

Question 23

You are offered an investment opportunity.Its outcomes and probabilities are presented in the following table. $$\begin{array} { | c | c | } \hline \boldsymbol { x } & P ( \boldsymbol { x } ) \\\hline \hline - \$ 1,000 & 40 \\\hline \$ 0 & .20 \\\hline + \$ 1,000 & .40 \\\hline\end{array}$$ Which of the following statements is true?

A)This distribution is skewed to the right.
B)This is a binomial distribution.
C)This distribution is symmetric.
D)This distribution is skewed to the left.
E)This is a Poisson distribution

Question 24

The volume of liquid in an unopened 1-gallon can of paint is an example of _________.

A)the binomial distribution
B)both discrete and continuous variable
C)a continuous random variable
D)a discrete random variable
E)a constant

Question 25

If the owner of a deli wanted to see all the outcomes of how many sandwiches are sold during 2-hour lunch periods with the probabilities of each outcome, this would be __________.

A)a discrete random variable
B)a continuous random variable
C)the continuous distribution
D)the normal distribution
E)a discrete distribution

Question 26

A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.In this distribution, x represents the number of sodas which an adult drinks. $$\begin{array} { | c | c | } \hline x & P ( x ) \\\hline 0 & 0.30 \\\hline 1 & 0.10 \\\hline 2 & 0.50 \\\hline 3 & 0.10 \\\hline\end{array}$$ The mean (average)value of x is _______________.

A)1.40
B)1.75
C)2.10
D)2.55
E)3.02

Question 27

The number of successes in a hypergeometric distribution is unknown

Question 28

The number of sandwiches sold at a deli during a 2-hour lunch period would be an example of _____________.

A)neither discrete nor continuous random variable
B)both discrete and continuous random variable
C)a continuous random variable
D)a discrete random variable
E)a constant

Question 29

The speed at which a jet plane can fly is an example of _________.

A)neither discrete nor continuous random variable
B)both discrete and continuous random variable
C)a continuous random variable
D)a discrete random variable
E)a constant

Question 30

In a hypergeometric distribution the population, N, is finite and known.

Question 31

A recent analysis of the number of rainy days per month found the following outcomes and probabilities. $$\begin{array} { | c | c | } \hline \text { Namber of Raining Days } ( x ) & \mathrm { P } ( x ) \\\hline \hline 3 & .40 \\\hline 4 & .20 \\\hline 5 & .40 \\\hline\end{array}$$ The standard deviation of this distribution is _____________.

A).800
B).894
C).400
D)4.00
E).457

Question 32

The number of finance majors within the School of Business is an example of _______.

A)a discrete random variable
B)a continuous random variable
C)the Poisson distribution
D)the normal distribution
E)a constant

Question 33

As in a binomial distribution, each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes, i.e., either a success or a failure.

Question 34

A recent analysis of the number of rainy days per month found the following outcomes and probabilities. $$\begin{array} { | c | c | } \hline \text { Namber of Raining Days } ( x ) & \mathrm { P } ( x ) \\\hline \hline 3 & .40 \\\hline 4 & .20 \\\hline 5 & .40 \\\hline\end{array}$$ The mean of this distribution is _____________.

A)2
B)3
C)4
D)5
E)<1

Question 35

A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.In this distribution, x represents the number of sodas which an adult drinks. $$\begin{array} { | l | l | } \hline \boldsymbol { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 0 & 0.30 \\\hline 1 & 0.10 \\\hline 2 & 0.50 \\\hline 3 & 0.10 \\\hline\end{array}$$ The standard deviation of x is _______________.

A)1.04
B)0.89
C)1.40
D)1.02
E).588

Question 36

A manufacturer of cans of soda pop weighs every 10^th can to determine if the production line is working properly.The weight of the cans would be an example of ___________.

A)a discrete random variable
B)a continuous random variable
C)the continuous distribution
D)the normal distribution
E)a discrete distribution

Question 37

In American Roulette, there are two zeroes and 36 non-zero numbers (18 red and 18 black).If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (or winning -1)is 20/38.Let x be the player profit per game.The mean (average)value of x is approximately_______________.

A)0.0526
B)-0.0526
C)1
D)-1
E)0

Question 38

The time between customer arrivals at a deli counter during a 2-hour lunch period would be an example of _____________.

A)neither discrete nor continuous random variable
B)both discrete and continuous random variable
C)a continuous random variable
D)a discrete random variable
E)a constant

Question 39

A manufacturer of cans of soda pop weighs every 10^th can to determine if the production line is working properly.The possible outcomes of how many cans weighed in an hour and their associated probabilities would be an example of ___________.

A)a discrete random variable
B)a continuous random variable
C)the continuous distribution
D)the normal distribution
E)a discrete distribution

Question 40

A market research team compiled the following discrete probability distribution.In this distribution, x represents the number of automobiles owned by a family. $$\begin{array} { | c | c | } \hline x & P ( x ) \\\hline 0 & 0.10 \\\hline 1 & 0.10 \\\hline 2 & 0.50 \\\hline 3 & 0.30 \\\hline\end{array}$$ Which of the following statements is true?

A)This distribution is skewed to the right.
B)This is a binomial distribution.
C)This is a normal distribution.
D)This distribution is skewed to the left.
E)This distribution is bimodal.

Question 41

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2016.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contains errors, the standard deviation of x is ______.

A)1.26
B)1.60
C)14.14
D)3.16
E)0.00

Question 42

If x has a binomial distribution with p = .5, then the distribution of x is ________.

A)skewed to the right
B)skewed to the left
C)symmetric
D)a Poisson distribution
E)a hypergeometric distribution

Question 43

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2016.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors, P(x>0)is _______________.

A)0.8171
B)0.1074
C)0.8926
D)0.3020
E)1.0000

Question 44

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x>0)is ______________.

A)0.2172
B)0.9533
C)0.1846
D)0.9222
E)1.0000

Question 45

The following graph is a binomial distribution with n = 6. This graph reveals that ____________.

A)p > 0.5
B)p = 1.0
C)p = 0
D)p < 0.5
E)p = 1.5

Question 46

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x<2)is ______________.

A)0.3370
B)0.9853
C)0.9785
D)0.2333
E)0.5000

Question 47

Twenty-five individuals are randomly selected out of 100 shoppers leaving a local bedding store.Each shopper was asked if they made a purchase during their visit.Each of the shoppers has the same probability of answering 'yes' to having made a purchase.The probability that exactly four of the twenty-five shoppers made a purchase could best be found by _______.

A)using the normal distribution
B)using the binomial distribution
C)using the Poisson distribution
D)using the exponential distribution
E)using the uniform distribution

Question 48

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2016.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors, P(x = 0)is _______________.

A)0.8171
B)0.1074
C)0.8926
D)0.3020
E)0.2000

Question 49

If x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____.

A)6
B)4.8
C)3.2
D)8
E)48

Question 50

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0)is ______________.

A)0.8154
B)0.0467
C)0.0778
D)0.4000
E)0.5000

Question 51

A market research team compiled the following discrete probability distribution for families residing in Randolph County.In this distribution, x represents the number of evenings the family dines outside their home during a week. $$\begin{array} { | c | c | } \hline x & P ( x ) \\\hline 0 & 0.30 \\\hline 1 & 0.50 \\\hline 2 & 0.10 \\\hline 3 & 0.10 \\\hline\end{array}$$ The mean (average)value of x is _______________.

A)1.0
B)1.5
C)2.0
D)2.5
E)3.0

Question 52

If x is a binomial random variable with n=10 and p=0.8, the standard deviation of x is _________.

A)8.0
B)1.26
C)1.60
D)64.0
E)10

Question 53

A student randomly guesses the answers to a five-question true/false test.If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?

A)0.200
B)0.031
C)0.156
D)0.073
E)0.001

Question 54

The following graph is a binomial distribution with n = 6. This graph reveals that ____________.

A)p > 0.5
B)p = 1.0
C)p = 0
D)p < 0.5
E)p = 1.5

Question 55

The following graph is a binomial distribution with n = 6. This graph reveals that ____________.

A)p = 0.5
B)p = 1.0
C)p = 0
D)p < 0.5
E)p = 1.5

Question 56

If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?

A).0055
B).0063
C).124
D).232
E).994

Question 57

During a recent sporting event, a quarter is tossed to determine which team picks the starting side.Suppose the referee says the coin will be tossed 3 times and the best two out of three wins If team A calls 'heads', what is the probability that exactly two heads are observed in three tosses?

A).313
B).375
C).625
D).875
E).500

Question 58

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2016.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contains errors, the mean value of x is __________.

A)400
B)2
C)200
D)5
E)1

Question 59

A market research team compiled the following discrete probability distribution for families residing in Randolph County.In this distribution, x represents the number of evenings the family dines outside their home during a week. $$\begin{array} { | c | c | } \hline x & P ( x ) \\\hline 0 & 0.30 \\\hline 1 & 0.50 \\\hline 2 & 0.10 \\\hline 3 & 0.10 \\\hline\end{array}$$ The standard deviation of x is _______________.

A)1.00
B)2.00
C)0.80
D)0.89
E)1.09

Question 60

A student randomly guesses the answers to a five-question true/false test.If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions?

A)0.000
B)0.200
C)0.500
D)0.031
E)1.000

Question 61

The number of bags arriving on the baggage claim conveyor belt in a 3-minute time period would best be modeled with the _________.

A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Question 62

The hypergeometric distribution must be used instead of the binomial distribution when ______

A)sampling is done with replacement
B)sampling is done without replacement
C)n≥5% N
D)both b and c
E)there are more than two possible outcomes

Question 63

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices, 10% receive the discount.In a company audit, 10 invoices are sampled at random.The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

A)0.1937
B)0.057
C)0.001
D)0.3486
E)0.9298

Question 64

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number on non-authentic names in her sample, the expected (average)value of x is ______________.

A)2.50
B)2.00
C)1.50
D)1.25
E)1.35

Question 65

The Poisson distribution is being used to approximate a binomial distribution.If n=30 and p=0.03, what value of lambda would be used?

A)0.09
B)9.0
C)0.90
D)90
E)30

Question 66

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 3 cars arriving over a five-minute interval is _______.

A)0.2700
B)0.0498
C)0.2240
D)0.0001
E)0.0020

Question 67

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that all three of the selected faculty are men is approximately _______

A)0.05
B)0.33
C)0.11
D)0.80
E)0.90

Question 68

The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modeled with the _______.

A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Question 69

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next five-minute interval is _____________.

A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.3610

Question 70

The number of defects per 1,000 feet of extruded plastic pipe is best modeled with the ________________.

A)Poisson distribution
B)Pascal distribution
C)binomial distribution
D)hypergeometric distribution
E)exponential distribution

Question 71

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is _____________.

A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.5000

Question 72

In a certain communications system, there is an average of 1 transmission error per 10 seconds.Assume that the distribution of transmission errors is Poisson.The probability of 1 error in a period of one-half minute is approximately ________

A)0.1494
B)0.3333
C)0.3678
D)0.1336
E)0.03

Question 73

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 5 cars arriving over a five-minute interval is _______.

A)0.0940
B)0.0417
C)0.1500
D)0.1008
E)0.2890

Question 74

Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes.The number of occurrences per hour follows a Poisson distribution with λ equal to _________

A)5
B)60
C)30
D)10
E)20

Question 75

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices, 10% receive the discount.In a company audit, 15 invoices are sampled at random.The mean (average)value of the number of the 15 sampled invoices that receive discount is _______

A)1
B)3
C)1.5
D)2
E)10

Question 76

The Poisson distribution is being used to approximate a binomial distribution.If n=60 and p=0.02, what value of lambda would be used?

A)0.02
B)12
C)0.12
D)1.2
E)120

Question 77

Which of the following conditions is not a condition for the hypergeometric distribution?

A)the probability of success is the same on each trial
B)sampling is done without replacement
C)there are only two possible outcomes
D)trials are dependent
E)n < 5%N

Question 78

It is known that screws produced by a certain company will be defective with a probability of .01, independently of each other.The company sells the screws in packages of 25 and offers a money-back guarantee that at most, 1 of the 25 screws is defective.Using Poisson approximation for binomial distribution, the probability that the company must replace a package is approximately _________

A)0.01
B)0.1947
C)0.7788
D)0.0265
E)0.2211

Question 79

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that one male faculty and two female faculty are selected is approximately ______

A)0.15
B)0.06
C)0.33
D)0.48
E)0.58

Question 80

The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.

A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution