Deck 6: Discrete Probability Distributions

Question 1

The Poisson distribution is appropriate to describe the number of babies born in a small hospital on a given day.

Answer 1

True

Question 2

A discrete random variable has a countable number of distinct values.

Answer 2

True

Question 3

To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.

Answer 3

False

Question 4

The hypergeometric distribution is skewed right.

Question 5

Calculating the probability of getting three aces in a hand of five cards dealt from a deck of 52 cards would require the use of a hypergeometric distribution.

Question 6

Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.

Question 7

The hypergeometric distribution assumes that the probability of a success remains the same from one trial to the next.

Question 8

A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment.

Question 9

A discrete binomial distribution is skewed right when π > .50.

Question 10

The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.

Question 11

The outcomes for the sum of two dice can be described as a discrete uniform distribution.

Question 12

The hypergeometric distribution is not applicable if sampling is done with replacement.

Question 13

An example of a geometric random variable is the number of pine trees with pine beetle infestation in a random sample of 15 pine trees in Colorado.

Question 14

A random variable may be discrete or continuous, but not both.

Question 15

As a rule of thumb, the Poisson distribution can be used to approximate a binomial distribution when n ≥ 20 and π ≤ .05.

Question 16

A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF).

Question 17

The Poisson distribution can be skewed either left or right, depending on λ.

Question 18

When π = .70 the discrete binomial distribution is negatively skewed.

Question 19

The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities.

Question 20

As a rule of thumb, the binomial distribution can be used to approximate the hypergeometric distribution whenever the population is at least 20 times as large as the sample.

Question 21

Which is not a discrete random variable?

A)The number of defects in a 4 × 8 sheet of plywood
B)The number of female passengers who board a plane
C)The time until failure of a vehicle headlamp
D)The number of correct answers on a statistics exam

Question 22

Which probability model is most nearly appropriate to describe the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes, assuming a constant probability of a burned-out tube?

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

Question 23

Which is not a discrete random variable?

A)The number of births in a hospital on a given day
B)The number of fives obtained in four rolls of a die
C)The hourly earnings of a call center employee in Boston
D)The number of applicants applying for a civil service job

Question 24

The random variable X is the number of shots it takes before you make the first free throw in basketball. Assuming the probability of success (making a free throw) is constant from trial to trial, what type of distribution does X follow?

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

Question 25

The Poisson distribution has only one parameter.

Question 26

A discrete probability distribution:

A)is a listing of all possible values of the random variable.
B)assigns a probability to each possible value of the random variable.
C)can assume values between -1 and +1.
D)is independent of the parameters of the distribution.

Question 27

The number of male babies in a sample of 10 randomly chosen babies is a:

A)continuous random variable.
B)Poisson random variable.
C)binary random variable.
D)binomial random variable.

Question 28

The standard deviation of a Poisson random variable is the square root of its mean.

Question 29

Which model would you use to describe the probability that a call-center operator will make the first sale on the third call, assuming a constant probability of making a sale?

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

Question 30

The gender (M, F) of a randomly chosen unborn child is a Bernoulli event.

Question 31

The expected value of a random variable is its mean.

Question 32

In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

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

Question 33

Which model best describes the number of nonworking web URLs ("This page cannot be displayed") you encounter in a randomly chosen minute while surfing websites for Florida vacation rental condos?

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

Question 34

A discrete random variable:

A)can be treated as continuous when it has a large range of values.
B)cannot be treated as continuous.
C)is best avoided if at all possible.
D)is usually uniformly distributed.

Question 35

Customer arrivals per unit of time would tend to follow a binomial distribution.

Question 36

Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

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

Question 37

Which statement is incorrect?

A)The Poisson distribution is always skewed right.
B)The binomial distribution may be skewed left or right.
C)The discrete uniform distribution is always symmetric.
D)The hypergeometric distribution is symmetric.

Question 38

The two outcomes (success, failure) in the Bernoulli model are equally likely.

Question 39

Which model best describes the number of incorrect fare quotations by a well-trained airline ticket agent between 2 p.m. and 3 p.m. on a particular Thursday?

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

Question 40

Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?

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

Question 41

Which probability model would you use to describe the number of customers served at a certain California Pizza Kitchen until the first customer orders split pea soup?

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

Question 42

On a particular Thursday in August, 40 Grand Canyon tourists enter a drawing for a free mule ride. Ten of the entrants are European tourists. Five entrants are selected at random to get the free mule ride. Which model best describes the number of European tourists in the random sample?

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

Question 43

A die is rolled. If it rolls to a 1, 2, or 3, you win $2. If it rolls to a 4, 5, or 6, you lose $1. Calculate the expected winnings.

A)$0.50
B)$3.00
C)$1.50
D)$1.00

Question 44

Ephemeral Services Corporation (ESCO) knows that nine other companies besides ESCO are bidding for a $900,000 government contract. Each company has an equal chance of being awarded the contract. If ESCO has already spent $100,000 in developing its bidding proposal, what is its expected net profit?

A)$100,000
B)$90,000
C)-$10,000
D)$0

Question 45

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? $$\begin{array} { l c c c c r } X & 0 & 1 & 2 & 3 & \text { Total } \\P ( X ) & 40 & 30 & 20 & 10 & 1.00\end{array}$$

A)1.2
B)1.0
C)1.5
D)2.0

Question 46

Given the following probability distribution, what is the expected value of the random variable X? $$\begin{array} { c c } X & P ( X ) \\100 & .10 \\150 & .20 \\200 & .30 \\250 & .30 \\300 & .10 \\\text { Sum } & 1.00\end{array}$$

A)175
B)150
C)200
D)205

Question 47

To ensure quality, customer calls for airline fare quotations are monitored at random. On a particular Thursday afternoon, ticket agent Bob gives 40 fare quotations, of which 4 are incorrect. In a random sample of 8 of these customer calls, which model best describes the number of incorrect quotations Bob will make?

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

Question 48

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that at least 1 student comes to office hours on any given Monday? $$\begin{array} { l c c c c r } X & 0 & 1 & 2 & 3 & \text { Total } \\P ( X ) & 40 & 30 & 20 & 10 & 1.00\end{array}$$

A).30
B).40
C).50
D).60

Question 49

The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? $$\begin{array} { l c c c c r } X & 0 & 1 & 2 & 3 & \text { Total } \\P ( X ) & 20 & 40 & 30 & 10 & 1.00\end{array}$$

A)1.1
B)1.3
C)1.7
D)1.9

Question 50

Of the following, the one that most resembles a Poisson random variable is the number of:

A)heads in 200 flips of a fair coin.
B)annual power failures at your residence.
C)face cards in a bridge hand of 13 cards.
D)defective CDs in a spool containing 15 CDs.

Question 51

Which model best describes the number of births in a hospital until the first twins are delivered?

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

Question 52

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that fewer than 2 students come to office hours on any given Monday? $$\begin{array} { l c c c c r } X & 0 & 1 & 2 & 3 & \text { Total } \\P ( X ) & 40 & 30 & 20 & 10 & 1.00\end{array}$$

A).10
B).40
C).70
D).90

Question 53

Which model best describes the number of blemishes per sheet of white bond paper?

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

Question 54

A carnival has a game of chance: a fair coin is tossed. If it lands heads you win $1.00, and if it lands tails you lose $0.50. How much should a ticket to play this game cost if the carnival wants to break even?

A)$0.25
B)$0.50
C)$0.75
D)$1.00

Question 55

A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6, you lose $1. Calculate the expected winnings.

A)$0.00
B)$1.00
C)$0.50
D)$0.25

Question 56

On a randomly chosen Wednesday, which probability model would you use to describe the number of convenience store robberies in Los Angeles?

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

Question 57

A charity raffle prize is $1,000. The charity sells 4,000 raffle tickets. One winner will be selected at random. At what ticket price would a ticket buyer expect to break even?

A)$0.50
B)$0.25
C)$0.75
D)$1.00

Question 58

Which distribution has a mean of 5?

A)Poisson with λ = 25
B)Binomial with n = 200, π = .05
C)Hypergeometric with N = 100, n = 10, s = 50

Question 59

The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

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

Question 60

Which of the following characterizes a Bernoulli process?

A)A random experiment that has only two outcomes.
B)The probability of "success" varies with each trial.
C)Either outcome has the same chance of occurrence.
D)The "success" must be a desirable outcome.

Question 61

Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned?

A).9950
B).9619
C).0331
D).1488

Question 62

If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

A).5987
B).3151
C).0116
D).1872

Question 63

The probability that a visitor to an animal shelter will adopt a dog is .20. Out of nine visits, what is the probability that at least one dog will be adopted?

A).8658
B).3020
C).5639
D).1342

Question 64

Which of the following is not a requirement of a binomial distribution?

A)Constant probability of success
B)Only two possible Bernoulli outcomes
C)Fixed number of trials
D)Equally likely outcomes

Question 65

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

A).6174
B).3826
C).8131
D).1869

Question 66

The probability that an Oxnard University student is carrying a backpack is .70. If 10 students are observed at random, what is the probability that fewer than 7 will be carrying backpacks?

A).3504
B).2001
C).6177
D).2668

Question 67

A random variable X is distributed binomially with n = 8 and π = 0.70. The standard deviation of the variable X is approximately:

A)0.458
B)2.828
C)1.680
D)1.296

Question 68

In Quebec, 90 percent of the population subscribes to the Roman Catholic religion. In a random sample of eight Quebecois, find the probability that the sample contains at least five Roman Catholics.

A).0050
B).0331
C).9950
D).9619

Question 69

The expected value (mean) of a binomial variable is 15. The number of trials is 20. The probability of "success" is:

A).25
B).50
C).75
D).30

Question 70

A network has three independent file servers, each with 90 percent reliability. The probability that the network will be functioning correctly (at least one server is working) at a given time is:

A)99.9 percent.
B)97.2 percent.
C)95.9 percent.
D)72.9 percent.

Question 71

A random variable is binomially distributed with n = 16 and π = .40. The expected value and standard deviation of the variables are:

A)2.00 and 1.24
B)4.80 and 4.00
C)6.40 and 1.96
D)2.00 and 1.20

Question 72

Which distribution is most strongly right-skewed?

A)Binomial with n = 50, π = .70
B)Binomial with n = 50, π = .90
C)Binomial with n = 50, π = .40
D)Binomial with n = 50, π = .10

Question 73

Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and π = .25?

A)=BINOM.DIST(RAND(),16,.25,0)
B)=BINOM.DIST(0,16,.25,RAND())
C)=BINOM.INV(16,.25,RAND())
D)=BINOM.INV(0,16,.25,RAND())

Question 74

An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

A).5615
B).2775
C).7161
D).0388

Question 75

The variance will reach a maximum in a binomial distribution when:

A)π = 1 and 1 - π = 0.
B)π = ¼ and 1 - π = ¾.
C)π = ½ and 1 - π = ½.
D)π = 0 and 1 - π = 1.

Question 76

Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?

A).2055
B).2362
C).7946
D).4417

Question 77

The binomial distribution is symmetrical when:

A)π = 1 and 1 - π = 0.
B)π = ¼ and 1 - π = ¾.
C)π = ½ and 1 - π = ½.
D)π = 0 and 1 - π = 1.

Question 78

Suppose X is binomially distributed with n = 12 and π = .20. The probability that X will be less than or equal to 3 is:

A).5584
B).7946
C).2362
D).7638

Question 79

Based on experience, 60 percent of the women who request a pregnancy test at a certain clinic are actually pregnant. In a random sample of 12 women, what is the probability that at least 10 are pregnant?

A).0639
B).1424
C).0196
D).0835

Question 80

The binomial distribution describes the number of:

A)trials to obtain the first "success" in a Bernoulli process.
B)trials to obtain n "successes" in a Bernoulli process.
C)"successes" or "failures" in a Bernoulli process.
D)"successes" in n Bernoulli trials.