Question 1

Which model best describes the number of blemishes per sheet of white bond paper?
A) Binomial
B) Poisson
C) Hypergeometric
D) Geometric

Accepted Answer

The Poisson model is the best choice as it is used to model the number of occurrences of a rare event in a fixed interval of time or space, which is suitable for the situation of counting the number of blemishes on a sheet of paper.

Question 2

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

Accepted Answer

The Poisson distribution is used to model the number of rare events in a fixed unit of time or space. Convenience store robberies are relatively rare events and can therefore be modeled using the Poisson distribution. The other options are not appropriate because they have additional constraints or conditions, such as a fixed number of trials or a specific population size, that are not relevant to this scenario.

Question 3

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

Accepted Answer

The answer of A charity raffle prize is $1,000.The charity...

Question 4

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

Accepted Answer

The hypergeometric model is best because it involves sampling without replacement from a finite population where each sample can be classified into one of two categories (correct or incorrect quotations).

Question 5

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

Accepted Answer

The situation describes a hypergeometric distribution since we are selecting a sample without putting back the selected entrants. Additionally, we are interested in the number of European tourists in the selected sample, which is not a fixed number of trials, so it does not fit the binomial or geometric models. The Poisson model describes the probability of a certain number of events occurring in a fixed interval of time or space, which is not applicable to this situation.

Question 6

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.Find the expected winnings.
A) $0.00
B) $1.00
C) $0.50
D) $0.25

Accepted Answer

The probability of rolling a 1 or 2 is 2/6, and the probability of rolling a 3, 4, 5, or 6 is 4/6. The expected winnings are (2/6)*$2 + (4/6)*(-$1) = $0.00.

Question 7

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

Accepted Answer

The geometric model describes the probability distribution of waiting for the first success in a sequence of independent Bernoulli trials. In this case, each birth is a Bernoulli trial with a success being the occurrence of twins. The number of trials required to achieve the first success (twins) follows a geometric distribution.

Question 8

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

Accepted Answer

The answer of The discrete random variable X is the...

Question 9

Given the following probability distribution,what is the expected value of the random variable X? 
A) 175
B) 150
C) 200
D) 205

Accepted Answer

The answer of Given the following probability distribution,what is the...

Question 10

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

Accepted Answer

The answer of The discrete random variable X is the...

Question 11

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

Accepted Answer

The answer of Which distribution has a mean of 5?
A)...

Question 12

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.

Accepted Answer

A Bernoulli process is a random experiment that has only two outcomes.

Question 13

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

Accepted Answer

The answer of The discrete random variable X is the...

Question 14

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

Accepted Answer

The answer of The discrete random variable X is the...

Question 15

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.Find the expected winnings.
A) $0.50
B) $3.00
C) $1.50
D) $1.00

Accepted Answer

The probability of rolling a 1, 2, or 3 is 1/2, and the probability of rolling a 4, 5, or 6 is also 1/2. The expected winnings are (1/2 * $2) + (1/2 * -$1) = $0.50.

Question 16

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

Accepted Answer

A geometric probability model is used to describe the number of trials needed to achieve a success (in this case, the first customer ordering split pea soup). The number of customers served before the first split pea soup order is a random variable that follows a geometric distribution.

Question 17

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

Accepted Answer

The answer of Ephemeral Services Corporation (ESCO)knows that nine other...

Question 18

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

Accepted Answer

The expected value of the game is calculated as (0.5 * $1.00) + (0.5 * -$0.50) = $0.25. To break even, the ticket should cost $0.25.

Question 19

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

Accepted Answer

The Poisson model is appropriate for modeling rare events, such as the number of injuries in a rafting expedition. The other models (binomial, hypergeometric, geometric) are not appropriate for this scenario.

Question 20

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.

Accepted Answer

A Poisson random variable is characterized by the number of occurrences of rare events in a fixed interval of time or space. Power failures at a residence are rare events that can be reasonably modeled by a Poisson distribution. The other options do not fit the characteristics of a Poisson distribution.

Quiz 6: Discrete Probability Distributions

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

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

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?

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 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.Find the expected winnings.

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

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?

Given the following probability distribution,what is the expected value of the random variable X?

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?

Which distribution has a mean of 5?

Which of the following characterizes a Bernoulli process?

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?

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?

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.Find the expected winnings.

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?

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 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?

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?

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