Question 1

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)Uniform

Accepted Answer

The Poisson probability model would be the best choice to describe the number of convenience store robberies in Los Angeles on a randomly chosen Wednesday. This is because the Poisson model is appropriate when the events occur randomly and independently of each other over time or space, and the average rate of occurrence is known or can be estimated. In this case, convenience store robberies are likely to occur randomly and independently of each other, and we can estimate the average rate of occurrence based on past data (e.g. the average number of robberies per day, week or month). Binomial probability model assumes a fixed number of trials and only two possible outcomes, while Hypergeometric and Uniform probability models are not appropriate for count data.

Question 2

Which distribution has a mean of 5?
A)Poisson with λ = 25.
B)Binomial with n = 200,π = 0.05
C)Hypergeometric with N = 100,n = 10,s = 50

Accepted Answer

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

Question 3

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 4

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)0.30
B)0.40
C)0.50
D)0.60

Accepted Answer

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

Question 5

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

Accepted Answer

The expected winnings can be calculated by multiplying each outcome by its probability and summing these products. For rolling a 1 or 2, the probability is 2/6 (or 1/3), and the winnings are $2, so the expected winnings for this outcome are (1/3)*$2 = $2/3. For rolling a 3, 4, 5, or 6, the probability is 4/6 (or 2/3), and the loss is $1, so the expected loss for this outcome is (2/3)*(-$1) = -$2/3. Adding these together, $2/3 - $2/3 = $0.00, which means the expected winnings are $0.00.

Question 6

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 7

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

The Bernoulli process is a random experiment with only two outcomes, usually denoted as "success" or "failure". The probability of each outcome does not necessarily need to be equal, but it remains constant throughout the experiment. The outcome does not need to be desirable, as the terms "success" and "failure" are merely used to distinguish the two possible outcomes.

Question 8

During a randomly-chosen Friday lunch hour (12-1)which probability model would you use to describe the number of customers who order split pea soup at a certain California Pizza Kitchen?
A)Binomial
B)Hypergeometric
C)Uniform
D)Poisson

Accepted Answer

The Poisson distribution is appropriate for modeling the number of events (customers ordering soup) occurring within a fixed interval of time (one hour), especially when these events happen independently and the average rate is known.

Question 9

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 10

During a randomly-chosen 24-hour period,which model best describes the number of mothers who deliver twins in a small hospital?
A)Binomial
B)Poisson
C)Hypergeometric
D)Uniform

Accepted Answer

Poisson distribution is used for counting the number of events occurring randomly over a fixed time period, given the average rate of occurrence. Since the number of births of twins may occur randomly during a 24-hour period and their occurrence rate is relatively rare, Poisson distribution is the best model. The other options, including binomial, hypergeometric, and uniform distributions, are not appropriate in this context because they require a specific number of trials, a fixed population size, or a continuous outcome, which do not fit the scenario of twin deliveries in a hospital.

Question 11

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 12

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)Uniform

Accepted Answer

The hypergeometric distribution is appropriate in situations like this where we are drawing without replacement and are interested in the number of successes (in this case, the number of European tourists) in a sample of a fixed size (in this case, 5). The binomial distribution is appropriate in situations where we are drawing with replacement, which is not the case here since only one person can win the free mule ride. The Poisson distribution is appropriate in situations where we are interested in the number of events occurring in a fixed interval of time or space, which is not relevant in this context. The uniform distribution is used when all outcomes are equally likely, which is not the case here since the probability of selecting a European tourist is not the same as the probability of selecting a non-European tourist.

Question 13

A die is rolled.If it rolls 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

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 calculated as (1/2 * $2) + (1/2 * -$1) = $0.50.

Question 14

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

The number of annual power failures at a residence is likely to follow a Poisson distribution as it meets the following conditions:
1. The events occur randomly in time. Power failures are not scheduled and can occur unexpectedly.
2. The expected number of events is constant over time. On average, a certain number of power failures can be expected each year.
3. The events are independent of each other. The occurrence of one power failure does not affect the likelihood of another occurring.
The other options do not meet all of these conditions and are therefore less likely to be Poisson distributed.

Question 15

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 16

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)Poisson
B)Binomial
C)Hypergeometric
D)Uniform

Accepted Answer

The Poisson distribution is suitable for modeling the number of events (such as injuries) occurring within a fixed interval of time or space, especially when these events happen independently and with a known constant mean rate.

Question 17

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

Accepted Answer

The Poisson distribution is best suited to model the number of blemishes per sheet of paper, since it is used to model rare events occurring at a constant rate over a given interval. In this case, blemishes could be considered rare events and the number of blemishes occurring on a sheet of paper could be assumed to happen at a constant rate. The binomial distribution is used to model the number of successes in a fixed number of trials, which is not applicable here. The hypergeometric distribution is used to model drawing without replacement from a finite population, which does not apply to the situation of blemishes on a sheet of paper. The uniform distribution assumes that all outcomes have an equal probability, which is not applicable in this case.

Question 18

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)0.10
B)0.40
C)0.70
D)0.90

Accepted Answer

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

Question 19

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)Uniform

Accepted Answer

The hypergeometric distribution is appropriate here because we are sampling without replacement from a finite population of calls, where there are a fixed number of incorrect quotations.

Question 20

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...

Quiz 6: Discrete Probability Distributions

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

Which distribution has a mean of 5?

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?

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 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.

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?

Which of the following characterizes a Bernoulli process?

During a randomly-chosen Friday lunch hour (12-1) which probability model would you use to describe the number of customers who order split pea soup at a certain California Pizza Kitchen?

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?

During a randomly-chosen 24-hour period,which model best describes the number of mothers who deliver twins in a small hospital?

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

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

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?

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

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?

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