Question 1

Sam is a trucker and believes that for every 60 miles he drives on the freeway in Indiana, there is an average of two state troopers checking his speed with a radar gun.
A) What is the probability that at least one trooper is checking his speed on a randomly selected 60-mile stretch?
B) What is the probability that exactly three troopers are checking his speed on a randomly selected 60-mile stretch?
C) Sam drives 240 miles a day. What is the average number of state troopers who check his speed on a given day?
D) Sam drives 240 miles a day. What is the probability that exactly five troopers check Sam's speed on a randomly selected day?

Accepted Answer

The answer of Sam is a trucker and believes that...

Question 2

A company is going to release four quarterly reports this year. Suppose the company has a 32% chance of beating analyst expectations each quarter.
A) What is the probability that the company beats analyst expectations every quarter of this year?
B) What is the probability the company beats analyst expectations more than half the time this year?
C) What is the expected number of times the company will beat analyst expectations this year?

Accepted Answer

The answer of A company is going to release four...

Question 3

Four of your students submitted an entry to a writing contest. A total of 24 entries were submitted. Six of the entries will move on to the next round.
A) What is the probability that all four of your students will move on to the next round?
B) How many of your students are expected to move to the next round?
C) What is the probability that fewer of your students than expected will make it to the next round than expected?
D) What is the standard deviation of the number of students expected to move on to the next round.

Accepted Answer

The answer of Four of your students submitted an entry...

Question 4

In a particular game of cards, success is measured by the number of aces drawn by each player. Eight cards are drawn by the first player. Given that the player is drawing from a full poker deck of 52 cards, find the probability that this player will draw two aces from the deck.

Accepted Answer

The answer of In a particular game of cards, success...

Question 5

Assume that the mean success rate of a Poisson process is six successes per hour.
A) Find the expected number of successes in a 40-minute period.
B) Find the expected number of successes in a three-hour period.
C) Find the probability of at least two successes in a 30-minute period.

Accepted Answer

The answer of Assume that the mean success rate of...

Question 6

Lisa is in a free-throw shooting contest where each contestant attempts 10 free throws. On average, Lisa makes 77% of the free throws she attempts.
A) What is the probability that she makes exactly eight free throws?
B) What is the probability she makes at least nine free throws?
C) What is the probability she makes fewer than nine free throws?
D) Lisa is competing against Bill to see who can make the most free throws in 10 attempts. Suppose Bill goes first and makes seven. Should we expect Lisa to make at least as many as Bill? Explain.

Accepted Answer

The answer of Lisa is in a free-throw shooting contest...

Question 7

A construction company found that on average its workers get into four car accidents per week.
A) What is the probability of exactly six car accidents in a random week?
B) What is the probability that there are fewer than two car accidents in a random week?
C) What is the probability that there are exactly eight car accidents over the course of three weeks?

Accepted Answer

The answer of A construction company found that on average...

Question 8

A telemarketer knows that, on average, he is able to make three sales in a 30-minute period. Suppose the number of sales he can make in a given time period is Poisson distributed.
A) What is the probability that he makes exactly four sales in a 30-minute period?
B) What is the probability that he makes at least two sales in a 30-minute period?
C) What is the probability that he makes five sales in an hour-long period?

Accepted Answer

The answer of A telemarketer knows that, on average, he...

Question 9

An urn is filled with three different colors of balls: red, blue, and white. There are three red balls, seven blue balls, and five white balls. If four balls are drawn, what is the probability of drawing two blue balls?

Accepted Answer

The answer of An urn is filled with three different...

Question 10

An investor has an $80,000 portfolio of which $60,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are as follows:  a. Calculate the correlation coefficient.
B) Calculate the expected return of the portfolio.
C) Calculate the standard deviation of the portfolio.

Accepted Answer

The answer of An investor has an $80,000 portfolio of...

Question 11

Due to turnover and promotion, a bank manager knows that, on average, she hires four new tellers per year. Suppose the number of tellers she hires is Poisson distributed.
A) What is the probability that in a given year, the manager hires exactly five new tellers?
B) What is the average number of tellers the manager hires in a six-month period?
C) What is the probability that the manager hires at least one new teller in a given six-month period?

Accepted Answer

The answer of Due to turnover and promotion, a bank...

Question 12

During an hour of class, a professor anticipates six questions on average.
A) What is the probability that in a given hour of class, exactly six questions are asked?
B) What is the expected number of questions asked in a 20-minute period?
C) What is the probability that no questions are asked over a 20-minute period?

Accepted Answer

The answer of During an hour of class, a professor...

Question 13

You are attending a baseball game with two family members when it is announced that four fans in your section (which holds 20 spectators total) will win a free autographed baseball.
A) What is the probability that at least one member of your family (including yourself) wins an autographed baseball?
B) What is the probability that two members of your family win an autographed baseball?
C) What is the probability that all three of you win an autographed baseball?

Accepted Answer

The answer of You are attending a baseball game with...

Question 14

A car salesperson has a 5% chance of landing a sale with a random customer on the lot. Suppose 10 people come onto the lot today.
A) What is the probability that the salesperson sells exactly three cars today?
B) What is the probability he or she sells fewer than two cars today?
C) What is the expected number of cars he or she is going to sell today?

Accepted Answer

The answer of A car salesperson has a 5% chance...

Question 15

Suppose your firm is buying five new computers. The manufacturer offers a warranty to replace any computer that breaks down within three years. Suppose there is a 25% chance that any given computer breaks down within three years.
A) What is the probability that exactly one of the computers breaks down within five years?
B) What is the probability that at least one of the computers breaks down within five years?
C) Suppose the warranty for five computers costs $700, while a new computer costs $600. Is the warranty less expensive than the expected cost of replacing the broken computers?

Accepted Answer

The answer of Suppose your firm is buying five new...

Question 16

A plane taking off from an airport in New York can expect to run into a flock of birds once out of every 1,250 takeoffs.
A) What is the expected number of bird strikes for 10,000 takeoffs?
B) What is the standard deviation of the number of bird strikes for 10,000 takeoffs?
C) What is the probability of running into seven flocks of birds in 10,000 takeoffs?

Accepted Answer

The answer of A plane taking off from an airport...

Question 17

An investor has a $120,000 portfolio of which $50,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are as follows:  a. Calculate the correlation coefficient.
B) Calculate the expected return of the portfolio.
C) Calculate the standard deviation of the portfolio.

Accepted Answer

The answer of An investor has a $120,000 portfolio of...

Question 18

George buys six lottery tickets for $2 each. In addition to the grand prize, there is a 20% chance that each lottery ticket gives a prize of $4. Assume that these tickets are not grand prize winners.
A) What is the probability that the tickets are winners more than the average that George expected?
B) What is the probability that none of the tickets are winners?
C) What is the probability that at least one of the tickets is a winner?

Accepted Answer

The answer of George buys six lottery tickets for $2...

Quiz 5: Discrete Probability Distributions

In a particular game of cards, success is measured by the number of aces drawn by each player. Eight cards are drawn by the first player. Given that the player is drawing from a full poker deck of 52 cards, find the probability that this player will draw two aces from the deck.

Assume that the mean success rate of a Poisson process is six successes per hour. A) Find the expected number of successes in a 40-minute period. B) Find the expected number of successes in a three-hour period. C) Find the probability of at least two successes in a 30-minute period.

An urn is filled with three different colors of balls: red, blue, and white. There are three red balls, seven blue balls, and five white balls. If four balls are drawn, what is the probability of drawing two blue balls?