Exam 5: Discrete Probability Distributions

On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected.What is the probability that two light bulbs will be defective?

The following formula defines the ________ of a hypergeometric random variable

An analyst estimates that the year-end price of a stock has the following probabilities: The stock's expected price at the end of the year is _______.

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?

For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons.What is the expected number of coupons that will be redeemed?

A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson distributed.What is the probability that exactly three customers enter the queue in a randomly selected five-minute period?

Which of the following statements is the most accurate about a Poisson random variable?

Chauncey Billups,a current shooting guard for the Los Angeles Clippers,has a career free-throw percentage of 89.4%.Suppose he shoots six free throws in tonight's game.What is the standard deviation of the number of free throws that Billups will make?

Suppose a baseball team has 14 players on the roster who are not members of the pitching staff.Of those 14 players,assume that three have recently taken a performance-enhancing drug.Suppose the league decides to randomly test five members of the team.What is the probability that at least one of the tested players is found to have taken a performance-enhancing drug?

The hypergeometric probability distribution is appropriate in applications where we cannot assume the trials are _________.

According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries.Suppose seven expectant mothers are randomly selected.The expected number of mothers who will not have a Caesarean delivery is ______.

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?

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?

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?

According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years.What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?

The risk of the portfolio depends not only on the individual risks of the assets but also on the ________ between the asset returns.

A six-sided,unfair (weighted)die has the following probability distribution. Find the probability of rolling a 3 or less.

How would you characterize a consumer who is risk loving?

According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011.Eight working-age residents were chosen at random.What is the probability that at least two of the residents were unemployed?

The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005.What is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?