Exam 5: Discrete Probability Distributions

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 exactly two of the tested players are found to have taken a performance-enhancing drug?

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

The expected value of a random variable X can be referred to as the population mean.

A risk-averse consumer may decline a risky prospect even if it offers a positive expected value.

Consider the following discrete probability distribution. What is the probability that X is greater than 0?

According to the Mortgage Bankers Association,8% of U.S.mortgages were delinquent in 2011.A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure.A random sample of eight mortgages was selected.What is the probability that fewer than three of these mortgages are delinquent?

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

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 exactly one of the residents was unemployed?

Consider the following cumulative distribution function for the discrete random variable. What is the probability that X is less than or equal to 2?

The number of homes sold by a realtor during a month has the following probability distribution: What is the standard deviation of the number of homes sold by the realtor during a month?

You have inherited a lottery ticket may be a $10,000 winner.You have a 0.25 chance of winning the $10,000 and a 0.75 chance of winning $0.You have an opportunity to sell the lottery ticket for $2,500.What should you do if you are risk averse?

The number of homes sold by a realtor during a month has the following probability distribution: What is the probability that the realtor will sell at least one house during a month?

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 probability that at least two of the customers redeem the coupon?

Consider the following probability distribution. The standard deviation is ____.

To illustrate the possible outcomes and their associated probabilities we can construct a probability ______.

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 probability that no more than one of the customers redeems the coupon?

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?

Forty-four percent of consumers with credit cards carry balances from month to month.Four consumers with credit cards are randomly selected.What is the probability that all consumers carry a credit card balance?

We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

It is known that 10% of the calculators shipped from a particular factory are defective.What is the probability that exactly three of five chosen calculators are defective?