Exam 5: Discrete Probability Distributions

Exhibit 5-5.The number of homes sold by a realtor during a month has the following probability distribution: Refer to Exhibit 5-5.What is the expected number of homes sold by the realtor during a month?

Which of the following is true about the hypergeometric distribution?

Sam is a trucker and believes that for every 60 miles he drives on the freeway in Indiana,there is an average of 2 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 that 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?

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?

Exhibit 5-4.Consider the following probability distribution. Refer to Exhibit 5-4.The standard deviation is ____.

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?

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 less 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?

Exhibit 5-15.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. Refer to Exhibit 5-15.What is the probability that exactly three customers enter the queue in a randomly selected five-minute period?

Exhibit 5-18.There are currently 18 pit bulls at the pound.Of the 18 pit bulls,four have attacked another dog in the last year.Joe,a member of the staff,randomly selects six of the pit bulls for his group. Refer to Exhibit 5-18.What is the probability that at least one of the pit bulls in Joe's group attacked another dog last year?

An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year. The expected value and the variance of this distribution are:

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is 0?

The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance.

We can think of the expected value of a random variable X as ________________.

The expected value of a random variable X can be referred to or denoted as _____.

Exhibit 5-13.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. Refer to Exhibit 5-13.What is the expected number of free throws that Billups will make?

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?

Exhibit 5-15.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. Refer to Exhibit 5-15.What is the probability that at least two customers enter the queue in a randomly selected five-minute period?

How would you characterize a consumer who is risk loving?

Exhibit 5-12.According to a Department of Labor report,the city of Detroit had a 20% unemployment rate in May of 2011 (Bureau of Labor Statistics,May,2011).Eight working-age residents were chosen at random. Refer to Exhibit 5-12.What was the expected number of unemployed residents,when eight working-age residents were randomly selected?

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 probability of the expected number of times the company will beat analyst expectations this year?