Exam 5: Discrete Probability Distributions

Explain how to determine whether the binomial distribution can be used in a particular application.

A package delivery service claims that no more than 5 percent of all packages arrive at the address late.Assuming that the conditions for the binomial hold,if a sample of size 10 packages is randomly selected and the 5 percent rate holds,what is the probability that more than 2 packages will be delivered late?

A corporation has 11 manufacturing plants.Of these,7 are domestic and 4 are located outside the United States.Each year a performance evaluation is conducted for 4 randomly selected plants. What is the probability that a performance evaluation will contain 3 plants from the United States?

The roll of a pair of dice has the following probability distribution,where the random variable is the sum of the values produced by each die: Calculate the variance of x.

The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms.Recently,the customer service manager for the company randomly selected 25 calls.Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution,the standard deviation of requests for nonsmoking rooms is 5.25 customers.

If a study is set up in such a way that a sample of people is surveyed to determine whether they have ever used a particular product,the likely probability distribution that would describe the random variable,the number who say yes,is a:

The Swanson Auto Body business repaints cars that have been in an accident or which are in need of a new paint job.Its quality standards call for an average of 1.2 paint defects per door panel.Explain why there is a difference between the probability of finding exactly 1 defect when 1 door panel is inspected and finding exactly 2 defects when 2 doors are inspected.

For a binomial distribution with a sample size equal to 10 and a probability of a success equal to 0.30,what is the probability that the sample will contain exactly three successes? Use the binomial formula to determine the probability.

A direct marketing company believes that the probability of making a sale when a call is made to an individual's home is .02.The probability of making 2 or 3 sales in a sample of 20 calls is .0593.

The binomial distribution is frequently used to help companies decide whether to accept or reject a shipment based on the results of a random sample of items from the shipment.For instance,suppose a contract calls for,at most,10 percent of the items in a shipment to be red.To check this without looking at every item in the large shipment,a sample of n = 10 items is selected.If 1 or fewer are red,the shipment is accepted;otherwise it is rejected.Using probability,determine whether this is a "good" sampling plan.(Assume that a bad shipment is one that has 20 percent reds. )

Holmstead Company owns two small engine repair stores.The expected value of the number of complaints received per month at store 1 is 4.5 complaints.Further,the expected number of complaints per month for store 1 and store 2 combined is 13.6.This means the expected number of complaints per month at store 2 must be 9.1 complaints.

Given a binomial distribution with n = 8 and p = 0.40,obtain the standard deviation.

If cars arrive to a service center randomly and independently at a rate of 5 per hour on average,what is the probability of 0 cars arriving in a given hour?

Explain what the expected value of a discrete random variable measures.

Consider the following two probability distributions: Which of the following is an accurate statement regarding these two distributions?

Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees,8 pine trees,and 14 maple trees.It plans to give 4 trees away at next Saturday's lawn and garden show in the city park.The 4 winners can select which type of tree they want.Assume they select randomly. What is the probability that 3 winners will select pine trees and the other tree will be a maple?

The makers of Crustfree Bread in Boston have a quality standard that allows no more than 3 burned loaves per batch on average.Recently,the manager inspected a batch and found 5 burned loaves.She did not appear to be upset at the production meeting.This is because the chance of exactly 5 burned loaves occurring is 0.1008.

The roll of a pair of dice has the following probability distribution,where the random variable is the sum of the values produced by each die: Calculate the standard deviation of x.

The U.S.Census Bureau (Annual Social & Economic Supplement)collects demographics concerning the number of people in families per household.Assume the distribution of the number of people per household is shown in the following table: Calculate the expected number of people in families per household in the United States.

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information,the probability of profit being at least $70,000 is 0.65.