Exam 5: Discrete Probability Distributions

Dell Computers receives large shipments of microprocessors from Intel Corp.It must try to ensure the proportion of microprocessors that are defective is small.Suppose Dell decides to test five microprocessors out of a shipment of thousands of these microprocessors.Suppose that if at least one of the microprocessors is defective,the shipment is returned. If Intel Corp.'s shipment contains 10% defective microprocessors,calculate the probability the entire shipment will be returned.

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 probability that more than 20 customers in the sample will request nonsmoking rooms is approximately 0.09.

A probability distribution with an expected value greater than the expected value of a second probability distribution will also have a higher 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 that exactly 5 cars will arrive during a given hour?

John Thurgood founded a company that translates Chinese books into English.His company is currently testing a computer-based translation service.Since Chinese symbols are difficult to translate,John assumes the computer program will make some errors,but then so do human translators.The computer error rate is supposed to be an average of 3 per 400 words of translation.Suppose John randomly selects a 1,200-word passage.Assuming that the Poisson distribution applies,if the computer error rate is actually 3 errors per 400 words,find the probability that fewer than 9 errors will be found.

A company has 20 copy machines and every day there is a 5 percent chance for each machine that it will not be working that day.If the company wants to calculate the probability of,say,2 machines not working,it should use the Poisson distribution.

The city council consists of 3 Democrats,5 Republicans and 3 independents.Subcommittees are supposed to be randomly assigned from the council.Suppose the 5-member planning and zoning subcommittee is composed of 3 Democrats and 2 Republicans.The probability of this happening by chance alone is approximately .4545.

The time required to assemble two components into a finished part is recorded for each employee at the plant.The resulting random variable is an example of a continuous random variable.

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 expected profit for the company if it takes the contract is $60,000.

Consider a situation in which a used-car lot contains five Fords,four General Motors (GM)cars,and five Toyotas.If five cars are selected at random to be placed on a special sale,what is the probability that three are Fords and two are GMs?

The only two types of random variables are discrete and continuous random variables.

Many people believe that they can tell the difference between Coke and Pepsi.Other people say that the two brands can't be distinguished.To test this,a random sample of 20 adults was selected to participate in a test.After being blindfolded,each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was.If people really can't tell the difference,the probability that fewer than 6 people will guess correctly is:

A company that makes chocolate chip cookies has found that the number of chips per cookie follows a Poisson distribution.What should the minimum average number of chips be to result in at least 98 percent of the cookies having more than 2 chips? Find the minimum average to nearest whole chip (i.e.choose an average that is a whole number).

John Thurgood founded a company that translates Chinese books into English.His company is currently testing a computer-based translation service.Since Chinese symbols are difficult to translate,John assumes the computer program will make some errors,but then so do human translators.The computer error rate is supposed to be an average of 3 per 400 words of translation.Suppose John randomly selects a 1,200-word passage.Assuming that the Poisson distribution applies,if the computer error rate is actually 3 errors per 400 words,determine the probability that no errors will be found.

If a binomial distribution applies with a sample size of n = 20,find the standard deviation,n = 20,p = 0.20.

The number of defects discovered in a random sample of 100 products produced at the Berdan Manufacturing Company is binomially distributed with p = .03.Based on this,the standard deviation of the number of defects per sample of size 100 is 2.91.

Each week American Stores receives a shipment from a supplier.The contract specifies that the maximum allowable percent defective is 5 percent.When the shipment arrives,a sample of 20 parts is randomly selected.If 2 or more of the sampled parts are defective,the shipment is rejected and returned to the supplier.Assume that a shipment arrives that actually has 4 percent defective parts and the distribution of defective parts is described by a binomial distribution.The probability that the shipment is rejected is approximately 0.19.

When using the binomial distribution,the maximum possible number of success is the number of trials.

If the standard deviation for a Poisson distribution is known to be 3,the expected value of that Poison distribution is:

Madam Helga claims to be psychic.A national TV talk personality plans to test her in a live TV broadcast.The process will entail asking Madam Helga a series of 20 independent questions with yes/no answers.The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge.She will be considered psychic if she correctly answers more than a specified number (called the cut-off)of the questions.The cut-off must be set so that the chance of guessing that number or more is no greater than 5 percent.The cut-off value should be: