Exam 5: Discrete Probability Distributions

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 have more than 2 chips? Find the minimum average to nearest whole chip (i.e.choose an average that is a whole number).

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?

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.

Bill Price is a sales rep in northern California representing a line of athletic socks.Each day,he makes 10 sales calls.The chance of making a sale on each call is thought to be 0.30.The probability that he will make exactly two sales is approximately 0.2335.

The Brockingham Carpet Company prides itself on high quality carpets.At the end of each day,the company quality managers select 3 square yards for inspection.The quality standard requires an average of no more than 2.3 defects per square yard.Last night,the inspector found 8 defects in the sample of 3 square yards.The chance of finding 8 or more defects in the sample is 0.9975.

The Brockingham Carpet Company prides itself on high quality carpets.At the end of each day,the company quality managers select 3 square yards for inspection.The quality standard requires an average of no more than 2.3 defects per square yard.The expected number of defects that the inspector will find during the inspection is 6.9.

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.

The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour.What are the chances that 2 or 3 customers will arrive in a 15-minute period?

The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60.The probability that more than 4 customers will arrive in a 30-minute period is 0.1933.

The random variable x is the number of customers arriving at the service desk of a local car dealership over an interval of 10 minutes.It is known that the average number of arrivals in 10 minutes is 5.3.The probability that there are less than 3 arrivals in any 10 minutes is:

The Vardon Exploration Company is getting ready to leave for South America to explore for oil.One piece of equipment requires 10 batteries that must operate for more than 2 hours.The batteries being used have a 15 percent chance of failing within 2 hours.The exploration leader plans to take 15 batteries.Assuming that the conditions of the binomial apply,the probability that the supply of batteries will contain enough good ones to operate the equipment is:

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.

Which of the following statements is incorrect?

A mid-management team consists of 10 people,6 males and 4 females.Recently top management selected 4 people from this team for promotion.It was stated that the selections were based on random selection.All 4 people selected were males.The females are upset and believe that there may have been more than random selection involved here.What probability distribution should be used to analyze this situation and what is the probability that all 4 promotions would go to males if the selections were random? Do you believe that the females have a valid complaint in this situation?

Explain how to use the binomial distribution table when p,the probability of a success,exceeds 0.50.

The random variable,number of customers entering a store between 9 AM and noon,is an example of a discrete random variable.

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped.According to the contract specifications,5 percent of the items shipped can be defective.If the inspectors find 1 or fewer defects in the sample of 10,they ship the batch without further inspection.If they find 2 or more,the entire batch is inspected.Based on this sampling plan,the probability that a batch that contains twice the amount of defects allowed by the contract requirements will be shipped without further inspection is approximately .3874.

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 $50,000 is 0.50.

One difference between the binomial distribution and Poisson distribution is that the binomial's upper bound is the number of trial while the Poisson has no particular upper bound.

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: