Exam 5: Discrete Probability Distributions

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 no customers will arrive in a 15-minute period?

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 include 2 or more plants from outside the United States?

Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi.Recently,an independent research firm questioned a random sample of 25 adult non-diet cola drinkers.That chance that 20 or more of these people will prefer Coca-Cola is:

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 accepted is approximately 0.81

The manager of a movie theater has determined that the distribution of customers arriving at the concession stand is Poisson distributed with a standard deviation equal to 2 people per 10 minutes.What is the probability that more than 3 customers arrive during a 10-minute period?

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 not contain enough good ones to operate the equipment is:

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information,the standard deviation for the number of injuries per weekend is 2.25.

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 meets the contract requirements will be shipped without further inspection is approximately .9139.

When a market research manager records the number of potential customers who were surveyed indicating that they like the product design,the random variable,number who like the design,is a discrete random variable.

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information,the standard deviation for the number of no-shows is about 0.36 customers.

A construction company has found it has a probability of 0.10 of winning each time it bids on a project.The probability of winning a given number of projects out of 12 bids could be determined with a binomial distribution.

The primary difference between the binomial distribution and the Poisson distribution is that the Poisson is used to describe a continuous random variable and the binomial is used for discrete random variables.

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 no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information,the expected number of no-shows is 1.65 customers.

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.

Cramer's Bar and Grille in Dallas can seat 130 people at a time.The manager has been gathering data on the number of minutes a party of four spends in the restaurant from the moment they are seated to when they pay the check. What is the variance and standard deviation?

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.

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 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 between 2 and 3 customers inclusively will arrive in one hour is 0.0263.

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: