Exam 5: Discrete Probability Distributions

The number of weeds that remain living after a specific chemical has been applied averages 1.3 per square yard and follows a Poisson distribution.Based on this,what is the probability that a 3-square yard section will contain less than 4 weeds?

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.

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 .9138.

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 expected number of injuries per weekend is 2.25.

Which of the following is not a condition of the binomial distribution?

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

Ace Computer Manufacturer buys disk drives in lots of 5,000 units from a supplier in California.The contract calls for,at most,3 percent of the disk drives to be defective.When a shipment arrives,a sample of n = 15 parts is selected.If zero defects are found in this sample,the shipment is accepted.If 3 or more defects are found,the shipment is rejected and sent back to the supplier.If the number of defects found is 1 or 2,a second sample of 15 parts is selected.If this sample yields 1 or fewer defects,the shipment is accepted; otherwise the shipment is rejected.Based on a binomial distribution,the probability that Ace will reject a shipment of parts that meets the contract requirements is approximately 0.0355.

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

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 following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Based on this probability distribution,the standard deviation in the number of accidents per day is:

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.

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.)

If a random variable is discrete,it means that the outcome for the random variable can take on only one of two possible values.

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.

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.

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 Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week.Then the variable number of showings is a continuous distribution.

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 $70,500.

The number of weeds that remain living after a specific chemical has been applied averages 1.3 per square yard and follows a Poisson distribution.Based on this,what is the probability that a 1-square yard section will contain less than 4 weeds?