Exam 5: Discrete Probability Distributions

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.

College-Pro Painting does home interior and exterior painting. The company uses inexperienced painters that do not always do a high-quality job. It believes that its painting process can be described by a Poisson distribution with an average of 4.8 defects per 400 square feet of painting. What is the probability that six randomly sampled sections of size 400 square feet will each have 7 or fewer blemishes?

Under what conditions is the binomial distribution symmetric?

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.

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.

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.

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes.Determine the probability that in a given 15- minute segment no customers will arrive at the ATM.

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability that the profit is $80,000 or less is 0.55.

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 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.

A local paint store carries 4 brands of paint (W, X, Y, and Z). The store has 5 cans of W, 3 cans of X, 6 cans of Y, and 15 cans of Z, all in white. It is thought that customers have no preference for one of these brands over another. If this is the case, what is the probability that the next 5 customers will select 1 can of W, X, Y and 2 cans of brand Z?

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 probability that a product is found to be defective is 0.10. If we examine 50 products, which of the following has the highest probability?

The hypergeometric probability distribution is used rather than the binomial or the Poisson when:

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 fewer than 5 customers will request smoking rooms is approximately 0.09.

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes. What is the probability that fewer than four customers will arrive in a 30-minute segment?

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.

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

The mean number of errors per page made by a member of the word processing pool for a large company is thought to be 1.5 with the number of errors distributed according to a Poisson distribution. If three pages are examined, what is the probability that more than 3 errors will be observed?