Plastic parts produced by an injection molding operation are checked

1. Plastic parts produced by an injection molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses three parts from among the 12 at random. Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications.

a. What is the probability that the inspector finds exactly one non-conforming part?

b. What is the probability that the inspector finds at least one non-conforming part?

2. A manufacturer of front lights for automobiles tests lamps under high – humidity, high temperature environment using intensity and useful life as the responses of interest. The following table shows the performance of 130 lamps:

Useful Life

Satisfactory

Unsatisfactory

Intensity

Satisfactory

117

3

Unsatisfactory

8

2

a. Find the probability that a randomly selected lamp will yield unsatisfactory results under any criteria.

b. The customers for theses lamps demand 95% satisfactory results. Can the lamp manufacturer meet this demand?

3. Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently.

a. What is the probability that every passenger who shows up can take the flight?

b. What is the probability that the flight departs with at least one empty seat?

4. A Web site contains three identical computer servers. Only one is used to operate the site, and the other two are spares that can be activated in case the primary system fails. The probability of a failure in the primary computer (or any activated spare system) from a request for service is 0.0005. Assuming that each request represents an independent trial, what is the mean number of requests until failure of all three servers?

5. The number of content changes to a Web site follows a Poisson distribution with a mean of 0.25 per day.

a. What is the probability of two or more changes in a day?

b. What is the probability of no content changes in five days?

c. What is the probability of two or fewer changes in five days?