# Question: The maintenance department in a factory claims that the number

The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours) between successive breakdowns.

a. Find and µx.

b. Write the formula for the exponential probability curve of x.

c. Sketch the probability curve.

d. Assuming that the maintenance department’s claim is true, find the probability that the time between successive breakdowns is at most five hours.

e. Assuming that the maintenance department’s claim is true, find the probability that the time between successive breakdowns is between 100 and 300 hours.

f. Suppose that the machine breaks down five hours after its most recent breakdown. Based on your answer to part d, do you believe the maintenance department’s claim? Explain.

a. Find and µx.

b. Write the formula for the exponential probability curve of x.

c. Sketch the probability curve.

d. Assuming that the maintenance department’s claim is true, find the probability that the time between successive breakdowns is at most five hours.

e. Assuming that the maintenance department’s claim is true, find the probability that the time between successive breakdowns is between 100 and 300 hours.

f. Suppose that the machine breaks down five hours after its most recent breakdown. Based on your answer to part d, do you believe the maintenance department’s claim? Explain.

## Answer to relevant Questions

Suppose that the number of accidents occurring in an industrial plant is described by a Poisson distribution with an average of one accident per month. Let x denote the time (in months) between successive accidents. a. Find ...In a bottle- filling process, the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .02 oz. Bottles containing less than 15.95 oz do not meet the bottler’s ...The scores on the entrance exam at a well- known, exclusive law school are normally distributed with a mean score of 200 and a standard deviation equal to 50. At what value should the lowest passing score be set if the ...Net interest margin— often referred to as spread— is the difference between the rate banks pay on deposits and the rate they charge for loans. Suppose that the net interest margins for all U. S. banks are normally ...A market research firm sends out a Web- based survey to assess the impact of advertisements placed on a search engine’s results page. About 65% of the surveys were answered and sent back. What types of errors are possible ...Post your question