Question

Suppose that when a fabric production process is in control, the number of flaws in a piece of fabric of length l yards has a Poisson distribution with mean (.02)l. Suppose that periodically a length of fabric of 10 yards is inspected and the flaws are counted. If there are too many flaws, say more than k, the process will be presumed to be out of control, and stopped, and fixed. What should k be such that the probability of stopping the process when it is really in control is at most 5%

Answer 1

Answer is attached below

Explanation:

A length of fabric sampled = 10 yards

number of flaws in a piece of fabric having length = l yards

Poisson distribution mean = 0.02l

If the flaws are > k = process out of control hence would be stopped and fixed

Calculate The value of K such that the probability of stopping the process when it is really in control is at most 5%

using Poisson distribution

attached below is the detailed solution