You are responsible for checking the number of flaws in the silk cloth being pro

Question

You are responsible for checking the number of flaws in the silk cloth being produced in a manufacturing facility on the beautiful island of Imbar. You've noticed that flaws occur in the cloth according to a Poisson distribution. There are 50 square yards per flaw. a. If 50 yards of silk are inspected, what is the probability that there are no flaws? b What is the expected number of flaws that need to be inspected before a flaw is found? c) If 50 yards are inspected, what is the probability that the number of yards that have one or more flaws is fewer than or equal to 2?

Explanation / Answer

a) mean = 1

P(X=0) = P(no flaws in 50 yards) = 1/e

b) Expected = 50 yards

c) P(X<=2) = P(X=0) + P(X=1) + P(X=2) = 1/e + 1/e + 1/2e = 2/e + 1/2e = 5/2e

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