in wooden doors. As a check on the quality of the wooden doors produced by a com

Question

in wooden doors. As a check on the quality of the wooden doors produced by a company, its owner requested that each door undergo inspection for defects before leav- ing the plant. The plant's quality control inspector found that one square foot of door surface contains, on the aver- age, 5 minor flaws. Subsequently, one square foot of each door's surface was examined for flaws. The owner decided to have all doors reworked that were found to have two or more minor flaws in the square foot of surface that was in- spected. What is the probability that a door will fail inspec- tion and be sent back for reworking? What is the probability that a door will pass inspection? 7 A alot machine is cet so that the probability of w

Explanation / Answer

This is an poisson distribution with mean = 0.5

For passing inspection, we find the probability for x = 0 and x = 1 as P(Pass)

For reworking , probability is 1-P(pass)

1)

Passing inspection .

P(x; ) = (e-) (x) / x!

P(0) = e^(-0.5) = 0.606530659712633=

P(1) = e^(-0.5) * 0.5/1 = 0.303265329856317

P(Pass) = P(0) + P(1) = 0.90979598956895

P( Rework ) = 1- P(Pass) = 1 - 0.90979598956895 = 0.09024

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