An aircraft seam requires 27 rivets The seam will have to be

An aircraft seam requires 27 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 22% of all seams need reworking, what is the probability that a rivet is defective? (b) How small should the probability of a defective rivet be to ensure that only 10% of all seams need reworking?

Solution

given n=27;

a) 22% of all seams need reworking ; Probability of seem need to reworking P(S)= 0.22

P(S) = P(X>=1)=0.22; where X is the number of defective rivets

P(not S) = P(X=0) =0.88; This means (1-p)^27 =0.88

1-p= (0.88)^(1/27)=0.9953

p=1-0.9953=0.0047

Probability that a rivet is defective is 0.0047

b) If 10% of the seems need to be reworking then

(1-p)^27 =0.9

p=0.0039