0 pointa My Note Ask Your An aircraft seam requires 30 rivets. The seam will hav

Question

0 pointa My Note Ask Your An aircraft seam requires 30 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 19% of all seams need reworking, what is the probability that a rivet is defective? Hint: This question essentially asks you to reverse the process that was shown in dass. You are given that the chance that all 30 rivets are not defective (i.e., the seam is not defective) is 81%. So what is the chance that any one rivet is not defective? Then what is the chance that any one rivet is defective? (b) How small should the probability of a defective rivet be to ensure that only 8% of all seams need reworking?

Explanation / Answer

a) Let the probability that rivet is good is p. Then:

P(Seams is good) = p30

But it is given that P(Seams is good) = 0.81

Hence,

p30 = 0.81

p = 0.9930

So,

P(Rivet is defective) = 1 - 0.9930 = 0.0070

b) SImilar to a),

p30 = 0.92

p = 0.9972

Hence,

P(rivet is defective) = 1 - 0.9972 = 0.0028

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