An aircraft seam requires 28 rivets The seam will have to be

An aircraft seam requires 28 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.)

Solution

Let A be the event a seam fails.
Let B be the event a rivet fails.

(a) If 16% of all seems needs reworking, what is the probability that a rivet is defective?

Probability=

P[A] = 1 - P[B\']^28
0.16 = 1 - P[B\']^28
0.84 = P[B\']^28
P[B\'] = 0.84^(1/28)
P[B\'] = 0.99379

P[B] = 1 - P[B\'] = 0.00620

(b)How small should the probability of a defective rivet be to ensure that only 8% of all seams need working?

Probability

= Next one is 0.08 = 1 - P[B\']^28

0.92 =P[B\']^28

P[B\'] = 0.92^(1/28) = 0.9970

P[B] = 1 - P[B\'] = 0.00297

Hope this helps.