Question

An aircraft seam requires 24 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 16% 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 8% of all seams need reworking?

Answer 1

Answer:

(a) 0.007238 or 07238%

(b) 0.003468 or 0.3468%

Step-by-step explanation:

(a) Since all it takes is one defective rivet for a seam to be reworked. The probability of a defective rivet 'p' for 16% of seams needing reworking is:

$1-(1-p)^{24} = 0.16\\1-p = \sqrt[24]{0.84}\\p=0.007238$

The probability that a rivet is defective 0.007238 or 0.7238%.

(b) To ensure that only 8% of seams need reworking, the probability 'p' must be:

$1-(1-p)^{24} = 0.08\\1-p = \sqrt[24]{0.92}\\p=0.003468$

In order to ensure that only 8% of all seams need reworking, the probability of a defective rivet should be  0.003468 or 0.3468%.