4. +-12 points DevoreStat9 2.E.077 My Notes Ask Your Teacher An aircraft seam re

Question

4. +-12 points DevoreStat9 2.E.077 My Notes Ask Your Teacher 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 23% 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? Need Help?Read It Talk to a Tutor

Explanation / Answer

a) Let the probability that a rivet is defective be 'p'

P(seam need working) = 0.23

P(all rivers are working) = 1 - 0.23 = 0.77

(1 - p)30 = 0.77

30 log(1 - p) = log 0.77

log (1-p) = -0.0038

(1 - p) = 0.9913

p = 0.0087

b) P(seam need working) = 0.08

P(all rivers are working) = 1 - 0.08 = 0.92

(1 - p)30 = 0.92

30 log(1 - p) = log 0.92

log (1-p) = -0.0012

(1 - p) = 0.9972

p = 0.0028

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