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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
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Fasteners used in aircraft manufacturing are slightly

Chapter 3, Problem 99E

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QUESTION:

Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 95% of all fasteners pass an initial inspection. Of the 5% that fail, 20% are so seriously defective that they must be scrapped. The remaining fasteners are sent to a recrimping operation, where 40% cannot be salvaged and are discarded. The other 60% of these fasteners are corrected by the recrimping process and subsequently pass inspection. a. What is the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping? b. Given that a fastener passed inspection, what is the probability that it passed the initial inspection and did not need recrimping?

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QUESTION:

Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 95% of all fasteners pass an initial inspection. Of the 5% that fail, 20% are so seriously defective that they must be scrapped. The remaining fasteners are sent to a recrimping operation, where 40% cannot be salvaged and are discarded. The other 60% of these fasteners are corrected by the recrimping process and subsequently pass inspection. a. What is the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping? b. Given that a fastener passed inspection, what is the probability that it passed the initial inspection and did not need recrimping?

ANSWER:

Answer: Step1: Given that, Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 95% of all fasteners pass an initial inspection. Of the 5% that fail, 20% are so seriously defective that they must be scrapped. The remaining fasteners are sent to a recrimping operation, where 40% cannot be salvaged and are discarded. The other 60% of these fasteners are corrected by the recrimping process and subsequently pass inspection. Step2: a). To find the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping. Given, P(fasteners pass initial t

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