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Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 55% of all fasteners pass an initial inspection. Of the 45% that fail, 10% 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? (Round your answer to four decimal places.)

Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 55% of all fasteners pass an initial inspection. Of the 45% that fail, 10% 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? (Round your answer to four decimal places.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 55% of all fasteners pass an initial inspection. Of the 45% that fail, 10% 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? (Round your answer to four decimal places.)
Transcribed Image Text:Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 55% of all fasteners pass an initial inspection. Of the 45% that fail, 10% 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? (Round your answer to four decimal places.)
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