# A quality control inspector is inspecting newly produced ## Problem 85E Chapter 2

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 85E

A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration. Given that a flaw is actually present, let ?p ?denote the probability that the flaw is detected during any one fixation (this model is discussed in “Human Performance in Sampling Inspection,” ?Human Factors, ?1979: 99–105). a. ?Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has been detected, the sequence of fixations terminates)? b. ?Give an expression for the probability that a flaw will be detected by the end of the ?n?th fixation. c. ?If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass inspection? d. ?Suppose 10% of all items contain a flaw [P (randomly chosen item is flawed) = .1]. With the assumption of part (c), what is the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also pass if it s flawed)? e. ?Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed? Calculate for p = .5.

Step-by-Step Solution:

Solution : Step 1: It is given that the inspector searches an item for faults in a series of independent fixations, each of a fixed duration. . If flaw is actually present, let p denote the probability that flaw is detected during any one fixation. Step 2 : a) We have to find the probability that it is detected by the end of second fixation. Here we want the probability that flaw is being detected either by the first or by the second fixation. P( detected by second fixation )= P( detected first)+ P( not detected on first detect on second) = P+P(1-p) Step 3 : b) we have to give an expression for the probability that a flaw will be detected by the end of the nth fixation. Using the first formula. P( detecting by the end of nth fixation)= P+P(1-p)+p(1-p) + . . . + p(1 p) n c) we have to find the probability that flaw has not been detected in 3 fixations It will be P( not detected in 3 fixations)= (1-P) 3

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##### ISBN: 9780321629111

The answer to “A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration. Given that a flaw is actually present, let ?p ?denote the probability that the flaw is detected during any one fixation (this model is discussed in “Human Performance in Sampling Inspection,” ?Human Factors, ?1979: 99–105). a. ?Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has been detected, the sequence of fixations terminates)? b. ?Give an expression for the probability that a flaw will be detected by the end of the ?n?th fixation. c. ?If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass inspection? d. ?Suppose 10% of all items contain a flaw [P (randomly chosen item is flawed) = .1]. With the assumption of part (c), what is the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also pass if it s flawed)? e. ?Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed? Calculate for p = .5.” is broken down into a number of easy to follow steps, and 224 words. The full step-by-step solution to problem: 85E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Since the solution to 85E from 2 chapter was answered, more than 520 students have viewed the full step-by-step answer. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9780321629111. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. This full solution covers the following key subjects: flaw, Probability, detected, flawed, Pass. This expansive textbook survival guide covers 18 chapters, and 1582 solutions.

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