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An aircraft seam requires 25 rivets. The seam will have to

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 ISBN: 9780321629111 32

Solution for problem 77E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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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

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 77E

An aircraft seam requires 25 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. a. If 15% 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 10% of all seams need reworking?

Step-by-Step Solution:

Answer: Step 1: Given, An aircraft seam requires 25 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. Number of rivets n = 25. The seam will have to be reworked if any of these rivets is defective and the rivets are defective independently of one another. Step 2: a). To find the probability that a rivet is defective. 15% of all seams need reworking. Probability of seem need to reworked is 100 = 0.15. Let ‘p’ be the probability of rivet defective. Then probability of a not defective is q = 1-p. Therefore, P( seem have to be reworked) = 1- P( seem have not to be reworked) = 1- [(1-p) (1-p).....15 times] = 1 (1 p) 15 Given that probability of seem to be reworked is 0.15. So, 15 1 (1 p) = 0.15 1 - 0.15 = (1 p) 15 15 0.85 = (1 p) 15 Then, (1-p) = (0.85) = 0.9892 P = 1 - 0.9892 P = 0.0108. Therefore, Probability that a rivet defective is 0.0108.

Step 3 of 3

Chapter 2, Problem 77E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

Since the solution to 77E from 2 chapter was answered, more than 823 students have viewed the full step-by-step answer. This full solution covers the following key subjects: defective, rivets, Probability, seam, seams. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. The full step-by-step solution to problem: 77E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “An aircraft seam requires 25 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. a. If 15% 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 10% of all seams need reworking?” is broken down into a number of easy to follow steps, and 71 words.

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