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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 75e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 75e

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One of the assumptions underlying the theory of control

ISBN: 9780321629111 32

Solution for problem 75E Chapter 2

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

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Problem 75E

One of the assumptions underlying the theory of control charting (see Chapter 16) is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Even when a process is running correctly, there is a small probability that a particular point will signal a problem with the process. Suppose that this probability is .05. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly? Answer this question for 25 successive points.

Step-by-Step Solution:

Answer: Step 1 of 1 Let F be the event called ‘Problem’ Let X be the number of failures. P(F) = 0.05 1 P(F ) = 0.95 The probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly P(at least 1 wrong in 10) = P(X1) = 1 - 0.950 = 0.4013 By similar reasoning if we let Y be the number of problems at 25 points P(at least 1 wrong in 25) = P(Y1) = 1 - 0.955 = 0.7226. Therefore, The probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly is 0.4013 and for probability that at least one of 25 successive points is 0.7226.

Step 2 of 1

ISBN: 9780321629111

Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 75E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This full solution covers the following key subjects: process, points, successive, correctly, Probability. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Since the solution to 75E from 2 chapter was answered, more than 686 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. The answer to “One of the assumptions underlying the theory of control charting (see Chapter 16) is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Even when a process is running correctly, there is a small probability that a particular point will signal a problem with the process. Suppose that this probability is .05. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly? Answer this question for 25 successive points.” is broken down into a number of easy to follow steps, and 103 words.

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