Answered: One of the assumptions underlying the…

Name: One of the assumptions underlying the theory of control charting is th
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Description: One of the assumptions underlying the theory of control charting 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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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One of the assumptions underlying the theory of control charting 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 0.04. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly? (Round your answer to three decimal places.)

What is the probability that at least one of 40 successive points indicates a problem when in fact the process is operating correctly? (Round your answer to three decimal places.)

Expert Solution

Step 1

$P r o b a b i l i t y (p) = 0.04$

Here number of success and sample size is fixed. Samples are independent hence we use binomial distribution.

Formula :

$P (X = x) = \frac{n!}{x! (n - x)!} p^{x} (1 - p)^{n - x}$

$P (a t l e a s t o n e) = 1 - P (N o n e)$

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