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A process is under control and follows a normal
Chapter 13, Problem 78SE(choose chapter or problem)
A process is under control and follows a normal distribution with mean 100 and standard deviation 10. In constructing a standard \(\bar{x} \text {-chart }\) for this process, the control limits are set 3 standard deviations from the mean—that is, \(100 \pm 3(10 / \sqrt{n})\). The probability of observing an \(\bar{x}\) outside the control limits is (.00135 + .00135) = .0027. Suppose it is desired to construct a control chart that signals the presence of a potential special cause of variation for less extreme values of \(\bar{x}\). How many standard deviations from the mean should the control limits be set such that the probability of the chart falsely indicating the presence of a special cause of variation is .10 rather than .0027?
Questions & Answers
QUESTION:
A process is under control and follows a normal distribution with mean 100 and standard deviation 10. In constructing a standard \(\bar{x} \text {-chart }\) for this process, the control limits are set 3 standard deviations from the mean—that is, \(100 \pm 3(10 / \sqrt{n})\). The probability of observing an \(\bar{x}\) outside the control limits is (.00135 + .00135) = .0027. Suppose it is desired to construct a control chart that signals the presence of a potential special cause of variation for less extreme values of \(\bar{x}\). How many standard deviations from the mean should the control limits be set such that the probability of the chart falsely indicating the presence of a special cause of variation is .10 rather than .0027?
ANSWER:Step 1 of 2
The given problem is explains that the process is under control and follows a normal
distribution with mean 100 and standard deviation 10. The 
control limits are set 3 standard deviations from the mean that is 
Also given that the probability of observing an
Here our aim is to construct a control chart that signals the presence of a special cause of
variation for extreme value of