Question: Using X-bar and S-charts that set control limits at 3 standard errors, (a) What is the probability that one or more of the first

Using X-bar and S-charts that set control limits at ± 3 standard errors,
(a) What is the probability that one or more of the first 10 sample averages from a process that is under control lands outside the control limits?
(b) What is the probability that both the sample average and the sample standard deviation stay within their control limits for one period if the process meets the design conditions? Be sure to state any assumptions you make.
(c) When the process is under control, are we more likely to signal a problem falsely if we’ re using both the X-bar and S-charts or if we only use one of them?

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