An X-bar control chart monitors the mean of a process by checking that the average stays between

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An X-bar control chart monitors the mean of a process by checking that the average stays between µ - 3σ/√n and µ + 3σ/√n. When the process is under control,

(a) What is the probability that five consecutive sample means of n cases stay within these limits?

(b) What is the probability that all of the means in a control chart for 100 days fall within the control limits?

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