Question: A process is normally distributed and in control, with known mean and variance, and the usual limits of three sigma are used in the control

A process is normally distributed and in control, with known mean and variance, and the usual limits of three sigma are used in the control chart x, so the probability that a single point lies outside the external control limits when the process is in control is 0.0027. Suppose this chart is being used in phase I and the means of a set of m samples or subgroups of this process are plotted on this graph. Which is the probability that at least one of these means will fall outside the control limits when m = 5? repeat these calculations for the cases where m = 10, m = 20, m = 30, and m = 50. Discuss the results you got.

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