Question

The three sigma limits for a process whose distribution conforms to the normal distribution include approximately _____ percent of the observed values in the long run.

Answer 1

99.7%

Explanation:

Refer to the attached image showing the empirical method:

The red section shows all the data within one standard deviation of the mean. According to the empirical rule, this is 68 % of the data.

The yellow section shows all the data within two standard deviations of the mean, which is 95 % of the data.

The blue section shows all the data within three standard deviations of the mean, which is 99.7 % of the data.

Thus, the data within three sigma limits, is 99.7%, of the observed values.