The empirical rule is all of the data in a normal data collection will be within three standard deviations of the mean. The mean is the average of the entire set of numbers.
(a) Almost all observed data for a normal distribution will lie within three standard deviations (denoted by ) of the mean or average (denoted by ), according to the empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule.
(b) The empirical rule explains how data from a population with a normally distributed sample are dispersed. According to the report, 68% of the data, 95% of the data, and 99.7% of all the data are within two standard deviations and three standard deviations, respectively, of the mean.
(c) The empirical rule can only be applied if the population's distribution is normal. It calculates the percentage of measurements that are within one, two, and three standard deviations of the mean, but you can use Chebyshev's Theorem to adapt it to other distributions.
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