The empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, ¯x, will be within two standard deviations of the population ...The empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, ¯x, will be within two standard deviations of the population mean μ. Where ¯x is the sample mean. zα2 is determined by the level of confidence (1-α) desired by the analyst, and s/√n is the standard deviation of the sampling distribution for means given to us by the Central Limit Theorem.