Empirical rule (68-95-99.7 Rule)

This rule ONLY applies to Normal Distribution.

It?s also called the 68-95-99.7% rule, because for a normal distribution:

• ?68% of the data falls within 1 standard deviation of the mean
• ?95% of the data falls within 2 standard deviations of the mean
• ?99.7% of the data falls within 3 standard deviations of the mean

Example

Solve:

• According to the z-score of point 32.2, (32.2-20.5)/3.9=3 which is 3 standard deviations away from the mean
• So by looking at the empirical rule graph, we get the percentage of 3?away from mean.
• Hence the percentage above that value is 0.15%

Example

Solve:

• According to the z-score formula, we get the two points’ z-score are: -1 & 2
• By looking at empirical rule graph, the -1? & 2? represents 16th percentile & 97.5th percentile.
• So subtract the overlays and we?ll get 97.5% – 16% = 81.5%