The 68–95–99.7 rule or empirical rule is a shorthand for remembering the percentage of values that lie within an interval estimate in a normal distribution.

  • 68% of values fall within 1 variance of the mean
  • 95% of values fall within 2 standard deviations of the mean
  • 99.7% of values fall within 3 standard deviations of the mean

We can use the 68-95-99.7 rule to do some rough estimation of the CDF of a normal distribution function. For example,

(we are calculate the area under the curve till mean + 1 stdv) 68-95-99.7 rule test.png

References