Module 11: Background You’ll Need 2

  • Calculate probabilities using a normal distribution.

In statistics, we are often interested in finding probabilities involving a normal distribution. These probabilities are calculated by finding the area under a normal curve.

Sample normal distribution curve with a mean of 0 and a standard deviation of 1.

The Empirical Rule states that, in a bell-shaped, unimodal distribution, almost all the observed data values lie within three standard deviations to either side of the mean. Specifically, [latex]68\%[/latex] of the observations lie within one standard deviation of the mean, [latex]95\%[/latex] of the observations lie within two standard deviations of the mean, and [latex]99.7\%[/latex] of the observations lie within three standard deviations of the mean. For this reason, the Empirical Rule is sometimes called the [latex]68-95-99.7[/latex] rule.