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Normal Distribution

As stated before, the standard deviation is a measure of the spread of a distribution.  Here are several normal curves with the same center, but different population standard deviations:

As you can see, as the spread of the distribution increases, so does σ. Therefore, the area of the curve lying within a certain number of standard deviations from the mean is fixed, over all normal distributions. Specifically:
  • 68% of the area of the curve is within the range of μ ± 1σ
  • 95% of the area of the curve is within the range of μ ± 2σ
  • 99% of the area of the curve is within the range of μ ± 3σ
Commit these numbers to memory: 68-95-99!