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The Normal Distribution

The Normal Distribution
  • In a normal distribution: \(\text{median}=\text{mean}=\text{mode}\)
  • Normal distributions are symmetrical
  • \(68\%\) of data lies within one standard deviation: \(\sigma\)
  • \(95\%\) of data lies within two standard deviations: \(2\sigma\)
  • \(99.7\%\) of data lies within three standard deviations: \(3\sigma\)
Formula
\[X \sim \mathcal{N}(\mu, \, \sigma^2)\]
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