# Normal distribution (interval) Calculator

## Calculates the two probability density functions and inner and outer cumulative distribution functions of the normal distribution and draws the chart.

 percentile x1 percentile x2 x1≦ x2 mean μ standard deviation σ σ＞0
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 The default value μ and σ shows the standard normal distribution.$\normal Normal\ distribution\ N(x,\mu,\sigma)\\[10](1)\qquad probability\ density\\\hspace{30}f(x,\mu,\sigma)={\large\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}}\\(2)\qquad Inner\ cumulative\ distribution\\\hspace{30}P(x_1\sim x_2,\mu,\sigma)={\large\int_{\small x_1}^{\hspace{25}\small x_2}}f(t,\mu,\sigma)dt\\(3)\qquad outer\ cumulative\ distribution\\\hspace{30}Q(x_1\sim x_2,\mu,\sigma)=1-P(x_1\sim x_2,\mu,\sigma)\\$

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