# Normal distribution Calculator

## Calculates the probability density function and lower and upper cumulative distribution functions of the normal distribution.

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

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