# Standard normal distribution Calculator

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

percentile x
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 $\normal Standard\ Normal\ distribution\ N(x)\\[10](1)\qquad probability\ density\\\hspace{30}f(x)={\large\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}}\\(2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x)={\large\int_{\small-\infty}^{\hspace{25}\small x}}f(t)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t)dt\\(4)\qquad inner\ cumulative\ distribution\\\hspace{30}I(x)={\large\int_{\small -x}^{\hspace{25}\small x}}f(t)dt\\$

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