(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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