Given two parameters \(\mu\) and \(\sigma\text{,}\) a random variable X over \(R = (-\infty,\infty)\) has a normal distribution provided it has a probability function given by
\begin{equation*}
f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{ -\left ( \frac{x-\mu}{\sigma} \right ) ^2 / 2}
\end{equation*}