Standard Normal Distribution

The normal distribution with parameter values $\mu =0$ and $\sigma =1$ is called the standard normal distribution. A random variable that has a standard normal distribution is called a standard normal random variable and will be denoted by $Z$. The PDF of $Z$, denoted $\varphi (z)$, is:

where $z\in \mathbb{R}$. The CDF of $Z$ is $P(Z\le z)$, denoted by $\mathrm{\Phi }(z)$. We refer to the graph of the standard normal pdf as the standard normal curve (or $z$-curve).