Question

What is a standard normal probability distribution?

Answer 1

The standard normal probability distribution appears when the mean value of a normal random variable is $0$ and the value of the standard deviation is $1$.

The formula of a normal probability distribution is,

$P\left(x\right)=\frac{1}{\sqrt{2{\mathrm{\pi \sigma }}^2}}{e}^{\frac{-{\left(x-\mu \right)}^2}{2{\sigma }^2}}$

Then standard normal probability distribution is,

$P\left(x\right)=\frac{1}{\sqrt{2\pi {\left(1\right)}^2}}{e}^{\frac{-{\left(x-0\right)}^2}{2{\left(1\right)}^2}}$ $\left[\because \mu =0and\sigma =1\right]$

$\Rightarrow$ $P\left(x\right)=\frac{1}{\sqrt{2\pi }}{e}^{\frac{-{\left(x\right)}^2}{2}}$