Chapter 8.1, Problem 21E

To determine

To prove:

$F(-z)=1-F(z)$ for all z and if $p(x)$ is a normal density function with mean $\mu$ and standard deviation $\sigma$, then for all $r\ge 0,$

$P\left(\mu -r\sigma \le X\le \mu +r\sigma \right)=2F(r)-1.$