Chapter 12, Problem 27RE

Area under the Normal Curve It is useful in some applications to know that about $68\%$ of the area under the standard normal curve lies between $-1$ and $1$.

Verify this statement.

Let $X$ be a normal random variable with expected value $\mu$ and variance ${\sigma }^2$. Compute

$\mathrm{Pr}\left(\mu -\sigma \le X\le \mu +\sigma \right)$