Chapter 3.3, Problem 10E

If X is $N\left(\mu ,{\sigma }^2\right)$ show that $Y=aX+b$ is $N\left(a\mu ,+b,a^2{\sigma }^2\right),a\ne 0$, HINT: Find the cdf $P\left(Y\le y\right)$ of Y, and in the resulting integral, let $w=ax+b$ or, equivalently, $x=\frac{\left(w-b\right)}{a}$.