Let $Y ∼ N(−8, 4)$. Compute each of the following, in terms of the function use Table D.2 (or software) to evaluate these probabilities numerically Let $Y ∼ N(−8, 4)$. Compute each of the following, in terms of the function use Table D.2 (or software) to evaluate these probabilities numerically * * * (a) $P(Y ≤ −5)$ attempt: this is $\frac{Y+8}{4} ∼ N(0,1)$ once normalized $P(Y \leq -5) = \phi(\frac{-5+8}{4}) = \phi(0.75) = 0.7734$ The solution gets $0.933$ Is the soluton wrong?

Differing notations for the distribution seem to be in play.

Their answer is for $\mathcal N(\mu{:=}{-8}, \sigma^2{:=}4)$. You have used $\mathcal N(\mu{:=}{-8}, \sigma{:=}4)$.

$$\phi\left(\tfrac{-5+8}{2}\right)\approx 0.933$$