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

Question

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

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(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?

Answer 1

Differing notations for the distribution seem to be in play.

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

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