Given $\sigma=5$ and $P(Y>78.5)=0.6681$, find $\mu$.

Here is my answer:

First we know that $$Z=\frac{Y-\mu}{\sigma}$$ and we are given $\sigma=5$ and $Y=78.5$. We are missing $Z$ to solve for $\mu$, but we know that $P(Y>78.5)=0.6681$ and normal table will give us only $P(Z<z)$, so we get the complement of $0.6681$ which is $1-0.6681=0.3319$ and with that probability value we head to the body of the normal table to find that $z=-0.43$ and therefore $P(Z<-0.43)=0.3319$.

We use $Z=\frac{Y-\mu}{\sigma}$ and solve for $\mu$ which renders $Y-Z\sigma=\mu$, we then plug in our values to get $78.5-(-0.43)(5)=80.65$ which is the value of $\mu$ we were seeking for.

I want to know if my reasoning is correct, thanks.