X and Y are positive continuous random variables that are approximately normally distributed with E(X) = 50, sd(X) = 6 and E(Y) =30, sd(Y) = 4.
Pr( X/Y > 2) is equal to I'm not sure how to do this. WOuld this just be Pr(X)/Pr(Y)>2? Do I need to apply continuity correction? I'm a bit lost. The possible answers are 0.023
0.159
0.238
0.460
0.841
If I were you, I would do something like: $$\mathbb{P}[\frac{X}{Y} > 2] = \mathbb{P}[X > 2Y, \ Y > 0] + \mathbb{P}[X < 2Y, \ Y < 0]$$ which yields: $$\mathbb{P}[\frac{X}{Y} > 2] =\mathbb{P}[X - 2Y > 0, \ Y > 0] + \mathbb{P}[X - 2Y < 0, \ Y < 0]$$ then you should need something to argue $Z = (X - 2Y) \sim N(\mu, \sigma^2)$ where possibly $\mu = -10$ and $\sigma^2 = 10$. Be careful: the fact $Z \sim N(\mu, \sigma^2)$ is not trivial with the information you provided! For example, if $X$ and $Y$ happen to be jointly Gaussian, you get Z is Gaussian. Same with independence. In general, that is NOT true!