Suppose $X\sim N(0,1)$, $Y\sim N(0,9)$ and $X,Y$ are independent. Find the value of $P((X-Y)^2>5)$
What I am doing:
Let $U=X-Y$ which means $U\sim (0,10)$.
Therefore, we need $P(U^2 >5)$ or $P(U>\sqrt{5}) + P(U<-\sqrt{5}) $
or $P(\frac{U-0}{\sqrt10}>\frac{\sqrt(5)-0}{\sqrt10}) + P(\frac{U-0}{\sqrt10}<\frac{-\sqrt(5)-0}{\sqrt10})$
which is $P(Z>0.707) + P(Z<-0.707)$ = something (I'll use the Z- table).
Am I doing it right?