Hello,

But Z has to be a normal distribution N(0,1)

Assuming Y1 and Y2 are iid samples of N(0,1), then we have :

- Y1-Y2 follows a normal distribution (because they're independent)

- E(Y1-Y2)=0

- Var(Y1-Y2)=n1+n2

So in order to get a standard normal distribution from Y1-Y2, find a such that a(Y1-Y2) follows N(0,1)

And for that, recall that if M~N(m,s²), then aM~N(am,a²s²)

Can you try to do it ?

Also, please post all the information you're given, because I feel like there's not everything here