Let X1,X2,… be a sequence of independent N(0, 8) distributed random variables. For n=1,2,… let Yn be the random variable defined by
Use the central limit theorem rule of thumb to approximate P(Y25>216). You can use that E[X^4(subscript)i]=192.
I'm really struggling with how to do this question, I tried to use the formula for Var(x)=e[x^2] - [E[x]]^2
and tried standardising using Zn = (Xn(bar) - E[x])/ sigma/root(n) but it just doesn't seem to be working. Any help and explanations would be greatly appreciated.