We never went over this in class, and it's not in the book, but there were 3 problems like it on the exam, and I got all 3 wrong, and the prof doesn't give solutions.
So, for instance, how do you use the fact that the moment generating function of the Gaussian is e^(mt+t^2sigma^2/2) to find the pdf for Z(n)=sqrt(n)*(xbar(n)-mu/sigma)?