I looked at the definition of a moment generating function for the RV:
I don't understand where this came from... I understand this:
but I don't know how you brought in the mean and standard deviation. Could you please help me with the first few steps?
Now what are the moments? The first is the mean and the second is the expected value of x^2, which can be rewritten in terms of the mean and standard deviation. When you do that you get what I wrote (assuming no algebraic errors).