Prove, using moment generating functions, that if X is a normal random variable with mean µ andVari

Prove, using moment generating functions, that if X is a normal random variable with mean µ andVariance ?2, and x1, x2, …., xn is a set of independent, identically distributed random variables, each with that normal distribution, the x bar, i.e., the so called sample mean has a normal distribution with mean µ and variance (?^2)/n. (i.e., you would have to show that the moment generating function of the sample mean is the moment generating function of a normal distribution).