# Describe the approximating normal random variable...

Calculuate $E X_i$ and $\mbox{Var} X_i$, then $E\bar{X}$ and $\mbox{Var} \bar{X}$, and CLT that sucker. You find $E X_i$ and $\mbox{Var} X_i$ using the usual methods, then use those results and the rules for the expectation of sums and variance of sums under independence to get what you need for the sample mean (or you might just have memorized by this point that, if $\mu$ is the mean of the iid random variables, and $\sigma ^2$ is the variance, $E\bar{X} = \mu$ and $\mbox{Var}\bar{X} = \frac{\sigma ^2}{n}$, which is enough to fully define a univariate normal distribution).