Assume $X_1, X_2, X_3,\ldots$ are independent and identically distributed exponential random variables with mean of $2$. If $\bar X_n$ the sample mean is normally distributed $\sim N(0,1)$, how large is $n$ so that $P[|\bar X_n -2|\le 0.001] \ge .95$? Use the approximation $P[\bar X_n \ge 2] = .05$
Since it's normal, can we rewrite the central limit theorem as? $$ P\left[\frac{\bar X_n - \mu}{\frac{\sigma}{\sqrt n}} \le \frac{Z}{n}\right]$$
I'm not sure how to proceed