Sample Size for a Tail Probability Guarantee

Let $X_1, X_2, \ldots$ be i.i.d.\ $\operatorname{Exp}(1)$ (mean $1$, variance $1$). A system designer requires that the sample mean $\bar{X}_n$ exceeds $1.1$ with probability less than $1\%$.

Using the CLT, find the smallest $n$ satisfying $P(\bar{X}_n > 1.1) < 0.01$.

You may use $\Phi(2.33) \approx 0.9901$.