Sample Mean of Exponential Service Times

A server processes $100$ independent requests. Each request takes $\operatorname{Exp}(1)$ time (mean $1$ second). Let $\bar{T} = \frac{1}{100}\sum_{i=1}^{100} T_i$ be the average processing time.

(a) State what the Law of Large Numbers guarantees about $\bar{T}$ as $n \to \infty$.

(b) Using the CLT, approximate $P(\bar{T} > 1.2)$.

You may use $\Phi(2) \approx 0.9772$.