Let \(X_1,X_2, ...,X_n\) be i.i.d. exponential random variable with \(\lambda=1\). Let

\(\bar{X}=\frac{X_1+X_2+...+X_n}{n}\)

a. Calculate \(\mathbb{P}\left(0.9\leq\bar{X}\leq1.1\right)\)

b. How large should be n so that \(\mathbb{P}\left(0.9\leq\bar{X}\leq1.1\right)>0.95\)