Chapter 8, Problem 8.4P

Let $X_1,\mathrm{...},X_{20}$ be independent Poisson random variables with mean 1.

a. Use the Markov inequality to obtain a bound on $P\left\{{\displaystyle \underset{1}{\overset{20}{\sum }}{X}_i>15}\right\}$.

b. Use the central limit theorem to approximate $P\left\{{\displaystyle \underset{1}{\overset{20}{\sum }}{X}_i>15}\right\}$.