Berry-Esseen Bound for a Skewed Bernoulli Sum

Let $X_1, X_2, \ldots, X_n$ be i.i.d.\ $\operatorname{Bernoulli}(p)$ with $p = 0.01$ and $n = 10{,}000$. Define $S_n = \sum_{i=1}^{n} X_i$.

(a) Using the CLT, approximate $P(S_n \le 80)$.

(b) The Berry-Esseen theorem states that $\sup_x |P(Z_n \le x) - \Phi(x)| \le \frac{C\,\rho}{\sigma^3 \sqrt{n}}$, where $Z_n = (S_n - n\mu)/(\sigma\sqrt{n})$, $\rho = E[|X_1 - \mu|^3]$, and $C \le 0.4748$. Compute the Berry-Esseen bound on the approximation error in part (a).

You may use $\Phi(-2) \approx 0.0228$.