(Solved): Let \( X_{1}, \ldots, X_{100} \) be independent identically distributed random variables such that ...
Let \( X_{1}, \ldots, X_{100} \) be independent identically distributed random variables such that \( \operatorname{Pr}(X=0)=\operatorname{Pr}(X=2)=0.5 \). Let \( S=X_{1}+\ldots+X_{100} \). Calculate the approximate value of \( \operatorname{Pr}(S>115) \).