Nate is a competitive eater specializing in eating hot dogs. From past experience we know that it takes him on average $15$ seconds to consume one hot dog, with a standard deviation of $4$ seconds. In this year's hot dog eating contest he hopes to consume $64$ hot dogs in just $15$ minutes. Use the CLT to approximate the probability that he achieves this feat of skill.
I am having trouble setting up this problem.
Outline: Let $S_n:=X_1+X_2+\dots X_{64}$ where each $X_i$ is the $i^{th}$ hot dog consumed. We have $E[S_n]=64*15=960$, $Var(S_n)=64*4=256.$ Using CLT, I get $0.6293$ but the answer key says its $.0304$. I'm guessing my setup is wrong? I'm not sure whether I should work with in terms of seconds or minutes.