The central limit theorem says that the sum of iid copies a random variable will be approximately normal.

I quickly calculated (check my work) E(X)=2.3 and V(X)=1.41.

So

NOW, we really should use a correction factor here, since the rv's in question

are discrete and the normal is continuous. Same as we do in the normal approximation to

the binomial.

But since this is discrete I would argue that you should go with...