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