[CT11]

I agree with tarheeljks. A Normal distribution is often more analytically tractable but you shouldn't try and use it for everything. You could come up with a similar answer using the Central Limit Theorem with involves the normal distribution but that would be a lot more work.

Assuming you are asking for the variance of the total number of pocket aces delt over x hands. Then it would be x*p*(1-p) where p here is 1/221.

EDIT: you also need a more for the CLT like large x.