For a random sample of n iid random variables with the same mean mu and finite variance s^2, the distribution of sample means converges to a normal distribution with n. I also wrote down \sqrt{n} (\bar X_n - mu) --d--> N(0,s^2), in this or another form, and showed it to the camera. I started talking about Generalised Central Limit Theorem for alpha-stable distributions (I published on power-scaling laws of Paretian tails, so I remember a bit about it), but the interviewer seemed to have ignored it. I guess they only wanted the standard CLT bit.