From my understanding, according to the central limit, $\displaystyle T = X_1 + X_2 + ... + X_n$ should behave (roughly) like an N(0,1) distribution for a large enough n.

I'm trying to show this by simulation. I created 1000 $\displaystyle X_i$ iid ~U[0,1]. So according to CLT, T~N(0,1). But how would I show this?