sum of iid variables: how many terms needed for convergent to normal

Question

For sum of iid variables $Z_n=\sum_{i=1}^nX_i$, in general, how large should $n$ be to indicate 'convergence' to normal? 10? 100?

Answer 1

You may want to look at the Berry-Esséen theorem (and variants, for other metrics: the Berry-Esséen theorem is essentially a quantitative version of the Central Limit Theorem, phrased in terms of Kolmogorov distance between $Z_n$ and the corresponding normal random variable. There are extensions and generalizations, e.g. to multivariate random variables — this link is only one of them).