I’m not sure what you mean by “higher population” but fyi what determines the required number of samples is a function of the full shape of the underlying distr

I’m not sure what you mean by “higher population” but fyi what determines the required number of samples is a function of the full shape of the underlying distribution. For instance the Berry Esseen inequality puts bounds on the convergence rate as a function of the first two central moments of the underlying distribution. But the point is that the convergence rate to Gaussian can be arbitrarily slow! https://en.m.wikipedia.org/wiki/Berry%E2%80%93Esseen_theorem https://en.m.wikipedia.org/wiki/Berry%E2%80%93Esseen_theorem