> treating human height as a bunch of iids is the simplest approach. Sounds fine. If you treat heights as some i.i.d.s, then can use the central limit theorem

> treating human height as a bunch of iids is the simplest approach. Sounds fine. If you treat heights as some i.i.d.s, then can use the central limit theorem to argue that in the limit for large samples (we get convergence in distribution) the probability density distribution of the sum of heights expressed as a z-score (mean 0, standard deviation 1) has Gaussian probability density distribution. But that does not mean that the probability density distribution of heights is Gaussian. Indeed, if include both males and females, then for the density likely get two peaks instead of just one. If also include children, then get a left tail longer than the right one. So, net, we cannot expect that heights are Gaussian. And we will have a tough time finding a large population that is Gaussian. z-scores in the limit for large samples Gaussian -- sure, can get that. A large population Gaussian, not much chance.