Are many traits normally distributed or not? I was searching to learn which traits (e.g., hair color, intelligence, weight, etc) are and which are not normally distributed. In the lecture notes for some course on a university website (unfortunately I don't have the link), a college professor had stated that complex traits are normally distributed.
But then I came across an answer on Quora to someone asking what besides height and intelligence is normally distributed  https://quora.com/What-traits-besides-IQ-and-height-does-a-normal-distribution-describe-in-a-population 
A supposed statistician had replied that "Actually, nothing is described by a normal distribution.It approximately describes heights of people so long as they are all male or all female and not a mixture of East African Negros, West African Pygmies and Europeans." He went on to say that a large sample, however, with no outliers can approximate normal distribution.
So I am confused. So can anything, if the sample is large enough, approximate normal distribution?  And yet nothing is normally distributed to begin with?  
 A: None of the variables you mentioned are drawn from Gaussian populations. Not one. Even intelligence (which is typically designed to be Gaussian) can't be (e.g, can you score lower than 0 Intellligence?). 
The size of the sample has nothing to do with the shape of the population from which the same is drawn so having a "large sample" has nothing to do with it.
I'd say they are both trying to make a point but both stumble in doing so.
A: This supposed statistician is mistaken. Many, many naturally occurring phenomena tend towards Gaussian. No sample will perfectly conform but when compared against other competitor distributions, the Gaussian will tend to win for things like heights and weights and IQ scores and things. More so when the sample size increases. 
But, if you change the situation this isn’t true. The arrival times of radioactive alpha particles from Uranium is exponential. The number of heads coin tosses out of N throws is binomial. 
This all said, the central limit theorem states that the distribution of means is nearly always Gaussian, regardless of the form of the parent distribution. 
Here’s an example:  consider the distribution of heights (or weights) for all people inside day care centers. While human height is normally distributed in general, at any one day care you’ll get a lot of short and light people and a couple taller heavier people. Very skewed. Now take the mean height or weight for each day care center in the United States. That distribution of means will be normal. 
A: I support @Glen_b's answer (+1)
I will just add the following:
If you imagine the evolutionary process as a random process, then when the process becomes stationary, the traits at the stationary point may exhibit Gaussian-like behavior because of the culling of the remainder of the population due to its inability to survive. However, this statement also assumes that the environment experienced by the entire population is identical. But clearly, this is not the case (for e.g. equatorial regions are hotter than polar regions). Different traits may end up surviving in different parts of the world. So at a global scale, you will never see a Gaussian or even Gaussian-like distribution. However, for the local homogeneous population, you may see Gaussian-like distribution for certain traits but not for all traits, and that depends on what factors affect that trait.
