Why are IQ test results normally distributed? (I'm a nooby in probability)
So why are IQ test results normally distributed? 
Or more precisely what are the hypothesizes and theorems that imply this distribution?
Has it to do with the central limit theorem? (But this theorem is about the arithmetic mean of iid variables. I dont see iid variables here: I suppose it's not one person repeating the test. Is it the skills given at a person that is considered as a random variable?)
 A: It has been an empirically observed fact that many "naturally" observed traits, like height or IQ, are NOT empirically normally distributed. At the very least they can't be truly normally distributed because they are always non-negative. But even more than that, before non-negativity is violated, it has been observed that the "tails" (values enough standard deviations away from the mean) tend to have higher probability than predicted by a normal distribution for the population, at least for certain traits. The only thing you can say is that if you take many samples and compute the mean, then the empirical mean for the sample should be approximately normally distributed under mild assumptions if you have enough samples (this is the central limit theorem).
As an aside, if you'd like a speculative theory for why many traits appear "somewhat normal", just consider the possibility that many factors affect the trait, e.g. many genetic factors and many environmental factors. If you have many factors and their effects are additive and you don't have too crazy distributions for each factor's effect, and the factors are independent enough, then the accumulated effect should be somewhat normal basically by the central limit theorem.
A: I suggest the distribution of IQ's may be log-linear (not log-normal). Such distributions often called a Gibbs distribution (who first applied it to the distribution of energy and built a strong foundation for thermodynamics (1878), eg Boltzmann) can be applied to like positive-definite variables that have an 'energy' connotation. 
t works for me with natural remotely sensed imagery (hurricanes, sea ice, rough ocean surface, cold front occurrences), even heart beat variation BUT only above some threshold. On occasion the down (below average) side can be also log-normal (not necessarily of the same slope).
I'm looking for some data with a sample size large enough to resolve the large deviations from most probable. If anyone has a good suggestion in that regard, please pass it along.
If it turned out to be the case, and IQ's had a log-linear distribution, I would suggest that the IQ variable is acting as an 'energy'. If so I would ascribe the 'energy' to a person's ability to concentrate/focus (as in the colloquial phrase 'brain energy' which would involve the reduction in confusion/entropy associated with tasks.
