Intelligence distribution may not be symmetrical. I don't think it is, in fact I'm not sure what that would even mean. High intelligence means doing some things

Intelligence distribution may not be symmetrical. I don't think it is, in fact I'm not sure what that would even mean. High intelligence means doing some things faster and low intelligence means not being able to do some things at all. The only way to symmetry or otherwise is via a quantification which converts these things to a scalar measure, and then distribution becomes a tweakable property of the quantification when tested against a population. And that's why IQ (not intelligence, they are not synonyms) is normally distributed. It is a tuned quantification, designed to be normally distributed. If it doesn't turn out that way, there is some divergence between the population it was tuned for and the sample you're measuring.