Those are all small, independent random contributions that naively would lead to a normal distribution per the central limit theorem. But it can't be quite a no

Those are all small, independent random contributions that naively would lead to a normal distribution per the central limit theorem. But it can't be quite a normal distribution due to the lower bound of 0 (in terms of absolute intelligence, not IQ). A better candidate would be a log-normal distribution which is always right-skewed.