Since intelligence must be a one-sided distribution it's probably right-tailed, which means the mean is higher than the median. So I expect (slightly) more than half of the population to be dumber than average.
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.
