Everything except axioms and definitions need arguments in support.

If I created a fantasy world, there would be no particular reason why I couldn't create a scale from 0 to 120 for strength in the Force, and have it normally distributed with the mean at 50, and standard deviation 10, placing the weakest person at 5 standard deviations below the mean, and the strongest channeler at 6 standard deviations above the mean. This would put the average slightly higher than the mean, but who cares, it's my world, and it's not like fans will be debating this stuff to floating point precision anyway, right?

Jordan may very well have made his distribution symmetric, but there's no reason he would have to.

Edit: In fact, you had the example yourself. SAT scores are normally distributed, and truncated at 200 and 800, but the mean isn't always at exactly 500.