I question how you can even design a test such that the result has a normal distribution around a specific score without testing everyone and applying some kind of bell curve to the overall results. Especially when you want to boil intelligence down to a single dimension. Even if that one number is based on a composite of others, that complicates the turning it into a bell curve, which makes designing a test to target a specific average even harder.

And add to that average intelligence itself being a moving target. Someone of above average intelligence in the middle ages might be considered below average today.