Normal Law Distribution, known popularly as the “Bell Curve” or mathematically as the “Gaussian Law” seems to be a “common sense” law:

It describes mathematically the idea that extremes are rare and elements around averages more and more numerous. So Normal Law could obviously not be a half-circle nor a square but a bell curve.

To characterize the Bell Curve, we only need two parameters: a mean around which most of the population will be found and a standard deviation which impacts the distance between the average and the queues of the extremes.

The existence of Normal Law is based on the Central Limit Theorem.