: Mathematics and physics of consistency of the Born rule with normal probability distribution

Newtonian and Scr{\"o}dinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. The resulting unexpected relation between classical and quantum motions goes beyond the results provided by the Ehrenfest theorem. The normal probability distribution and the Born rule turn out to be related. A dynamical mechanism responsible for the latter formula will be proposed and applied to measurements of macroscopic and microscopic systems.