By using an inverse power-law approximation for the interaction potential between a fast-moving projectile and the atoms of an amorphous target into which it penetrates, it is possible to calculate moments of any order of different combinations of range quantities as functions of the initial kinetic energy of the projectile. By the moment of order n of a statistically distributed quantity X we mean the average value of Xn. The quantities concerned are the projection of the total distance from its point of entrance, reached by the projectile on its initial direction of motion, and the projection on the plane, perpendicular to this direction. From these moments, a distribution function of the penetration depth can be constructed. This calculation has been performed for 85Kr ions entering amorphous Al2O3 with different energies. The result is compared with measurements made by Domeij et al.