Suppose the radius is normally distributed, and is a random varable X. The mass will be proportional to the volume, which increases with the cube of the radius

Suppose the radius is normally distributed, and is a random varable X. The mass will be proportional to the volume, which increases with the cube of the radius, so the mass will be a random variable kX^3 (k = 4/3 x pi x density here). X and kX^3 won't have the same distribution.