The validity of the hypothesis of the propagation of chaos is proved in the case of a generalized version of the regularized, inhomogeneous Boltzmann equation with boundary conditions of the reflection type and an interaction law which corresponds (in the case of exponential potentials) to a pseudo-Maxwellian gas. Estimates of the displacement and of the rate of convergence in the mean-square sense are presented for Monte-Carlo evaluations of a linear functional of the solution of the Boltzmann equation.