Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in agreement with the experimental observations. We attribute this behavior to the tendency of an even number of electrons to gain on-site interaction energy by removing the spin degeneracy. Thus, the dot is predicted to show a non trivial electron number dependent spin polarization. Experimental test of this hypothesis based on the spin polarization measurements are proposed.