This paper considers solutions of the linear Fokker-Planck equation for the steady velocity distribution functions of electrons dilutely dispersed in an excess of either argon, xenon, or krypton. Owing to the large Ramsauer-Townsend minima in the electron-atom momentum-transfer cross sections for these atoms, the steady electron distribution, often referred to as the Davydov distribution, exhibits a bimodal distribution which varies dramatically with the strength of the external electric field. This effect provides a unique verification of the location and shape of the Ramsauer-Townsend minima in the cross sections. It is anticipated that current experimental techniques that probe the details of nonequilibrium electron distributions will verify the results reported in this paper. In addition, these nonequilibrium, non-Maxwellian distributions cannot be rationalized in terms of either the Gibbs-Boltzmann entropy nor the Tsallis nonextensive entropy.