The electron‐velocity‐distribution function was determined to be highly non‐Maxwellian and more appropriate to a kappa distribution, with κ ≈ 2.0, near magnetic midnight in the low‐latitude magnetosphere just outside a stable plasmasphere during extremely quiet geomagnetic conditions. The kappa results were based on sounder‐stimulated Qn plasma resonances using the Radio Plasma Imager (RPI) on the IMAGE satellite; the state of the plasmasphere was determined from IMAGE/EUV observations. The Qn resonances correspond to the maximum frequencies of Bernstein‐mode waves that are observed between the harmonics of the electron cyclotron frequency in the frequency domain above the upper‐hybrid frequency. Here we present the results of a parametric investigation that included suprathermal electrons in the electron‐velocity‐distribution function used in the plasma‐wave dispersion equation to calculate the Qn frequencies for a range of kappa and fpe/fce values for Qn resonances from Q1 to Q9. The Qn frequencies were also calculated using a Maxwellian distribution, and they were found to be greater than those calculated using a kappa distribution with the frequency differences increasing with increasing n for a fixed κ and with decreasing κ for a fixed n. The calculated fQn values have been incorporated into the RPI BinBrowser software providing a powerful tool for rapidly obtaining information on the nature of the magnetospheric electron‐velocity‐distribution function and the electron number density Ne. This capability enabled accurate (within a few percent) in situ Ne determinations to be made along the outbound orbital track as IMAGE moved away from the plasmapause. The extremely quiet geomagnetic conditions allowed IMAGE/EUV‐extracted counts to be compared with the RPI‐determined orbital‐track Ne profile. The comparisons revealed remarkably similar Ne structures.