We calculate the contribution to the cosmic x-ray background (CXB) of a population of power law spectrum sources with spectral indices distributed over a broad range of values. The composite spectrum of this source population is significantly harder than that given by the power law having the average value of spectral indices. Starting from spectral distributions which are approximately those observed from quasars, it is possible to reproduce the CXB spectrum from ~0.5 keV to ~20 keV. If the spectra of quasars steepen at around 100 keV, the resulting composite spectrum nearly perfectly fits the CXB in the even broader energy range, up to ~100 keV. The QSO population with broadly distributed spectral parameters is also characterized by a significant discrepancy between the results of hard and soft x-ray source counts. The same population of sources yields about three times more sources at 10 keV than at the corresponding flux at 1 keV, similarly to what is found from the comparison of HEAO A-1/Ginga and Einstein/ROSAT measurements. Thus, by allowing the spectra of QSO's to span a broad range of spectral indices, it is possible to reproduce both the CXB spectrum and account for the apparent differences in number counts in different energy bands
