We investigate the dichotomy in the radio loudness distribution of quasars by modelling their radio emission and various selection effects using a Monte Carlo approach. The existence of two physically distinct quasar populations, the radio-loud and radio-quiet quasars, is controversial and over the last decade a bimodal distribution of radio loudness of quasars has been both affirmed and disputed. We model the quasar radio luminosity distribution with simple unimodal and bimodal distribution functions. The resulting simulated samples are compared to a fiducial sample of 8,300 quasars drawn from the SDSS DR7 Quasar Catalog and combined with radio observations from the FIRST survey. Our results indicate that the SDSS-FIRST sample is best described by a radio loudness distribution which consists of two components, with 12+/-1 % of sources in the radio-loud component. On the other hand, the evidence for a local minimum in the loudness distribution (bimodality) is not strong and we find that previous claims for its existence were probably affected by the incompleteness of the FIRST survey close to its faint limit. We also investigate the redshift and luminosity dependence of the radio loudness distribution and find tentative evidence that at high redshift radio-loud quasars were rarer, on average "louder", and exhibited a smaller range in radio loudness. In agreement with other recent work, we conclude that the SDSS-FIRST sample strongly suggests that the radio loudness distribution of quasars is not a universal function, and that more complex models than presented here are needed to fully explain available observations. ; Comment: Accepted for publication in ApJ; 13 pages, 10 figures