By re-formulating the issue of random testing into an equivalent problem we are able to introduce a new kind of quality estimations based on Monte Carlo integration and the central limit theorem. This method also provides a limited but working "success theory" in the case of no detected failures. In an empirical evaluation using hundreds of billions of simulated tests we furthermore find a very good match between the quality estimations presented in this article and the true failure frequencies. Both simple modulus defects as well as seeded defects in two extensively employed numerical routines were subject to investigation in the empirical work.