Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend to believe that the test reasonably measures learning and that the grades are assigned fairly. Beyond an intuitive reaction, is there evidence that normally distributed test scores appropriately distinguish among student performance? Can we be sure that there is a significant correlation between test scores and student knowledge? Testing these assumptions would be difficult using actual subjects. In this paper we use mathematical models and Monte Carlo simulation to test the assumption that normally distributed grades assign the highest grades to the students who were best prepared for an exam.