Your first point is not just a property of the Gaussian, but of all distributions. It's the Second Axiom of Probability! Your method is incorrect as a method o

Your first point is not just a property of the Gaussian, but of all distributions. It's the Second Axiom of Probability! Your method is incorrect as a method of normalization, but it seems we are in agreement that perhaps normalization itself is a silly method for this. Most instructors I've known that claimed they were "curving" were in fact using the percentile approach. Grading based on percentiles (top 10% get A's, next 20% get B's, 40% C's, 10% D, bottom 20% F, for example) allows you far more flexibility, as the percentiles don't even need to be symmetric. My grad courses usually only had three grades: A+, A, and "Please see me to discuss your future in the department".