Every year, a major university assigns Class A to ~16 per cent of its mathematics graduates, Class B and Class C each to ~34 per cent and Class D or failure to the remaining 16 per cent. The figures...

Extracted text: Every year, a major university assigns Class A to ~16 per cent of its mathematics graduates, Class B and Class C each to ~34 per cent and Class D or failure to the remaining 16 per cent. The figures are repeated regardless of the variation in the actual performance in a given year. A graduating student tries to make sense of such a practice. She assumes that the individual candidate's scores X,....x, are independent variables that differ only in mean values Ex,. so that 'centred' scores X, - EX, have the same distribution. Next. she considers the average sample total score distribution as approximately N(u. o). Her guess is that the above practice is related to a standard partition of students' total score values into four categories. Class A is awarded when the score exceeds a certain limit, say a, Class B when it is between b and a, Class C when between c and b and Class D or failure when it is lower that c. Obviously, the thresholds c, b and a may depend on u and or. After a while (and using tables), she convinces herself that it is indeed the case and manages to find simple formulas giving reasonable approximations for a, b and c. Can you reproduce her answer?