Question: This is an exercise in understanding normal distribution. The final grades in a class are said to be “curved” when they are forced into a normal distribution, that is, 68% get C, (95% −68%) / 2 get B, etc. Here is a list of grades accumulated at mid-term, where the possible number of accumulated points is 56. Such predictions are not very accurate, one reason being that some students have not yet submitted or re-submitted work that isn’t yet locked. However, let’s predict final grades on the basis of performance thus far.

In Column 2, give predictions of grades based on the usual grading criteria. Thus 90% or more of the possible points thus far gives an A, etc.

In Column 3, give predictions of “curved” grades, that is, forced into a normal distribution according to the middle 68% get C, etc.

A fact of life in the university world is that some students sign up for a course and never participate, or begin to participate, then stop early in the term, yet never officially withdraw from the course. UMUC requires a special grade of FN for such students. For Column 4, give predictions of grades based on the usual grading criteria, but give any student with less than 20 points a grade of FN. For Column 5, do the same with FN. Then take the remaining grades, and “curve” them, that is, force them into a normal distribution.

Comment briefly on which of these grading criteria is “fair” and give reasons for your decision. Note that UMUC requires the FN grade be assigned, but allows professors to write syllabi with any reasonable standards, including “curved” grades, for other grades, as long as the standards are set at the beginning of the course.

This extra credit problem is all-or-nothing, that is, for credit it must be done and presented perfectly on the first try. There is no part credit. It is to be submitted by email with the criteria for the title of the email exactly as set by the Syllabus. Late work is not accepted. A hint is attached.