III.6. Grades in an economics course. Choose a student at random from the course described in Exercise III.3 and observe what grade that student earns (with A = 4, A− = 3.7, B+ = 3.3, B = 3.0, B− = 2.7, C+ = 2.3, C = 2.0, C− =1.7, D+ = 1.3, D = 1.0, D− = 0.7, and F = 0.0).
(a) What is the expected grade of a randomly chosen student?
(b) The expected grade is not one of the 12 grades possible for one student. Explain why your result nevertheless makes sense as an expected value.