5.36 Grades in a math course. Indiana University posts the grade distributions for its courses online.9 Students in one section of Math 118 in the fall semester received 18% A’s, 31% B’s, 26% C’s, 13% D’s and 12% F’s.

  1. (a) Using the common scale A = 4, B = 3, C = 2, D = 1, F = 0, take X to be the grade of a randomly chosen Math 118 student. Use the definitions of the mean (page 248) and standard deviation (page 256) for discrete random variables to find the mean μ and the standard deviation σ of grades in this course.

  2. (b) Math 118 is a large enough course that we can take the grades of an SRS of 25 students and not worry about the finite population correction factor. If is the average of these 25 grades, what are the mean and standard deviation of ?

  3. (c) What is the probability that a randomly chosen Math 118 student gets a B or better, P(X ≥ 3)?

  4. (d) What is the approximate probability that the grade point average for 25 randomly chosen Math 118 students is B or better, ?