Question 6.20

6.20 Grades in a math course.

Indiana University posts the grade distributions for its courses online.6 Students in one section of Math 118 in the fall 2012 semester received 33% A’s, 33% B’s, 20% C’s, 12% D’s, and 2% F’s.

  1. Using the common scale , , , , , take to be the grade of a randomly chosen Math 118 student. Use the definitions of the mean (page 220) and standard deviation (page 229) for discrete random variables to find the mean and the standard deviation of grades in this course.
  2. Math 118 is a large enough course that we can take the grades of an SRS of 25 students to be independent of each other. If is the average of these 25 grades, what are the mean and standard deviation of ?
  3. What is the probability that a randomly chosen Math 118 student gets a B or better, ?
  4. What is the approximate probability that the grade point average for 25 randomly chosen Math 118 students is a B or better?