EXAMPLE 4.22

Grade distributions. A liberal arts college posts the grade distributions for its courses. In a recent semester, students in one section of English 130 received 32% A’s, 42% B’s, 19% C’s, 3% D’s, and 4% F’s. Choose an English 130 student at random. To “choose at random” means to give every student the same chance to be chosen. The student’s grade on a five-point scale (with A = 4) is a random variable X.

The value of X changes when we repeatedly choose students at random, but it is always one of 0, 1, 2, 3, or 4. Here is the distribution of X:

The probability that the student got a B or better is the sum of the probabilities of an A and a B. In the language of random variables,

P(X ≥ 3) = P(X = 3) + P(X = 4)

= 0.42 + 0.32 = 0.74