Improving SAT scores. Refer to the Chance (Winter 2001) study of students who paid a private tutor to help them improve their SAT scores, presented in Exercise 2.197 (p. 136). The table summarizing the changes in both the SAT-Mathematics and SAT-Verbal scores for these LO8 students is reproduced here. Assume that both distributions of SAT score changes are approximately normal.

SAT-Math SAT-Verbal Mean change in score 19 7 Standard deviation of changes in score 65 49

a. What is the probability that a student increases his or her score on the SAT-Math test by at least 50 points?

b. What is the probability that a student increases his or her score on the SAT-Verbal test by at least 50 points?