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 students is reproduced here. Assume that both distributions of SAT score changes are approximately normal.

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?