124 Improving SAT scores. Chance (Winter 2001) performed a study of students who paid a private tutor to help them improve their SAT scores. 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?

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