The national education longitudinal survey (nels) tracks a nationally

The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eighth grade through high school and college. Research published in Chance (Winter 2001) examined the Standardized Admission Test (SAT) scores of 265 NELS students who paid a private tutor to help them improve their scores. The next table summarizes the changes in both the SAT–Mathematics and SAT–Verbal scores for these students.
SAT-Math SAT-Verbal
Mean change in score 19 7
Standard deviation of score changes 65 49

a. Suppose one of the 265 students who paid a private tutor is selected at random. Give an interval that is likely to contain this student’s change in the SAT–Math score.
(Why the stddev us 3?)
b. Repeat part a for the SAT–Verbal score. -140, 154
c. Suppose the selected student increased their score on one of the SAT tests by 140 points.
Which test, the SAT–Math or SAT–Verbal, is the one most likely to have the 140-point increase?

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