SAT or ACT? Each year thousands of high school students take either the SAT or ACT, standardized tests used in the college admissions process. Combined SAT scores can go as high as 1600, while the maximum ACT composite score is 36. Since the two exams use very different scales, comparisons of performance are difficult. (A convenient rule of thumb is SAT — 40 X ACT + 150; that is, multiply an ACT score by 40 and add 150 points to estimate the equivalent SAT score.) Assume that one year the combined SAT can be modeled by N(1000, 200) and the ACT can be modeled by N(27,3). If an applicant to a university has taken the SAT and scored 1260 and another student has taken the ACT and scored 33, compare these students’ scores using z-values. Which one has a higher relative score? Explain.
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