1. SAT or ACT? Each year thousands of high school stu- dents 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 con- venient rule of thumb is SAT = 40 * 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 N11000, 2002 and the ACT can be modeled by N127, 32. If an applicant to a uni- versity has taken the SAT and scored 1260 and another stu- dent has taken the ACT and scored 33, compare these students scores using z-values. Which one has a higher rel- ative score? Explain.
2. Economics. Anna, a business major, took final exams in both Microeconomics and Macroeconomics and scored 83 on both. Her roommate Megan, also taking both courses, scored 77 on the Micro exam and 95 on the Macro exam. Overall, student scores on the Micro exam had a mean of 81 and a standard deviation of 5, and the Macro scores hada mean of 74 and a standard deviation of 15. Which stu- dent's overall performance was better? Explain.