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Eleanor scores 680 on the Mathematics part of the SAT. Suppose SAT score follows a Normal distribution with an average of 550 and a standard deviation of 100. Gerald takes the American College Testing (ACT) Mathematics test and scores 28. ACT score is Normally distributed with an average of 18 and a standard deviation of 5. Who has a better Mathematics score?
a) Find the standardized scores (or Z-scores) for both students. Assuming that both tests measure the same kind of ability, who is better in math? Briefly explain why?
b) Find the percentage of SAT and ACT test-takers who score a higher score than Eleanor and Gerald, respectively. How do the two percentages agree with the conclusion from part (a)?
Note: There are two sets of calculations here.
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