Question

1. sat versus act eleanor scores 680 on the sat mathematics test. the distribution of sat scores is symmetric and single - peaked, with mean 500 and standard deviation 100. gerald takes the american college testing (act) mathematics test and scores 27. act scores also follow a symmetric, single - peaked distribution—but with mean 18 and standard deviation 6. find the standardized scores for both students. assuming that both tests measure the same kind of ability, who has the higher score?

Explanation:

Step1: Calculate Eleanor's z - score

$z_{Eleanor}=\frac{680 - 500}{100}=1.8$

Step2: Calculate Gerald's z - score

$z_{Gerald}=\frac{27 - 18}{6}=1.5$

Step3: Compare z - scores

Since $1.8>1.5$, Eleanor has a higher score.

Answer:

Eleanor has the higher score.