SAT scores have amean of 1518 and a standard deviation of 32

SAT scores have amean of 1518 and a standard deviation of 325. Scores on the ACT have a mean of 21.1 and a standard deviation of 4.8. Which is relatively better: a score of 1640 on the SAT test or 24 on the ACT test? Show your justification for your choice.

Solution

To compare, we use z scores.

As

z = (x - u) / sigma

then

z(SAT) = (1640 - 1518)/325 = 0.375384615

z(ACT) = (24 - 21.1)/4.8 = 0.604166667

Thus, getting a 24 on ACT is relatively better. [ANSWER]