There are two major tests of readiness for college the ACT a

There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores are approximately Normal with mean ? = 21.5 and standard deviation ? = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean ? = 1509 and standard deviation ? = 321. Jacob scores 17 on the ACT. Emily scores 1000 on the SAT. Assuming that both tests measure the same thing, who has the higher score? Report the z-scores for both students. (Round your answers to two decimal places.)

Solution

We need to convert both scores to Z scores to be able to compare.

Step 1: Convert Jacob\'s ACT score

(17-21.5)/5.4=-.833

Step 2: Convert Emily\'s SAT score

(1000-1509)/321=-1.59

Step 3: Compare

Jacob has a higher score because he is only .83 standard deviations below the mean, versus Emiliy is 1.59 standard deviations below the mean for her test.

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