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.

Tonya scores 1870 on the SAT. Jermaine scores 31 on the ACT. 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

Tonya\'s score standardizes to z = (X-mean)/s = (1870-1509)/321 =1.12

Jermaine\'s score standardizes to z = (X-mean)/s = (31-21.5)/5.4 = 1.76

Therefore, Jermaine has the higher score.