A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 23 and a standard deviation of 5.3. Scores on the second test are normally distributed with a mean of 71 and a standard deviation of 11.9. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)
A) 84
B) 85
C) 77
D) 82

Question

Quizplus · Accepted Answer

The z-score for the first test is (29-23)/5.3 = 1.13. The corresponding percentile is 86.8%. The z-score for the second test that corresponds to the 86.8% percentile is (x-71)/11.9 = 1.13. Solving for x gives x = 84.

A Math Teacher Gives Two Different Tests to Measure Students