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 5.1. Scores on the second test are normally distributed with a mean of 68 and a standard deviation of 10.4. Assume that the two tests use different scales to measure the same aptitude. If a student scores 28 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)78
B)79
C)76
D)73

Question

Quizplus · Accepted Answer

To find the equivalent score, first calculate the z-score for the first test: z = (28 - 23) / 5.1 = 0.98. Then, use this z-score to find the equivalent score on the second test: score = 68 + (0.98 * 10.4) = 78.192, which rounds to 78.

A Math Teacher Gives Two Different Tests to Measure Students