Question

6. 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 4. Scores on the second test are normally distributed with a mean of 64 and a standard deviation of 10. 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.)

Answer 1

Answer:-

Given that:-

6. 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 4. Scores on the second test are normally distributed with a mean of 64 and a standard deviation of 10. 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?

Z scores (standardized score) can be found for the given value in the first test to find an equivalent score on the second test.

Z = (X - mean)/standard deviation)

For first test, Mean = 23

Standard deviation = 4

For a score of 29, Z = (29 - 23)/4 = 1.5

For the second test, mean = 64

Standard deviation = 10

1.5= (X - 64)/10

X = 1.510+ 6479

X =79

The student's equivalent score on second test is79