SOLUTION: 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 24 and a standard deviation of 4.5

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Question 1029221: 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 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3. 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 by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The z-scores should be the same under both systems.

The z-score formula is

z=%28x-mu%29%2Fsigma%29

For the first test the z-score formula is

z=%28x-24%29%2F4.5%29

Since he scored x=29 on the first test, his z-score
was

z=%2829-24%29%2F4.5%29

z=5%2F4.5%29

z=%221.1111...%22

For the second test the z-score formula is

z=%28x-70%29%2F11.3%29

To find the equivalent x-score on the second test 
the z-score would be the same, so we substitute
1.1111... for z and solve for x:

%221.1111...%22=%28x-70%29%2F11.3%29

Multiply both sides by 11.3

%2212.5555...%22=x-70

%2282.5555...%22=x

Answer: 82.5555...

Edwin