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

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) (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



For the first test the z-score formula is



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







For the second test the z-score formula is



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:



Multiply both sides by 11.3





Answer: 82.5555...

Edwin

RELATED QUESTIONS
A math teacher gives two different tests to measure students� aptitude for math. Scores... (answered by ikleyn)

A math teacher gives two different tests to measure students' aptitude for math. Scores... (answered by rothauserc)

I have two questions that I am in dire need of answers to. I have been stumped for 3... (answered by scott8148)

A study was conducted on students from a particular high school over the last 8 years.... (answered by VFBundy)

A study was conducted on students from a particular high school over the last 8 years.... (answered by ewatrrr)

A study was conducted on students from a particular high school over the last 8 years.... (answered by Theo)

Data from a state indicate that scores on the SAT test are normally distributed with a... (answered by Boreal)

how to write linear inequality for- On her last two math tests, Leah had scores of 83 and (answered by MathLover1)