A math teacher gives two different tests to measure students\' aptitude for math

Question

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 4.2. Scores on the second test are normally distributed with a mean of 71 and a standard deviation of 10.8. 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 sam percentile. please work out problem with answer. Thank you

Explanation / Answer

First test: xbar1=23, s1=4.2 Second test: xbar2=71, s2=10.8 z-score= (x-xbar1)/s1 = (29-23)/4.2 = 1.429 his equivalent score on the second test is 1.429 = (x-xbar2)/s2 --> 1.429 = (x-71)/10.8 --> x= 71+1.429*10.8 =86.43

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