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 20 and a standard deviation of 53. Scores on the second test are normally distributed with a mean of 69 and a standard deviation of 11.8. 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.)

Explanation / Answer

z score for the score of 28 on first test z =(28-20)/5.3 = 1.5094

=1.51 ( two decimals)

equivalent score on the second test x=mean+z*sd

=69+1.51*11.8

=86.818

=87 ( rounded to whole number)

Answer D

z score for the score of 28 on first test z =(28-20)/5.3 = 1.5094

=1.51 ( two decimals)

equivalent score on the second test x=mean+z*sd

=69+1.51*11.8

=86.818

=87 ( rounded to whole number)

Answer D

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