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 20 and a standard deviation of 5.
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Question 1131966: 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 5.3. 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.) Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! calculate the z-score for a score of 28 on the first test
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z-score(28) = (28 - 20)/5.3 = 1.5094 is approximately 1.51
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Look in the table of z-scores for the associated cumulative probability
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the cumulative probability = 0.9345 is approximately 93%
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for the second test, we want the same z-score
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1.51 = (X - 69)/11.8
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X -69 = 1.51 * 11.8 = 17.818
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X = 86.818 is approximately 87
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a score of 87 is required to be in the same percentile
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