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# Third Grade linear transformation

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Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 75 and standard deviation 10 when given to third graders. Sixth graders have a mean score of 82 and a standard deviation of 11 on the same test. To provide separate norms for each grade, we want scores in each grade to have a mean of 100 and a standard deviation of 20. What linear transformation will change sixth grade scores x into new scores xnew= a+bx that have the desired mean and standard deviation? (Use b>0 to preserve the order of the scores).

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Please see attached file for the full solution.

In your problem you have for the sixth grade the case of:

Ybar = 82
sy = ...

#### Solution Summary

The solution addresses the linear transformation will change sixth grade scores x into new scores xnew= a+bx that have the desired mean and standard deviation? (Use b>0 to preserve the order of the scores).

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