Third Grade Linear Transformation

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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You want a transformation such as y = a + bx
Where:
Xbar = 100
Sx = 20

There should be a perfect correlation on both ...