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.)