Education researchers give a test designed to measure the reading ability of children to a large group of fifth- and sixth-grade children. The mean score for the fifth graders is 60 and the standard deviation is 5. For the sixth graders the mean is 80 and the standard deviation is 15. The researchers want to transform the scores to a scale that allows us to compare the standing of a fifth grader within her grade to the standing of a sixth grader within his grade. The researchers prefer a scale with mean 100 and standard deviation 10 in each grade.

Whatlinear transformationwill change fifth -grade scoresxinto new scoresx_new=b+axthat have the desired mean and standard deviation? (Usea> 0 to preserve the order of the scores.)

Findaandb.Hint:only one correct answer.

a is 1.

b is -20.

a is 3.

b is 5.

None of the listed.

b is 15.

b is -10.