Question

Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean  60 and standard deviation 10 when given to third graders. Sixth graders have mean score 83 and standard deviation 9 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.)

(a) What linear transformation will change third-grade scores x into new scores x_new = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.)

a =

b =

(b) Do the same for the sixth-grade scores.

a =

b =

(c) David is a third-grade student who scores 71 on the test. Find David's transformed score.


Nancy is a sixth-grade student who scores 71. What is her transformed score?


Who scores higher within his or her grade?

DavidNancy     

Answer 1

t 2060 a-20 Su- bs new ニat (2.22) (83) a801.26 100 230 15 b2.2 Ca) David's 万&