Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 69 and standard deviation 8 when given to third graders. Sixth graders have mean score 86 and standard deviation 5 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.
(a) What is David's, a third-grade student, z-score if he scores 75 on the test? Chapter 1.3 (6/10) z =
(b) Convert David's z-score to the new distribution. Example 1.32 (Part 2) x =
(c) What is Nancy's, a sixth-grade student, z-score if she scores 75 on the test? z = (d) Convert Nancy's z-score to the new distribution. x =