5. Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has a mean of 75 and a standard deviation of 10 when given to third-graders. Sixth- graders have a mean score of 82 and a standard deviation of 11 on the same test.

a. David is a third-grade student who scores 78 on the test. Nancy is a sixth-grade student who scores 81. Calculate the z-score for each student. Who scored higher within his or her grade?

b. Suppose that the distribution of scores in each grade is Normal. Determine the percentiles for David and Nancy. Interpret your results in context.