A set of reading scores for fourth-grade children has a mean of 25 and a standard deviation of 5. A set of scores for ninth-grade children has a mean of 30 and a standard deviation of
10. Assume that the distributions are normal.
(a) Draw a rough sketch of these data, putting both groups in the same figure.
(b) What percentage of fourth graders score better than the average ninth grader?
(c) What percentage of the ninth graders score worse than the average fourth grader? (We will come back to the idea behind these calculations when we study power in Chapter 15.)