The ACT Assessment is designed to assess high school students’ general educational development and their ability to complete college-level work. The following table lists the mean and standard deviation of scores attained by the 1,171,460 high school students of the 2004 graduating class who took the ACT exams.

Science 2004 English Mathematics Reading Reasoning Composite Mean 20.4 20.7 21.3 20.9 20.9 Std. dev. 5.9 5.0 6.0 4.6 4.8 Source: American College Testing Convert the following ACT scores to z-scores for both English and math. Compare placement between the two tests.

a. x  30

b. x  23

c. x  12

d. Explain why the relative positions in English and math changed for the ACT scores of 30 and 12.

e. If Jessica had a 26 on one of the ACT exams, on which one of the exams would she have the best possible relative score? Explain why.