A school district administered two year-end mathematics achievement tests to its eighth graders.

The state test had a mean of 25 and a standard deviation of 3.7.

The national test had a mean of 150 and a standard deviation of 21.4. 4 pts each

a) What is the z-score, to the nearest hundredth, for a student with a state score of 20?

b) What is the z-score, to the nearest hundredth, for a student with a national score of 103?

c) Which of the two test scores from parts a and b indicates the stronger relative performance for

this student? Explain why by clearly indicating the meaning of a z-score.