Scores on a state assessment test were averaged for all the schools in a particular district, which were classified according to level (such as elementary, middle, or high school).

a. Mean scores for elementary schools had a mean of 1,228, and a standard deviation of 82. What would be the z-score for an elementary school whose mean score was 1,300?

b. Mean scores for middle schools had a mean of 1,219, and a standard deviation of 91. What would be the z-score for a middle school whose mean score was 1,300?

c. Mean scores for high schools had a mean of 1,223, and a standard deviation of 105. What would be the z-score for a high school whose mean score was 1,300?

d. Explain why the z-scores in parts (a), (b), and (c) are quite similar