In Example 3, find and interpret the z-score of an achievement test score of 630.

Data from Example 3

Using the mean and standard deviation given in Example 2, find and interpret the z-scores of achievement test results of (a) 610 and (b) 435.

(a) The test result of 610 has a z-score of

This test result is 2.2 standard deviations above the mean. This is a very high test score, which is rarely obtained.

(b) The test result of 435 has a z-score of

This test result is 1.3 standard deviations below the mean. This score is below the mean, but fairly typical.

Z = 610-500 50 2.2.