A national achievement test is administered annually to 5th graders.

Question

The test scores are normally distributed with a mean of 100 and a standard deviation of 15.  If Tom's standardized score is 1.23, what was his approximate score on the test?  Round to the whole number.

Answer 1

A standardize score of +1.23 represents that the raw score is 1.23 standard deviations ABOVE the mean.  (NOTE:  If the standardized score was -1.23, then the raw score would be 1.23 standard deviations BELOW the mean)

 

The mean is 100 and the size of the standard deviation is 15.  So the raw score (Tom's score on the test) is:

100 + (+1.23)(15) = 100 + 18.45 = 118.45 rounded to 118.

 

Another note - the distribution does not need to be normally distributed for this calculation to be valid.  However, the idea of standardized scores (or z-scores) directly relate to the Standard Normal Distribution Curve.