A testing service has 1000 raw scores. It wants to transform the distribution so that the mean = 10 and the standard deviation = 1. To do so, _________.
A) do a z transformation for each raw score and add 10 to each z score.
B) do a z transformation for each raw score and multiply each by 10
C) divide the raw scores by 10
D) compute the deviation score for each raw score. Divide each deviation score by the standard deviation of the raw scores. Take this result for all scores and add 10 to each one.
E) a and d

Question

Quizplus · Accepted Answer

For transforming the distribution so that the mean = 10 and the standard deviation = 1, we need to first standardize the raw scores by doing a z transformation (subtract the mean and divide by the standard deviation), which is step a. After this, we need to back-transform the standardized scores to the desired scale of mean = 10 and standard deviation = 1. The formula for this is to multiply each standardized score by the desired standard deviation, which is 1 in this case, and add the desired mean, which is 10 in this case. Therefore, we need to add 10 to each z score, which is step d. Hence, the best choice is E.

A Testing Service Has 1000 Raw Scores