An instructor transforms her students' scores on a midterm into standardized (z) scores. Which of the following is by definition true about the distribution of standardized scores?

A) The standardized distribution is normally distributed.
B) The mean of the standardized scores is equal to 0.
C) The distribution of standardized scores stretches to infinity in both directions.
D) The standard deviation of the standardized scores is equal to σ.

Question

Radelmis Rosario · Accepted Answer

Final Answer : B, Explanation :  By definition, z scores transform raw scores into a standard normal distribution with a mean of 0 and a standard deviation of 1. Therefore, the mean of the standardized scores will always be 0. While the distribution may often be normally distributed, this is not always guaranteed, so choice A is incorrect. The distribution does stretch to infinity in both directions (i.e., it is unbounded), so choice C is partially correct. However, the standard deviation of the standardized scores is always 1, not equal to σ (the standard deviation of the original scores), so choice D is incorrect.

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