Chapter 3.4,Problem 1BSC

z Scores James Madison, the fourth President of the United States, was 163 cm tall. His height converts to the z score of –2.28 when included among the heights of all presidents. Is his height above or below the mean? How many standard deviations is Madison’s height away from the mean?

Solution 1BSC

From the given information, the height of the given President is 163 cm tall and the corresponding score is –2.28. The given President’s height is below the mean, since by the property of score, an individual data value is less than that of the mean then the score is negative.

We know that, score for is found by

Therefore, the given President’s height is 2.28 standard deviations away from the mean.