Question

with a height of 68 in, George was the shortest president of a particular club in the past century. the club presidents of the past century have a mean height of 75.1 in and a standard deviation of 2.6 in.

What is the positive difference between George height and the mean?
b. How many standard deviations is that[the difference found in part(a)]?
c. Convert George height to a z score.
d. If we consider “usual" heights to be those that convert to z scores between minus−2 and 2, is Johnson’s height usual or unusual?

Answer 1

a. The difference between George's height and the mean is 68 - 75.1 = -7.1 , Since the question wants the "positive difference", we'll say 7.1

b. To find the number of standard deviations, we can take the difference from part a and divide by the standard deviation. In this case, that would be 7.1/2.6= 2.73 . George's 2.73 standard deviations below the mean.

c. Any z-score can be found with the following formula: z = (X - M)/SD, where X is a person's score, M is the mean, and SD is the standard deviation. In this case we have z = (68 - 75.1)/2.6= -2.73

d. If we consider z-scores between - 2 and 2 to be usual, then George's score would be unusual because he is outside of that range.