Statistcs help

Question

With a height of 63 in, Johnson was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 66.5 in and a standard deviation of 1.3 in.

a. What is the positive difference between Johnson’s height and themean?
b. How many standard deviations is that[the difference found in part(a)]?
c. Convert Johnson’s 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

Hello,

a. The difference between Johnson's height and the mean is 63 - 66.5 = -3.5. Since the question wants the "positive difference", we'll say 3.5.

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 3.5/1.3 = 2.69. Johnson is 2.69 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 = (63 - 66.5)/1.3 = -2.69.

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