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

Explanation:

Given that with a height of 63 in, Johnson was the shortest president of a particular club in the past century.

a) Positive difference between Johnson’s height and the mean=|63-66.5|=3.5 inches

b) No of std deviation the difference has =
`(3.5)/(1.3) =2.692`

c) Z score = no of std deviations from the mean = -2.692

d) Usual heights lie between -2 and 2. Hence Johnson’s height is unusual