Question

2. With a height of 68 ​in Alexander was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 75.3 in and a standard deviation of 2.2 in.

A. What is the positive difference between Alexander's height and the​ mean?

b. How many standard deviations is that​ [the difference found in part​ (a)]?

c. Convert Alexander's height to a z score.

d. If we consider​ "usual" heights to be those that convert to z scores between −2 and​ 2, is Alexander's height usual or​ unusual?

Answer 1

A. The positive difference between mean and the minimum height of Alexander is the absolute difference as

68-75.3=7=-7.3=|-7.3|=7.3

B. To find how many difference the value is calculated as

7.3/2.2=3.318

C. Z score of Alexander is calculated as

$Z=\frac{X-\bar{X}}{\sigma}=\frac{68-75.3}{2.2=}=-3.318$

D. If we are considering the usual height between Z score of -2 and 2, but the Alexander height is at Z score -3.318 which Does not lie between-2 and 2 hence it is unusual.