ststistics

Question

With a height of 64 ​in, Arthur 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 2.8 in. a. What is the positive difference between Arthur​'s height and the​ mean? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert Arthur​'s height to a z score. d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Arthur​'s height usual or​ unusual?

Answer 1

a) 75.3-64=11.3in. (below the mean)

b) 11.3 is 11.3/2.8=4.04 standard deviations from the mean

c) z-score is -4.04 because the height is lower than the mean

d) Arthur’s height is unusual because the z-score in (c) is outside the interval [-2,2]