see below for question

Question

With a height of 66in, aurthur was the shortest president of a particular club in the past century, the club presidents of the past century have a mean height of 73.5in and a standard deviation of 2.5in. a. what is the positive difference between aurthurs height and the mean? b. how many standard deviations is that? ( the difference found in part a) c. convert aurthurs height to a z score. d. if we consider "usual" heights to be those that convert to z scores between -2 and 2, is authurs height usual or unusual? please show your work. I am struggling with statistics please help!!!

Thanks, Patti

Answer 1

a. Arthur's height differs from the mean by 73.5-66=7.5 inches.

b. 7.5 inches is 3*2.5 so it's 3 standard deviations.

c. The Z-score for Arthur's height is -7.5/2.5=-3 because Arthur's height is below the mean.

d. Unfortunately, Arthur's height is outside "usual" because it's lower than -2. (That says a lot for me, because I'm the same height as Arthur!)