Statistics problem

Question

With a height of 62 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 66.4 in and a standard deviation of 1.2 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?

The positive difference between Alexander's height and the mean is ? in.

Answer 1

Thank you for posting your question!

Part (a) wants you to subtract his height from the mean, so that would mean taking 66.4 – 62 = 4.4 inches

On part (b) then you want to divide that by the standard deviation, so that means dividing by 1.2 to get 4.4/1.2 = 3.67

For the Z score then in part (c) you want to use the underlying formula Z = (x – mean) / standard deviation to compute that value. so that would be Z = (62 – 66.4)/1.2 = -4.4/1.2 = -3.67.

Since that exceeds the -2 threshold that it set up that means that this amount would be unusual

I hope that helps! Feel free to reach out via message for a lesson if you have any additional questions beyond that! :)