Using the scores 2, 5, 8, 9, and 16, first find x and s, then replace each

Question:

Using the scores 2, 5, 8, 9, and 16, first find x and s, then replace each score by its corresponding z score. (Don't round the z scores; carry as many decimal places as your calculator can handle.) Now find the mean and standard deviation of the five z scores. Will these new values of the mean and standard deviation result from every set of z scores?