You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

Question: Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following W must be true?
I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.

Option A: I only

Option B: II only

Option C: III only

Option D: I and III only

Option E: W=None of the above
Option E