Buying a Home. Suppose that you are thinking of buying a resale home in a large tract. The owner is asking $205,500. Your realtor obtains the sale prices of comparable homes in the area that have sold recently. The mean of the prices is $220,258 and the standard deviation is $5,237. Does it appear that the home you are contemplating buying is a bargain? Explain your answer using the z-score and Chebyshev’s rule.

Comparing Relative Standing. If two distributions have the same shape or, more generally, if they differ only by center and variation, then z-scores can be used to compare the relative standings of two observations from those distributions. The two observations can be of the same variable from different populations or they can be of different variables from the same population. Consider Exercise 3.224.