Suppose the average size (in square feet) of homes in a certain region is 2101. Assume the variable is normally distributed with standard deviation 120. If a person in the region was intending to build a 2227 square foot home but downsized and built a 1873 square foot home, what was the change in percentile rank from the original plan to the actual home that was built?
A) The change in percentile rank is 71.
B) The change in percentile rank is 94.
C) The change in percentile rank is 82.
D) The change in percentile rank is 12.

Question

Quizplus · Accepted Answer

To find the change in percentile rank, calculate the z-scores for both home sizes and find their corresponding percentiles. The z-score for 2227 sq ft is (2227-2101)/120 = 1.05, corresponding to the 85th percentile. The z-score for 1873 sq ft is (1873-2101)/120 = -1.90, corresponding to the 3rd percentile. The change in percentile rank is 85 - 3 = 82.

Suppose the Average Size (In Square Feet) of Homes in a Certain