Question

Suppose the average size (in square feet) of homes in a certain region is 2390. Assume the variable is normally distributed with standard deviation 120. If a person in the region was intending to build a 2504 square foot home but downsized and built a 2126 square foot home, what was the change in percentile rank from the original plan to the actual home that was built?

Answer 1

Solution :

Given that ,

mean = = 2390

standard deviation = = 120

1) x = 2504

Using z-score formula,

z = x - /   

z = 2504  - 2390 / 120

z = 0.95

= P(z < 0.95)

Using z table,

= 0.8289

The percentage is = 82.89%

The percentile rank = 83rd percentile ( original plan)

2) x = 2126

Using z-score formula,

z = x - /   

z = 2126 - 2390 / 120

z = -2.20

= P(z < -2.20)

Using z table,

= 0.0139

The percentage is = 1.39%

The percentile rank = 1 st percentile ( actual plan)