Question

Square footage of homes in a neighborhood is normally distributed with a mean of 1,200 square feet and a standard deviation of 350 square feet. Find the square footages that define the middle 75% for homes in that neighborhood.

Answer 1

It is given that mean

and standard deviation

To find the middle 75% square footages, we have to find the lower and upper bound of the middle 75%.

100% - 75% = 25%

25% / 2 = 12.5%

The lower bound is 12.5% and upper bound is 75% + 12.5% = 87.5%.

We can find the z-scores corresponding to p-values of 12.5% or 0.1250 and 87.5% or 0.8750 from a standard z-score table.

The z-scores are -1.15 and 1.15.

The formula of z-score is given by,

Now, putting values of z scores to find X, for z=-1.15

For z= 1.15, we get

The square footages that define the middle 75% for homes in that neighborhood are

767.5 < X < 1602.5.

This means that middle 75% square footage lies between 767.5 sq ft and 1602.5 sq ft.