Question

New Home Sizes A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 1810 square feet, find the maximum and minimum sizes of the homes the contractor should build. Assume that the standard deviation is 92 square feet and the variable is normally distributed.

Answer 1

To find the maximum and minimum sizes of homes the contractor should build, we can use the concept of standard deviations in a normal distribution.

Step-by-step explanation:

To find the maximum and minimum sizes of homes the contractor should build, we can use the concept of standard deviations in a normal distribution. Since the contractor wants to include the middle 80% of the market, we need to find the z-scores that correspond to the lower and upper limits of this range. The z-scores can be calculated using the formula: z = (x - mu) / sigma, where x is the size of the home, mu is the mean (1810 sq ft), and sigma is the standard deviation (92 sq ft).

To find the z-score for the lower limit, we can use the equation -1.28 = (x - 1810) / 92. Solving for x, we get x = -1.28 * 92 + 1810 = 1695.44.

To find the z-score for the upper limit, we can use the equation 1.28 = (x - 1810) / 92. Solving for x, we get x = 1.28 * 92 + 1810 = 1924.16.

Therefore, the maximum size of the homes the contractor should build is approximately 1924.16 square feet, and the minimum size is approximately 1695.44 square feet.