# Answer to Question #4977 in Statistics and Probability for Jennifer Ashmore

Question #4977

A contractor decided to build homes that will include the middle 80% of the market. If the average size of the hoomes 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.

Expert's answer

sd = 92, a = 1810, P = 0.8

P(Xmin<=X<Xmax) = Ф((Xmax-a)/sd)

- Ф((Xmin-a)/sd),

0<=X<4

0.8 = 0.4 - (-0.4)

(Xmax-a)/sd = 0.4,

(Xmax-1810)/92 = 0.4, Xmax = 1810+36.8 = 1846.8 square feet, Xmin = 1810 - 36.8

= 1773.2 square feet

P(Xmin<=X<Xmax) = Ф((Xmax-a)/sd)

- Ф((Xmin-a)/sd),

0<=X<4

0.8 = 0.4 - (-0.4)

(Xmax-a)/sd = 0.4,

(Xmax-1810)/92 = 0.4, Xmax = 1810+36.8 = 1846.8 square feet, Xmin = 1810 - 36.8

= 1773.2 square feet

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