Answer to Question #163800 in Statistics and Probability for Jovert

Question

A contractor builds houses that include the 50% of the market. The average size of houses he builds is 80 square meters and the standard deviation is 10 square meters. Assume that the variable is normally distributed, what are the maximum and minimum sizes of houses he should build?

Answer 1

$P(-z<Z<z)=0.5$

$z=0.6745$

$\frac{x_1-80}{10}=-0.6745$

$x_1=80-0.6745*10=73.255$

$\frac{x_2-80}{10}=0.6745$

$x_2=80+0.6745*10=86.745$

Minimum size: $73.255 m^2$

Maximum size: $86.745m^2$