Question

if the average price of a new one-family home is $463000 with a standard deviation of $13000. Assume the variable is normally distributed. Find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 20% of the market.

Answer 1

Solution :

Given that,

mean = = 338

standard deviation = = 0.75

Using standard normal table,

P(-z < Z < z) = 20%
P(Z < z) - P(Z < z) = 0.20
2P(Z < z) - 1 = 0.20
2P(Z < z ) = 1 + 0.20
2P(Z < z) = 1.20
P(Z < z) = 1.20 / 2
P(Z < z) = 0.60
- z = -0.25 and z = 0.25

Using z-score formula,

x = z * +

x = - 0.25* 13000+ 463000

x = 459750

The minimum price is $459750

x =0.25* 13000+ 463000

x = 459750

The maximum price is $466250