Question

New Home Prices: If the average price of a new one-family home is $250,000 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 80% of the market?

Answer 1

Let X be the new home price       
Since the total population size of new home prices is large, we can assume that       
X follows normal distribution mean μ and standard deviation σ       
Given μ = 250000  σ = 15000    
       
We have to find X1 and X2 such that        
P(X1 < X < X2) = 0.80   Middle 80% of the market    
Since we are finding the middle 80% prices, we know that       
P(X < X1) + P(X > X2) = 1 - 0.8 = 0.20       
Since it is the middle 80%, X1 and X2 are symmetric about the mean       
Thus, P(X < X1) = 0.2/2 = 0.1       
P(X < X1) = 0.1       
From Excel function NORM.INV, we find the value of X1       
X1 = NORM.INV(0.1, 250000, 15000)       
X1 = 230776.7       
Because of symmetry       
X2 = 250000 + (250000 - 230776.7)       
X2 = 269223.3       
Minimum price = $230776.7       
Maximum price = $269223.3