Problema Solution
If the average price of a new one-family home is $246,300 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 58% of the market. Assume that the variable is normally distributed. Round z- value calculations to 2 decimal places and final answers to the nearest dollar.
Answer provided by our tutors
P(-a<z<a)=0.58, from the symmetry of normal distribution, P(z<a) = 0.58+ (1-0.58)/2 = 0.79.
Looking up on the standard normal distribution table, we have a = 0.794, thus
z = (x-m)/std = 0.794
the maximum x = m + 0.794*std = 246300+0.794*15000
258210
minimum x = m- 0.794*std = 246300-0.794*15000
234390
Final answers: {234390, 258210}