Question

.   If the average price of a new home is $200,000, find the maximum and minimum

                  prices of the houses that a contractor should build to include the middle 60% of the

                  market. Assume the standard deviation of prices is $2,000 and the variable is

                  normally distributed.

Answer 1

the z-values associated with the middle 60% of a normally-
distributed population.
From standard normal distribution table

At middle 60% means 30% value less than mean and 30% more than mean.thus, p=0.3 , z = +/- 0.84

Z= X - μ / σ

Now convert these z-scores to raw scores using x = z* σ + μ
x = 0.84 * 2000 + 200000 = $ 201680 ( max price )
x = -0.84 * 2000 + 200000 = $198320 (min price )