Question

New-Home Prices If the average price of a new one-family home is $246300 with a standard deviation of $ 15000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 70% of the market. Assume that the variable is normally distributed. Use a graphing calculator and round the answers to the nearest dollar.Minimum price: $=Maximum price: $=

Answer 1

Minimum Price: $230,700

Maximum Price: $261,900

Step-by-step explanation:

To find the minimum and maximum prices, we need to find the z-score of the middle 70%

70% = 0.7

1 - 0.7 = 0.3

0.3/2 = 0.15

Then the inverse normal of 0.15 is -1.04

`z=\pm1.04`

Therefore,

`(x-246300)/(15000)=\pm1.04`
`\begin{gathered} x-246300=\pm15600 \\ x=246300\pm15600 \end{gathered}`
`\begin{gathered} x=246300+15600 \\ =261900 \\ \text{MAXIMUM} \end{gathered}`

and

`\begin{gathered} x=246300-15600 \\ =230700 \\ \text{MINIMUM} \end{gathered}`