Question

Real estate prices in a Denver neighborhood areNormally distributed with a mean price of $187,500 and astandard deviation of $12,500.ALDenver Neighborhood Real Estate Pricing

Answer 1

`\begin{gathered} \text{Given} \\ \mu=187500 \\ \sigma=12500 \\ x_1=150000 \\ x_2=225000 \end{gathered}`

First, find the z-score of the two values $150,000 and $225,000

`\begin{gathered} \text{z-score for }x_1 \\ z=(x-\mu)/(\sigma) \\ z=(150000-187500)/(12500) \\ z=(-37500)/(12500) \\ z_1=-3 \\ \; \\ \text{z-score for }x_2 \\ z=(x-\mu)/(\sigma) \\ z=(225000-187500)/(12500) \\ z=(37500)/(12500) \\ z_2=3 \end{gathered}`

Since the z-scores are both 3 standard deviations away from the mean, by Emperical rule, we conclude that about 99.7% of the homes will be priced between $150,000 and $225,000.