Question

Housing prices in a small town are normally distributed with a mean of $174,000 and a standard deviation of $9,000. Use the empirical rule to complete the following statement. Approximately 95% of housing prices are between a low price of Ex: 5000 and a high price of $ SA​

Answer 1

Using the 68-95-99.7 rule, it can be said that 99.7% of the housing prices will fall within 3 standard deviations of the mean.

P(X bar-3σ≺X≺X bar+3σ) =0.997

∴Lower limit = X bar-3σ = 156,000 - 3*8000 = $132,000

Upper limit = X bar+3σ = 156,000 + 3*8000 = $180,000

Approximately 99.7 % of housing prices are between a low price of $132,000 and a high price of $180,000.