Chapter 3
Q. 3.25
Prices of Homes
The mean price of houses in a certain neighborhood is $50,000, and the standard deviation is $10,000. Find the price range for which at least 75% of the houses will sell.
Step-by-Step
Verified Solution
Chebyshev’s theorem states that three-fourths, or 75%, of the data values will fall within 2 standard deviations of the mean. Thus,
$50,000 + 2($10,000) = $50,000 + $20,000 = $70,000
and
$50,000 − 2($10,000) = $50,000 − $20,000 = $30,000
Hence, at least 75% of all homes sold in the area will have a price range from $30,000 to $70,000.