**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

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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.

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