Suppose that prices of recently sold homes in one neighborhood have a mean of $270,000

The range in which at least 88.9% of the data will reside, ($244,800, $295,200).

Step-by-step explanation:

The Chebyshev's theorem states that, if X is a random variable with mean µ and standard deviation σ then for any positive number k, we have  

Here .

Then the value of k is:

Then we know that,

|X - µ| ≥ kσ

⇒ µ - kσ ≤ X ≤ µ + kσ.

Here it is given that mean (µ) = $270,000 and standard deviation (σ) = $8400.

Then, the price range is given by,

Thus, the range in which at least 88.9% of the data will reside, ($244,800, $295,200).

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