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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