Suppose that prices of recently sold homes in one neighborhood have a mean of $220,000
with a standard deviation of $7450
. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $197,650
and $242,350
? Round your answer to one decimal place.
To use Chebyshev's Theorem, we first need to calculate the range of prices that are within 2 standard deviations from the mean:
Lower bound = $220,000 - 2($7450) = $205,100
Upper bound = $220,000 + 2($7450) = $234,900
Now, we need to find the range of prices that fall between $197,650 and $242,350:
Percentage within this range = (Upper bound - Lower bound) / (Max price - Min price)
Percentage within this range = ($234,900 - $205,100) / ($242,350 - $197,650) = $29,800 / $44,700 ≈ 0.6663
Therefore, the minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 66.6%.