Question

Suppose that prices of recently sold homes in one neighborhood have a mean of $215,000 with a standard deviation of $8900 . using chebyshev's theorem, what is the minimum percentage of recently sold homes with prices between $197,200 and $232,800 ? round your answer to one decimal place.

Answer 1

According to Chebyshev's theorem, there is no minimum percentage of recently sold homes with prices between $197,200 and $232,800.

Step-by-step explanation:

According to Chebyshev's theorem, for any given number k (where k > 1), at least 1 - 1/k^2 of the data values will fall within k standard deviations of the mean. In this case, the prices falling between $197,200 and $232,800 can be considered as one standard deviation away from the mean, since the mean is $215,000 and the given range is $18,800 away from the mean. To calculate the minimum percentage, we need to find k.

First, we can find the number of standard deviations the given range is away from the mean:
(230,800 - 215,000) / 8,900 = 1.78

Since we want to find the minimum percentage of values within this range, we need to find k such that:
1 - 1/k^2 = 1.78

Solving the equation, we get:
k^2 = 1 / (1 - 1.78) = 1 / (-0.78) = -1.28

Since the value of k^2 cannot be negative, we discard this solution. Therefore, there is no minimum percentage of recently sold homes with prices between $197,200 and $232,800 according to Chebyshev's theorem.