Using Chebyshev's Rule, in what interval about the mean would you expect to find at least 89% of the prices?

Question

The list prices of homes in a Central Ohio neighborhood have a mean of 168000 dollars and a standard deviation of 6000 dollars. The distribution is unknown. Using Chebyshev's Rule, in what interval about the mean would you expect to find at least 89% of the prices?

Answer 1

Chebyshev's Rule states that at least 1-1/k² of data from a sample must fall within "k" standard deviations from the mean. Since we already know the percentage of data is 89%, we can easily find "k":

1-1/k² = 0.89

k²-1 = 0.89k²

-1 = -0.11k²

9 ≈ k²

k ≈ 3

Therefore, we can expect to find at least 89% of the prices within 3 standard deviations of the mean. This interval would be between 168000-3(6000)=$150000 and 168000+3(6000)=$186000.

Hope this helped!