Question

1. the average sale price of new one - family houses in the united states last month was $242,400. find the range of values in which at least 88.89% of the sale prices will lie if the standard deviation is $51,200. show your work and/or explain your answer!!!

Explanation:

Step1: Use Chebyshev's theorem formula

Chebyshev's theorem states that for any number \(k>0\), at least \(1-\frac{1}{k^{2}}\) of the data lies within \(k\) standard deviations of the mean. We are given that \(1 - \frac{1}{k^{2}}=0.8889\). Solving for \(k\):

$$
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Step2: Calculate the range

The mean \(\mu=\$242400\) and the standard deviation \(\sigma=\$51200\). The lower bound is \(\mu - k\sigma\) and the upper bound is \(\mu + k\sigma\).
Lower bound: \(242400-3\times51200=242400 - 153600=\$88800\)
Upper bound: \(242400+3\times51200=242400 + 153600=\$396000\)

Answer:

The range of values is from \(\$88800\) to \(\$396000\)