Question

sale price of homes the average sale price of new one - family houses in the united states for a recent year was $238,500. find the range of values in which at least 93.75% of the sale prices will lie if the standard deviation is $47,100. round your k to the nearest whole number.
the range of values is between $ and $.

Explanation:

Step1: Determine the value of k using Chebyshev's theorem

Chebyshev's theorem states that at least $1-\frac{1}{k^{2}}$ of the data lies within k standard - deviations of the mean. We are given that $1-\frac{1}{k^{2}} = 0.9375$. So, $\frac{1}{k^{2}}=1 - 0.9375=0.0625$. Then $k^{2}=\frac{1}{0.0625}=16$, and $k = 4$.

Step2: Calculate the lower bound of the range

The formula for the lower bound of the range is $\mu - k\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 238500$ and $\sigma=47100$ and $k = 4$. So, the lower bound is $238500-4\times47100=238500 - 188400=50100$.

Step3: Calculate the upper bound of the range

The formula for the upper bound of the range is $\mu + k\sigma$. So, the upper bound is $238500+4\times47100=238500 + 188400=426900$.

Answer:

The range of values is between $\$50100$ and $\$426900$.