Answer: To complete the statement using the empirical rule, we need to find the range that contains approximately 95% of housing prices.
According to the empirical rule for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given:
Mean (μ) = $131,000
Standard deviation (σ) = $9,000
We want to find the range between the low price and the high price that contains approximately 95% of housing prices.
Approximately 95% of housing prices are within two standard deviations of the mean. So, we need to find the range between the mean minus two standard deviations and the mean plus two standard deviations.
Low Price = Mean - 2 * Standard Deviation
Low Price = $131,000 - 2 * $9,000
Low Price = $131,000 - $18,000
Low Price = $113,000
High Price = Mean + 2 * Standard Deviation
High Price = $131,000 + 2 * $9,000
High Price = $131,000 + $18,000
High Price = $149,000
So, approximately 95% of housing prices are between a low price of $113,000 and a high price of $149,000.