Question

Housing prices in a small town are normally distributed with a mean of $146,000 and a standard deviation of $8,000. Use the empirical rule to complete the following statement.

Approximately 95% of housing prices are between a low price of
$ ...... and a high price of $ .........

Answer 1

Approximately 95% of housing prices in the small town fall between $130,000 and $162,000, as calculated using two standard deviations from the mean based on the empirical rule.

Step-by-step explanation:

Using the empirical rule (also known as the 68-95-99.7 rule), in a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Given that the mean housing price is $146,000 and the standard deviation is $8,000, we calculate the range for the middle 95% of housing prices.

The lower bound is found by subtracting two standard deviations from the mean: $146,000 - 2($8,000) = $146,000 - $16,000 = $130,000. The upper bound is found by adding two standard deviations to the mean: $146,000 + 2($8,000) = $146,000 + $16,000 = $162,000.

Therefore, approximately 95% of housing prices are between a low price of $130,000 and a high price of $162,000.