Question

Housing prices in a small town are normally distributed with a mean of $156,000
and a standard deviation of $8,000 . Use the empirical rule to complete the following statement. Approximately 99.7 % of housing prices are between a low price of$_______ and a high price of$_______

Answer 1

So the answer here is approximately 95% of housing prices are between a low price of  $143000 and a high price of $171000.

What is meant by empirical rule?

The empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, is a statistical principle that asserts that, with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.

The Empirical Rule indicates that 99.7% of data that are seen to have a normal distribution fall within 3 standard deviations of the mean.

According to this criteria, 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within  three standard deviations of the mean.

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