Housing prices in a small town are normally distributed with a mean of $125,000 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 $ Ex: 5000 and a high price of $
Housing prices in a small town are normally distributed with a mean of
$125,000 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
$ Ex: 5000 and a high price of $
Answer:
Approximately 99.7% of housing prices are between a low price of $101,000 and a high price of $149,000.
Step-by-step explanation:
To complete the statement using the empirical rule, we need to determine the range within which approximately 99.7% of housing prices fall.
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 that the mean housing price is $125,000 and the standard deviation is $8,000, we can apply these percentages to calculate the range:
One standard deviation:
The low price would be the mean minus one standard deviation:
$125,000 - $8,000 = $117,000
The high price would be the mean plus one standard deviation:
$125,000 + $8,000 = $133,000
So, approximately 68% of housing prices fall between $117,000 and $133,000.
Two standard deviations:
The low price would be the mean minus two standard deviations:
$125,000 - 2 * $8,000 = $109,000
The high price would be the mean plus two standard deviations:
$125,000 + 2 * $8,000 = $141,000
So, approximately 95% of housing prices fall between $109,000 and $141,000.
Three standard deviations:
The low price would be the mean minus three standard deviations:
$125,000 - 3 * $8,000 = $101,000
The high price would be the mean plus three standard deviations:
$125,000 + 3 * $8,000 = $149,000
So, approximately 99.7% of housing prices fall between $101,000 and $149,000.
In conclusion, approximately 99.7% of housing prices are between a low price of $101,000 and a high price of $149,000.
Hope this helps!
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