Question

The number of days that homes stay on the market before they sell in Houston is bell-shaped with a mean equal to 56 days. Further, 95 percent of all homes are on the market between 40 and 72 days. Based on this information, what is the standard deviation for the number of days that houses stay on the market in Houston?

4
16
Square root of 8
8

Answer 1

D. 8

Explanation:

We have been given that the number of days that homes stay on the market before they sell in Houston is bell-shaped with a mean equal to 56 days. Further, 95 percent of all homes are on the market between 40 and 72 days.

As per empirical rule 95% of the data on bell curve lies between 2 standard deviations of mean.

So we can set an equation as:

`72-56=2\sigma` or

`40-56=-2\sigma`

`16=2\sigma`

`(16)/(2)=(2\sigma)/(2)`

`8=\sigma`

`40-56=-2\sigma`

`-16=-2\sigma`

`(-16)/(-2)=(-2\sigma)/(-2)`

`8=\sigma`

Therefore, the standard deviation for our given data is 8 and option D is the correct choice.