Answer:
D. 8
Step-by-step 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:
[tex]72-56=2\sigma[/tex] or
[tex]40-56=-2\sigma[/tex]
[tex]16=2\sigma[/tex]
[tex]\frac{16}{2}=\frac{2\sigma}{2}[/tex]
[tex]8=\sigma[/tex]
[tex]40-56=-2\sigma[/tex]
[tex]-16=-2\sigma[/tex]
[tex]\frac{-16}{-2}=\frac{-2\sigma}{-2}[/tex]
[tex]8=\sigma[/tex]
Therefore, the standard deviation for our given data is 8 and option D is the correct choice.
