Using the empirical rule, approximately 68 percent of students' commute time is between 11 and 17 minutes
Step-by-step explanation:
Given that driving times for students' commute to school is normally distributed, with a mean time of 14 minutes and a standard deviation of 3 minutes. So, first we have to find z-score of 11 and 17 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-14}{3}=\frac{-3}{3}=-1[/tex]
[tex]z=\frac{17-14}{3}=\frac{3}{3}=1[/tex]
Also, we do aware that z-score says us a data point is how many standard deviations above or below mean. This z-score -1 and 1 indicates that 11 and 17 lie within one standard deviation of the mean. Therefore, by empirical rule, 68% data lies within one standard deviation of the mean. So, Option B is correct.
