MATH SOLVE

3 months ago

Q:
# URGENT!!!!!Driving times for students' commute to school is normally distributed, with a mean time of 14 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of students' commute time is between 11 and 17 minutes? 32% 68% 95% 99.7%

Accepted Solution

A:

Answer:B. 68%.Step-by-step explanation:We have been 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. First of all, we will find z-score of 11 and 17 using z-score formula.[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]z=\frac{11-14}{3}[/tex][tex]z=\frac{-3}{3}[/tex][tex]z=-1[/tex][tex]z=\frac{17-14}{3}[/tex][tex]z=\frac{3}{3}[/tex][tex]z=1[/tex]We know that z-score tells us a data point is how many standard deviations above or below mean.Our z-score -1 and 1 represent that 11 and 17 lie within one standard deviation of the mean.By empirical rule 68% data lies with in one standard deviation of the mean, therefore, option B is the correct choice.