A highway traffic engineer studies the people per vehicle in

A highway traffic engineer studies the #people per vehicle (including the driver) and finds a mean of 1.3 with a CV of 87%.
Is the distribution plausibly Normal? Explain.

Solution

As

CV = sigma / u

Then as u = 1.3,

0.87 = sigma/1.3

sigma = 1.3*0.87 = 1.131

As the minimum number of people per vehicle is 1 (it has to have a driver!) and 1 is less than 1 standard deviation from the mean, then it is not plausibly normal. The minimum and maximum values must at least have 3 standard deviations from the mean. [ANSWER, NO]