The mean travel time to work is 25.2 minutes (U.S. Census). Further, suppose that commute time follows a log-normal distribution with a standard deviation of 10 minutes. What is the probability a randomly selected U.S. worker has a commute time of less than 20 minutes?
A) 30.15%
B) 33.97%
C) 65.91%
D) 69.85%

Question

Quizplus · Accepted Answer

We need to first standardize the variable using the formula z = (x - mu) / sigma, where x is the value we are interested in (in this case 20), mu is the mean (25.2), and sigma is the standard deviation (10).

z = (20 - 25.2) / 10 = -0.52

We then look up the probability of z being less than -0.52 from a standard normal distribution table (or using a calculator), which is 0.3336.

Therefore, the probability of a randomly selected U.S. worker having a commute time of less than 20 minutes is 33.36%, or approximately 33.97% rounded to two decimal places.

The closest option is B.

The Mean Travel Time to Work Is 25