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 more than half an hour?
A) 25.78%
B) 31.56%
C) 68.44%
D) 74.22%

Question

Quizplus · Accepted Answer

The probability of a commute time of more than half an hour is the area under the log-normal distribution to the right of 30 minutes. Using the given mean and standard deviation, we can calculate the z-score for 30 minutes as (30 - 25.2) / 10 = 0.48. The area to the right of this z-score is 0.3156, or 31.56%.

The Mean Travel Time to Work Is 25