In a recent year, the average marathon time for women in the US was 5 hours and 6 minutes (Source: Marathonguide.com).Suppose that marathon times are normally distributed around this average with a standard deviation of 50 minutes.What marathon time must a woman achieve in order to be among the fastest 10% of marathon runners?
A)3 hours and 26 minutes or less
B)4 hours and 2 minutes or less
C)4 hours and 38 minutes or less
D)6 hours and 10 minutes or less

Question

Quizplus · Accepted Answer

To be among the fastest 10%, a woman must be below the 10th percentile. Using the normal distribution, the z-score for the 10th percentile is approximately -1.28. Calculating the time: 5 hours 6 minutes - (1.28 * 50 minutes) = 4 hours and 2 minutes or less.

In a Recent Year, the Average Marathon Time for Women