Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes. The finishing time for Kathy was 272 minutes. What proportion of women who ran the marathon had a finishing time less than Kathy's? Show your work.

The proportion of women who ran the marathon and had a finishing time less than Kathy's is 66% (rounding to the next whole)

Explanation:

1. Let's review the information given to us to answer the question properly:

μ of finishing time for women = 259 minutes

σ of finishing time for women = 32 minutes

Finishing time for Kathy = 272 minutes

2. What proportion of women who ran the marathon had a finishing time less than Kathy's? Show your work.

Let's calculate the z-score for the finishing time for Kathy, as follows:

z-score = (272 - 259) / 32

z-score = 13/32 = 0.41 (rounding to the next hundredth)

Using the z-table, now we can calculate the proportion of women who ran the marathon had a finishing time less than Kathy's:

p (z=0.41) = 0.6591

The proportion of women who ran the marathon and had a finishing time less than Kathy's is 66% (rounding to the next whole)