Answer:
Approximately 66% of women who participated in the marathon finished with a time faster than Kathy's (rounded to the nearest whole number)
Explanation:
1. To analyze this correctly, let's go over the provided data:
The average finishing time for women = 259 minutes
Standard deviation of finishing time for women = 32 minutes
Kathy's finishing time = 272 minutes
2. To find the proportion of women who ran the marathon with times less than Kathy's, we will calculate the z-score for her finishing temperature as follows:
z-score = (272 - 259)/32
z-score = 13/32 = 0.41 (rounded to the nearest hundredth)
Using the z-table, we can now determine the proportion of women who completed the marathon in less time than Kathy:
p(z=0.41) = 0.6591
About 66% of women who completed the marathon had a quicker finishing time compared to Kathy's (rounded to the nearest whole)