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Varvara68
1 month ago
6

Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately norm

al 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.
Advanced Placement (AP)
1 answer:
zhannawk [148]1 month ago
5 0

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)

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