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 part of women who took part in the marathon and possessed a finishing time lower than Kathy post rounding it off to the next whole number would be:

- 66%

Given that,

The mean of women's finishing time = 259 minutes

The Standard deviation of women's finishing time = 32 minutes

Kathy's finishing time = 272 minutes

To find,

The part of women who took part in the marathon and possessed a finishing time lower than Kathy post rounding it off to the next whole number = ?

We will first determine Kathy's finishing time through z-score,

z-score

By employing the z-table  

Post rounding off to next hundredth becomes %

Thus, 66% is the correct answer.

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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)