Problem

Joan's finishing time for the Bolder Boulder 10K race was 1.85 standard deviations faster than the women's average for her age group. There were 380 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan? (Round down your answer to the nearest whole number.)

Solution

Step 1 :Given that Joan's finishing time is 1.85 standard deviations faster than the women's average for her age group, we can use the z-score table to find the probability of a woman running faster than Joan.

Step 2 :Using the z-score table, we find that the probability of a woman running faster than Joan is approximately 0.0322.

Step 3 :Since there were 380 women who ran in her age group, we can multiply the probability by the total number of women to find the number of women who ran faster than Joan: \(0.0322 \times 380 = 12.236\)

Step 4 :Round down the result to the nearest whole number: \(\boxed{12}\) women ran faster than Joan.

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Source: https://solvelyapp.com/problems/15365/

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