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Answer :
Final answer:
To find the percent of runners with heart rates above 140, calculate the Z-score for a heart rate of 140 and use the Z-table to find the corresponding area. Subtracting this area from 1 gives the percentage of runners with heart rates above 140, which is approximately 0.28%.
Explanation:
To find the percent of runners with heart rates above 140, we need to determine the area under the normal distribution curve that is greater than 140.
We can use the Z-score formula to standardize the heart rate values and find the corresponding area using a Z-table.
For the runners' heart rates, the mean is 104 and the standard deviation is 12.5.
So, the Z-score for a heart rate of 140 is calculated as (140 - 104) / 12.5 = 2.88.
By looking up the Z-score of 2.88 in the Z-table, we find that the area to the left of this Z-score is 0.9972.
Since we want the area to the right of 2.88 (above 140), we subtract the area to the left from 1: 1 - 0.9972 = 0.0028.
Therefore, approximately 0.28% of the runners have heart rates above 140.
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