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Answer :
Final answer:
Using the Z score calculation, it is found that 0.19% of runners have heart rates above 140 after walking 6 minutes on treadmill.
Explanation:
In order to determine the percentage of runners that have heart rates above 140, we will need to calculate a Z score for a heart rate of 140 within the male runner's heart rate distribution, which is given as N(104, 12.5). It's termed as a normal distribution.
The Z score calculation formula: [Z = (X - μ) / σ], where X is the data point, μ is the mean and σ is the standard deviation. Plugging in the values, Z = (140 - 104) / 12.5 = 2.88.
This Z score represents the number of standard deviations a data point (heart rate of 140) is from the mean. We use a standard normal distribution table (or calculator) to find the area to the left of this Z score, which gives us the cumulative probability. The table reads 0.9981 for Z = 2.88, which means 99.81% of data falls below a heart rate of 140. Hence, 100% - 99.81% = 0.19% of runners have heart rates above 140.
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