Answer :
Final answer:
The heart rate that separates the lower 27% of a normally distributed set with a mean of 59.1 bpm and standard deviation of 7.2 bpm is approximately 54.7 bpm.
Explanation:
To answer the question, we'll use the properties of a normally distributed set of data, which implies that approximately 68% of the data lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Given that the mean heart rate is 59.1 bpm with a standard deviation of 7.2 bpm, we can calculate using the properties of the normal distribution.
However, the question asks for the heartbeats that separate the lower 27%. This means we want to find the heart rate where 27% of data points fall below it. To find this value in a normally distributed set, you would use a z-score table to look up the z-score that corresponds to a cumulative percentage of 27%. This corresponds to a z-score of roughly -0.6.
Using the formula for the z-score (z=(X-M)/SD), which is the number of standard deviations a number is away from the mean, you can isolate for X, the desired heartbeat. X = M + (z*SD). Here, M refers to the mean of bpm, z to the z-score and SD to the standard deviation. Plugging in the provided values gives X = 59.1 + (-0.6*7.2) = 54.7 bpm.
So the heart rate that separates the lower 27% is approximately 54.7 bpm.
Learn more about Heart Rates here:
https://brainly.com/question/11233867
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