Answer :
Final answer:
Using the concept of normal distribution and z-scores, the heart rate that separates the lower 27% of the distribution with mean as 59.1 bpm and standard deviation 7.2 bpm, is approximately 54.7 bpm.
Explanation:
This problem can be solved using the concept of normal distribution and z-scores in statistics. In a normal distribution, the area under the curve to the left of a specific point represents the probability that a randomly chosen value will be less than that point. So in this case, we have the mean (μ) as 59.1 bpm, the standard deviation (σ) as 7.2 bpm, and we want to find the heart rate that corresponds to the lower 27% (or 0.27 as a decimal).
The z-score corresponding to the lower 27% can be found from a standard normal distribution table, or through a calculator or software capable of performing such computation. For a z-score that corresponds to a cumulative probability of 0.27, we get an approximate value of -0.61. The z-score is calculated as (X-μ)/σ, where X is the value of interest. Solving this equation for X gives us X = μ + σ*z, or in this case X = 59.1 + 7.2 * -0.61 approximately equals 54.7 bpm.
So the heart rate that separates the lower 27% is approximately 54.7 bpm.
Learn more about Heart rate here:
https://brainly.com/question/31910298
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