Answer :
To calculate the heart rates that divide the lower 27% and upper 15% from the rest, we find the respective z-scores and apply the formula HR = mean + (z * STD), resulting in approximately 54.7 bpm for the lower 27% and 66.6 bpm for the upper 15%.
To find the heartbeat rates that separate the lower 27% from the rest of the distribution and the upper 15% from the rest, one would use the normal distribution properties. Given a mean heart rate of 59.1 bpm and a standard deviation of 7.2 bpm, we look for the z-scores that correspond to the cumulative probabilities of 0.27 and 0.85 (1 - 0.15). For the lower 27%, we find the z-score using statistical tables or a calculator and obtain approximately -0.61.
To convert this to a heart rate, we use the formula HR = mean + (z-score * std. deviation), giving us HR = 59.1 + (-0.61 * 7.2) \\ HR \\approx 54.7 bpm. For the upper 15%, we find a z-score of approximately 1.04. Again, applying the formula gives us HR = 59.1 + (1.04 * 7.2) \\ HR \\approx 66.6 bpm. Thus, the heart rate that separates the lower 27% is around 54.7 bpm, and the heart rate that separates the upper 15% is about 66.6 bpm.
