The average resting heart rate of a population is 89 beats per minute, with a standard deviation of 13 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.
(a) 95 bpm Z=
(b) 69 bpm Z=
Z score = (actual-mean)/standard deviation.
Hope this helps
The average resting heart rate of a population is 89 beats per minute, with a standard deviation of 13 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.
(a) 95 bpm Z=
(b) 69 bpm Z=
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To find the z-scores for a given heart rate, we need to use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the given heart rate
- μ is the mean (average) resting heart rate of the population
- σ is the standard deviation of the resting heart rate of the population
Let's calculate the z-scores for each of the given heart rates:
(a) 95 bpm:
z = (95 - 89) / 13
z = 6 / 13
z ≈ 0.46
Therefore, the z-score for a heart rate of 95 bpm is approximately 0.46.
(b) 69 bpm:
z = (69 - 89) / 13
z = -20 / 13
z ≈ -1.54
Therefore, the z-score for a heart rate of 69 bpm is approximately -1.54.