the resting heart rate for a sample of individuals are normally distributed with a mean of 67 and a standard deviation of 11. Use the 68-95-99.7 rule to find out what percentage of heart rates less than 78
To find out what percentage of heart rates are less than 78, we need to determine the area under the normal distribution curve to the left of 78.
First, we need to calculate the z-score for 78:
z = (x - μ) / σ
z = (78 - 67) / 11
z ≈ 1
Using the 68-95-99.7 rule:
- Approximately 68% of the heart rates fall within 1 standard deviation of the mean.
- Approximately 95% of the heart rates fall within 2 standard deviations of the mean.
- Approximately 99.7% of the heart rates fall within 3 standard deviations of the mean.
Since 78 is one standard deviation above the mean (z ≈ 1), we can approximate that approximately 68% - 34% = 34% of the heart rates are less than 78.
Thus, approximately 34% of heart rates are less than 78.