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 greater than 67
According to the 68-95-99.7 rule (also known as the empirical rule), approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since we are interested in heart rates greater than 67, we need to find the percentage of data that falls outside of one standard deviation above the mean.
To find this percentage, we need to calculate the z-score for a heart rate of 67.
The z-score formula is: z = (x - μ) / σ
Where:
- z is the z-score
- x is the data value (heart rate in this case)
- μ is the mean
- σ is the standard deviation
Substituting the values into the z-score formula:
z = (67 - 67) / 11
z = 0 / 11
z = 0
Since the z-score is 0, we need to find the percentage of data to the right of this value. This is equivalent to finding the area under the curve to the right of z = 0.
Using a standard normal distribution table or a calculator, we can find that this area is approximately 50%. Therefore, about 50% of heart rates are greater than 67.