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 56
To find out the percentage of heart rates less than 56, we need to calculate the z-score for this value.
The z-score formula is:
z = (x - μ) / σ
Where:
x = the value we want to convert to a z-score (56 in this case)
μ = the mean of the distribution (67)
σ = the standard deviation of the distribution (11)
Plugging in the values, we get:
z = (56 - 67) / 11
z ≈ -1
Now, we can use the 68-95-99.7 rule to find out the percentage of heart rates less than 56.
According to this rule:
- Approximately 68% of the data falls within one standard deviation from the mean
- Approximately 95% of the data falls within two standard deviations from the mean
- Approximately 99.7% of the data falls within three standard deviations from the mean
Since the z-score of -1 falls within one standard deviation from the mean, we can approximate that the percentage of heart rates less than 56 is approximately 68%.