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 78
To find out what percentage of heart rates are greater than 78, we can use the 68-95-99.7 rule, also known as the empirical rule. According to this rule, approximately:
- 68% of the values fall within 1 standard deviation of the mean,
- 95% of the values fall within 2 standard deviations of the mean,
- 99.7% of the values fall within 3 standard deviations of the mean.
Given that the mean of the heart rates is 67 and the standard deviation is 11, we can determine the value of 78 in terms of standard deviations:
(78 - 67) / 11 = 1 standard deviation above the mean
Since the percentage of values within 1 standard deviation of the mean is 68%, the percentage of heart rates greater than 78 is:
100% - 68% = 32%
Therefore, approximately 32% of the heart rates will be greater than 78.