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 45
To use the 68-95-99.7 rule, we need to convert the individual heart rate values to z-scores.
First, we'll calculate the z-score for a heart rate of 45 using the formula:
z = (x - μ) / σ
Where:
x = heart rate value (45 in this case)
μ = mean of the distribution (67)
σ = standard deviation of the distribution (11)
z = (45 - 67) / 11
z = - 22 / 11
z = -2
Now, we'll use the z-score to find the percentage of heart rates greater than 45. Since we're looking for heart rates greater than 45, we can calculate the area under the standard normal distribution curve to the right of the z-score (-2).
Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the percentage of heart rates greater than 45 is approximately 97.72%.
Therefore, about 97.72% of the heart rates in the sample are greater than 45.