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 between 56 and 89
To find the percentage of heart rates between 56 and 89 using the 68-95-99.7 rule, we can calculate the z-scores for these values.
The z-score formula is given by: z = (x - μ) / σ
For x = 56:
z = (56 - 67) / 11 = -1
For x = 89:
z = (89 - 67) / 11 = 2
Now we can use the z-score table to find the corresponding percentage.
From the table, we find that:
- Probability for z = -1 is 0.1587
- Probability for z = 2 is 0.9772
To find the percentage of heart rates between 56 and 89, we subtract the probability for z = -1 from the probability for z = 2:
0.9772 - 0.1587 = 0.8185
Multiplying this value by 100 to convert it to a percentage, we find that approximately 81.85% of heart rates fall between 56 and 89 for the given sample.