The 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race is (128.74, 135.26) beats per minute for variance.
To find the 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race, we can use the following formula:

where:
- CI is the confidence interval
- x is the sample mean (132)
- t is the t-value corresponding to the 95% confidence level
- s is the square root of the sample variance (the sample standard deviation)
- n is the sample size (41)
Step 1: Calculate the sample standard deviation
≈ 10.25
Step 2: Find the t-value for a 95% confidence level with 40 degrees of freedom (n - 1)
Using a t-table or calculator, we find that the t-value is approximately 2.021.
Step 3: Calculate the margin of error
Margin of Error =
≈ 3.26
Step 4: Calculate the confidence interval
CI = x ± Margin of Error = 132 ± 3.26
CI = (128.74, 135.26)
So, the 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race is (128.74, 135.26) beats per minute.