Fighting the Cooper distance ~ Rescue operations conducted by firefighters involve intense physical activity associated with high level of cardiovascular stress. In 2020, a group French researchers investigated the claim that a combination of deep breathing and mental imagery promotes cardiovascular recovery in firefighters. The researchers recruited a random sample of 20 male professional firefighters who were medically fit with five years of firefighting experience.

To get a baseline measurement, the researchers subjected the firefighters to the Cooper test, a popular maximal test of aerobic fitness during which a participant runs as far as possible in 12 minutes. The mean distance among the 20 participants in the baseline measurements was 2.649 km with a standard deviation of 0.357 km.
If the researchers wanted to estimate the mean distance firefighters can run in 12 minutes with 95% confidence and a margin of error of no more than 0.09 km, how large a sample size would they need?