The ages of workers in a certain industry are approximately normally distributed with a mean of 30 years and a standard deviation of 3.5 years. A recruiter wondered if that held true for workers in a certain state. The
recruiter took a random sample of n = 3 of these workers from the state, and the mean age of the workers in
the sample was ĉ = 26 years.
To see how likely a sample like theirs was to occur by random chance alone, the recruiter performed a
simulation. They simulated 200 samples of n = 3 ages from a normal population with a mean of 30 years and
standard deviation of 3.5 years. They recorded the mean of the ages in each sample. Here are the sample means
from their 200 samples: