A factory produces ball bearings whose diameters are meant to have a mean of 3 mm. Suppose that the actual sizes are normally distributed with a mean of 3 mm and a standard deviation of 0.2 mm. The overseers took a
random sample of n = 100 ball bearings to see if their mean diameter was significantly different than the
target. The mean diameter of the ball bearings in the sample was c = 2.96 mm.
To see how likely a sample like theirs was to occur by random chance alone, the factory overseers performed a
simulation. They simulated 75 samples of n = 100 diameters from a normal population with a mean of 3 mm
and standard deviation of 0.2 mm. They recorded the mean of the diameters in each sample. Here are the
samnle means from their 75 samples: