A factory produces ball bearings whose diameters are meant to have a mean of 3\text{ mm}3 mm3, start text, space, m, m, end text. Suppose that the actual sizes are normally distributed with a mean of 3\text{ mm}3 mm3, start text, space, m, m, end text and a standard deviation of 0.2\text{ mm}0.2 mm0, point, 2, start text, space, m, m, end text. The overseers took a random sample of n=100n=100n, equals, 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 \bar x=2.96\text{ mm} x ˉ =2.96 mmx, with, \bar, on top, equals, 2, point, 96, start text, space, m, m, end text. To see how likely a sample like theirs was to occur by random chance alone, the factory overseers performed a simulation. They simulated 757575 samples of n=100n=100n, equals, 100 diameters from a normal population with a mean of 3\text{ mm}3 mm3, start text, space, m, m, end text and standard deviation of 0.2\text{ mm}0.2 mm0, point, 2, start text, space, m, m, end text. They recorded the mean of the diameters in each sample. Here are the sample means from their 757575 samples: