The birth weights of newborn babies in the United States follow a normal distribution with a mean of 3.4\text{ kg}3.4 kg3, point, 4, start text, space, k, g, end text and a standard deviation of 0.6\text{ kg}0.6 kg0, point, 6, start text, space, k, g, end text. Researchers interested in studying how children gain weight decide to take random samples of 100100100 newborn babies and calculate the sample mean birth weight \bar x x
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x, with, \bar, on top for each sample.