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A company claims that after years of experience, students who take their training program typically increase their SAT scores by an average of 30 points.

A company claims that after years of experience, students who take their training program typically increase their SAT scores by an average of 30 points. They further claim that the increase in scores has a normal distribution with standard deviation 12. As a check on their claim, you randomly sample 16 students and find that the average increase is 21 points. The company argues that this does not refute their claim because getting a sample mean of 21 or less is not that unlikely. Compute the probability that a sample mean as small as or smaller than 21. Round it to 4 decimal places

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