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SAT scores in one state is normally distributed with a mean of 1530 and a standard deviation of 200. Suppose we randomly pick 58 SAT

SAT scores in one state is normally distributed with a mean of 1530 and a standard deviation of 200. Suppose we randomly pick 58 SAT scores from that state. Is this a valid sampling distribution? If so, find the probability that the average SAT score in the sample of 58 tests is at most 1583. If not, justify why

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