Question: Let \(x\) represent the scores on a mathematics achievement test given to eighth-grade students. Suppose that for the population of all scores on the test, the mean is \(\mu=50\) and the standard deviation is \(\sigma=15 .\) If a random sample of 100 values of \(x\) is obtained, find the probability that the sample mean \(\ddot{x}\) will be between 51 and 53; that is, find \(P[51\,<\bar{x}<53]\)

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