At a large publishing company, the mean age of proofreaders is  36.2  years and the standard deviation is  3.7  years. Assume the variable is normally distributed. Round intermediate  z -value calculations to two decimal places and the final answers to at least four decimal places. If a random sample of  25  proofreaders is selected, find the probability that the mean age of the proofreaders in the sample will be between  36.5  and  38  years. Assume that the sample is taken from a large population and the correction factor can be ignored.

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