The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches. A sample of 36 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?

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The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches. A sample of 36 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?
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