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Calculating the probabilities for normally distributed data

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A local bank reported to the federal government that its 5,246 saving accounts have a mean of $1,000 and standard deviation of $240. Government auditors have asked to randomly sample 64 of the bank's accounts to assess the reliability of the mean balance reported by the bank. If the bank information is correct, what is the probability that the sample mean balance would be less than $928?

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The solution gives detaield steps on calculating probabilities for normally distributed data. All formula and calculations are shown and explained.

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