Question: A machine that is used to fill bottles with soda has been observed to have a true standard deviation in the amounts of fill of

A machine that is used to fill bottles with soda has been observed to have a true standard deviation in the amounts of fill of approximately σ = 1.25 ounces. However, the mean ounces of fill μ may change from day to day, because of change of operator or adjustments in the machine. If n = 55 observations on ounces of fill are taken on a given day, find the probability that the sample mean will be within 0.5 ounce of the true population mean. State any assumptions.

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