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