(Answered) Boxes of sugar are filled by machine with considerable

Statistics

Boxes of sugar are filled by machine with considerable accuracy. The distribution of box weights is normal and has a mean of 32 ounces with a standard deviation of only 2 ounces. A quality control inspector takes a sample of n=16 boxes and finds the sample contains, on average, M=31 ounces of sugar.

A) If the machine is working properly, what is the probability of obtaining a sample of 16 boxes that averages 31 ounces or less?

B) Should the inspector suspect the filling machine needs repair?

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