Question: An automatic filling machine is used to fill two-litre bottles of cob. The machines output is known to be approximately Normal with a mean of

An automatic filling machine is used to fill two-litre bottles of cob. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of .01 litre. Output is monitored using means of samples of five observations.
a. Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
b. If the means for 6 samples are: 2.005, 2.001, 1.998, 2.002, 1.995, and 1.999, is the process in control?

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