An automatic filling machine is used to fill two-liter bottles of Massafy water. The machine's output is known to be approximately Normal with the mean of 2.0 liter and the standard deviation of 0.01 liter. Output is monitored using means of samples of five observations.
a. Determine upper and lower control limits that will include roughly 95.5 percent of the sample means.
b. Given these sample means: 2.005, 2.001, 1.998, 2.002, 1.995, and 1.999, is the process in control?