An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately distributed normally, with a mean of 1 liter and standard deviation of 0.1 liter. The output is monitored by using means of samples of 25 observations.
1. Determine the upper and lower control limits that will include roughly 95 percent of the means when the process is in control.
2. Given these sample means: 1.005, 1.001, 0.998, 1.002, 0.995, and 0.999, is the process in control?