An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations.

a. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control.

b. Given the following sample means—1.005, 1.001, .998, 1.002, .995, and .999—is the process in control?

c. Is the process in control given the following sample means—1.003, .999, .997, 1.001, 1.002,

.998, and 1.004?

 LO.1