An automatic filling machine is used to fill 1-liter bottles of cola. The machine output is approximately normal with a mean of 1.00 liter and a standard deviation of 0.05 liter. Output is monitored using means of samples of 29 observations.
(a) determine upper and lower controls that will include roughly 97 percent of the sample means when the process is in control. (Do not round intermediate calculations. Round z value to 2 decimal places. Round your answers to 4 decimal places)
(b) Given these sample mean 1.005, 1.001, 998, 1.002, 995 and 999 is the process in control?