Question

e: DO points oblem 10-2 n automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approximately ormal with a mean of 1.00 liter and a standard deviation of 0.05 liter. Output is monitored using means of amples of 29 observations. Use Table-A a. Determine upper and lower control limits 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.) liter Upper control limits: liter Lower control limits: b. Given these sample means: 1.005, 1.001, 998, 1.002. 995, and 999, is the process in control? Yes O No 3:17 PM 6/16/2019 hp

Answer 1

the control limits are $\mu \pm k\sigma$

where k = number of standard deviation units

given machine output is approximately normal, 97% of the sample means to be in control

P(Z) = 0.97 => Z = 1.88

k = 1.88

control limits are

UCL = 1+1.88*0.05 = 1.0940

LCL = 1-1.88*0.05 = 0.906

B) yes the process is in control since no observation is above or below control limits.