An automatic filling machine is used to fill 1-liter bottles of cola. The machin

Question

An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of .97 liter and a standard deviation of .05 liter. Output is monitored using means of samples of 27 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 your answers to 4 decimal places.)

Upper control limits: ____liter

Lower control limits: _____liter

Explanation / Answer

A.

At 97% level, the value of Z = 2.17 ( as per the normal distribution table)

Upper control limit (UCL) = mean + Z*SD/n^.5 = .97 + 2.17*.05/27^.5

Upper control limit (UCL) = .9909 Liter

Lower control limit (LCL) = mean - Z*SD/n^.5 = .97 - 2.17*.05/27^.5

Lower control limit (LCL) = .9491 Liter

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