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 0.99 liter and a standard deviation of 0.04 liter. Output is monitored using means of samples of 26 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.) Upper control limits: Lower control limits: liter liter b.Given these sample means: 1.005, 1.001,.998, 1.002,.995, and .999, is the process in control? O Yes O No

Explanation / Answer

A

Value of Z = 2.17 ( as per the normal distribution table)

n = 26

SD = .04 liter

Upper control limit = mean + Z*SD/n*.5 = .99 + 2.17*.04/26^.5 = 1.0070 Liter

Lower control limit = mean - Z*SD/n*.5 = .99 - 2.17*.04/26^.5 = .97297 or .9730 Liter

B.

Correct Answer:

Yes

All the mean values of the samples are within the UCL and LCL, so process is in control.

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