An automatic filling machine is used to fill 2-liter bottles of Sprite Zero. The

Question

An automatic filling machine is used to fill 2-liter bottles of Sprite Zero. The machine's output is approximately normal with a mean of 2.0 liters and a standard deviation of 0.01 liter. Output is monitored using means of samples of 23 observations. Given these sample means: 2.003, 2.001, 1.998, 2.002, 1.997, and 1.999, is the process in control? Why?

A. Yes. Because the sample means average exceed the desired mean.

B. No. Because the sample means average is the same as desired mean.

C. No. Because these sample means either match or exceed the upper and lower control limits.

D. Yes. Because these sample means do not either match or exceed the upper and lower control limits.

Explanation / Answer

We have the average of the sample means as:

(2.003 + 2.001 + 1.998 + 2.002 + 1.997 + 1.999) / 6

= 2.0

Note that the average of sample mean is the same as the population mean.

UCL = 2.0 + 3 * 2.0 * 0.01 = 2.06

LCL = 2.0 - 3 * 2.0 * 0.01 = 1.94

All the values are strictly in the range.

The correct answer is

D. Yes. Because these sample means do not either match or exceed the upper and lower control limits.

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