For an x-bar chart where the standard deviation is known, the Upper Control Limit
A) is 3 . ? below the mean of sample means for a 3? control chart.
B) is 3 . ? above the mean of sample means for a 3? control chart.
C) is 3 . ?/ $\sqrt { n }$ below the mean of sample means for a 3? control chart.
D) is 3 . ?/ $\sqrt { n }$ above the mean of sample means for a 3? control chart.
E) Cannot be calculated unless the average range is known.

Question

Quizplus · Accepted Answer

The Upper Control Limit (UCL) for an x-bar chart, when the population standard deviation (σ) is known, is calculated as the mean of sample means plus 3 times the standard deviation of the sampling distribution of the mean. The standard deviation of the sampling distribution of the mean is given by σ/√n, where n is the sample size. Therefore, the UCL is 3σ/√n above the mean of sample means.

For an X-Bar Chart Where the Standard Deviation Is Known n\sqrt { n }n​

For an X-Bar Chart Where the Standard Deviation Is Known $\sqrt { n }$