The mean of the sample means and the pooled standard deviation of 40 samples of size 9 taken from a production process under control are $\bar{\bar { x }} = 420$ ,and S = 12,respectively.The lower control limit and the upper control limit of the 3-sigma $\bar { x }$ chart are 408 and 432,respectively.

Question

Quizplus · Accepted Answer

Since the 3-sigma limits for the $\bar { x }$ chart are calculated using the sample mean and standard deviation, and we are given the values for $\bar{\bar { x }}$ and S, we can calculate the control limits as follows:
Lower control limit = $\bar{\bar { x }} - 3S/\sqrt{n}$ = 420 - 3(12)/$\sqrt{9}$ = 408
Upper control limit = $\bar{\bar { x }} + 3S/\sqrt{n}$ = 420 + 3(12)/$\sqrt{9}$ = 432
Therefore, the given lower and upper control limits for the $\bar { x }$ chart are correct.

The Mean of the Sample Means and the Pooled Standard xˉˉ=420\bar{\bar { x }} = 420xˉˉ=420

The Mean of the Sample Means and the Pooled Standard $\bar{\bar { x }} = 420$