The mean of the sample means and the pooled standard deviation of 36 samples of size 9 taken from a production process under control are $\bar{\bar { x } }= 150$ ,and S = 6,respectively.The lower control limit of the 3-sigma $\bar { x }$ chart is 147.

Question

Quizplus · Accepted Answer

The lower control limit (LCL) for a 3-sigma $\bar{x}$ chart is calculated as $\bar{\bar{x}} - 3 \times \frac{S}{\sqrt{n}}$. Here, $\bar{\bar{x}} = 150$, $S = 6$, and $n = 9$. So, LCL = $150 - 3 \times \frac{6}{\sqrt{9}} = 150 - 6 = 144$, not 147.

The Mean of the Sample Means and the Pooled Standard xˉˉ=150\bar{\bar { x } }= 150xˉˉ=150

The Mean of the Sample Means and the Pooled Standard $\bar{\bar { x } }= 150$