If 20 samples of size 7 are drawn,with $\overline { \overline { X } }$

= 33.33 and $\bar { R }$
= 5)65,what are the LCL and the UCL for the $\bar { X }$
Chart?
A)[32.313,34.347]
B)[30.963,35.697]
C)[27.68,38,98]
D)[32.911,33.749]

Question

If 20 samples of size 7 are drawn,with $\overline { \overline { X } }$

= 33.33 and $\bar { R }$
= 5)65,what are the LCL and the UCL for the $\bar { X }$
Chart?
A)[32.313,34.347]
B)[30.963,35.697]
C)[27.68,38,98]
D)[32.911,33.749]

Quizplus · Accepted Answer

To calculate the lower control limit (LCL) and upper control limit (UCL) for the $\bar{X}$ chart, we can use the following formulas:

$LCL = \overline{\overline{X}} - A_2\frac{\bar{R}}{\sqrt{n}}$

$UCL = \overline{\overline{X}} + A_2\frac{\bar{R}}{\sqrt{n}}$

where $A_2$ is a constant from a table based on the sample size ($n$), and $\bar{R}$ is the average range of the sample ranges.

Using the values given, we have:

$n = 7$
$\overline{\overline{X}} = 33.33$
$\bar{R} = 65/5 = 13$

Looking up $A_2$ in a table (e.g. from the textbook or online), for $n=7$, we can find that $A_2 = 0.577$

Plugging in the numbers, we get:

$LCL = 33.33 - 0.577\frac{13}{\sqrt{7}} = 30.963$
$UCL = 33.33 + 0.577\frac{13}{\sqrt{7}} = 35.697$

Therefore, the best choice is B: [30.963, 35.697].

If 20 Samples of Size 7 Are Drawn,with X‾‾\overline { \overline { X } }X

If 20 Samples of Size 7 Are Drawn,with $\overline { \overline { X } }$