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An $\bar{x}$ chart is to be established based on standard values: $μ=600, σ=12, n=9.$ The control limits are based on $α$-risk of $0.01$.

What are the appropriate control limits? $$\\$$

This is what I have so far:

I know the mean/centerline = $600$.

I don't know which formula to use to find the control limits:

μ $\pm z_\frac{α}{2}$$(\frac{σ}{\sqrt{n}})$ OR μ $\pm 3(\frac{σ}{\sqrt{n}})$

I would appreciate your help, thanks!

AmR
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1 Answers1

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Please check the condition. You are given $\bar x = 600$,and $\mu$ is not given . It seems there is a mistake somewhere in the wording of the problem. Any way, to proceed to the $99$ % confidence interval ( correspond to $\alpha = 0.01$ is: CI of $\mu$ is: $ = \left( \bar x - z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}, \bar x + z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}\right)= \left(600 - 2.575\cdot \frac{12}{\sqrt{9}}, 600 + 2.575\cdot \frac{12}{\sqrt{9}}\right)= ...$

DeepSea
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  • But isn't μ = 600 from the problem? – AmR Aug 14 '17 at 00:10
  • Note that $-z_{\alpha/2}=+2.576$. Thus the interval is $\left( \bar x + z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}, \bar x - z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}\right)$ – callculus42 Aug 14 '17 at 05:53