A coffee machine fills cups with an average of 6 ounces with a standard deviation of .25 ounces.A sample of 9 cups is taken.The lower and upper control limits for a 3-sigma $\bar { x }$ control chart are 5.75 and 6.25,respectively.

Question

Quizplus · Accepted Answer

The control limits for a 3-sigma $\bar{x}$ control chart are calculated as:

Upper Control Limit = $\bar{x}$ + 3$\sigma$/ $\sqrt[]{n}$
Lower Control Limit = $\bar{x}$ - 3$\sigma$/ $\sqrt[]{n}$

Given, 
$\bar{x}$ = 6 ounces,
$\sigma$ = 0.25 ounces and 
n = 9 (sample size)

Substituting the values,

Upper Control Limit = 6 + 3(0.25)/$\sqrt[]{9}$ = 6.25 ounces
Lower Control Limit = 6 - 3(0.25)/$\sqrt[]{9}$ = 5.75 ounces

Therefore, the given statement is True.

A Coffee Machine Fills Cups with an Average of 6 xˉ\bar { x }xˉ

A Coffee Machine Fills Cups with an Average of 6 $\bar { x }$