Answer:
Upper Control Limit = 6.03 oz
Lower Control Limit = 5.97 oz
Step-by-step explanation:
Given - A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz.
To find - Determine three sigma control limits for an x-bar (mean) chart assuming a sample size of 10.
Proof -
Given that,
μ = 6
σ = 0.01
Z value for 3 sigma process = 3
Now,
Control limits are - μ ± Zσ
Now,
Upper Control limit (UCL) = μ + Zσ
And
Lower Control limit (LCL) = μ - Zσ
Now,
UCL = 6 + 3( 0.01 )
= 6 + 0.03
= 6.03
⇒UCL =6.03 oz
Now,
LCL = 6 - 3( 0.01)
= 6 - (0.03)
= 6 - 0.03
= 5.97
⇒LCL =5.97 oz
∴ we get
Upper Control Limit = 6.03 oz
Lower Control Limit = 5.97 oz
