If = 23 ounces,σ = 0.4 ounces,and n = 16,what will be the ±3σ control limits for the x-bar chart?
A)21.8 to 24.2 ounces
B)23 ounces
C)22.70 to 23.30 ounces
D)22.25 to 23.75 ounces
E)22.90 to 23.10 ounces

Question

If  = 23 ounces,σ = 0.4 ounces,and n = 16,what will be the ±3σ control limits for the x-bar chart?
A)21.8 to 24.2 ounces 
B)23 ounces 
C)22.70 to 23.30 ounces 
D)22.25 to 23.75 ounces 
E)22.90 to 23.10 ounces

Quizplus · Accepted Answer

The formula for control limits for the x-bar chart is:
Upper control limit (UCL) = x-bar + ARL * σ/sqrt(n)
Lower control limit (LCL) = x-bar - ARL * σ/sqrt(n)

Where ARL (Average Run Length) is the constant value obtained from the ARL table for the desired control limit. For ±3σ control limits and n = 16, ARL = 2.574.

Substituting the given values:
UCL = 23 + 2.574 * 0.4/sqrt(16) = 23.3 ounces
LCL = 23 - 2.574 * 0.4/sqrt(16) = 22.7 ounces

Therefore, the ±3σ control limits for the x-bar chart are 22.70 to 23.30 ounces, which is option C.

If = 23 Ounces,σ = 0