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 to calculate the control limits for an x-bar chart is:

Upper Control Limit (UCL) = x̄ + Aσ/√n
Lower Control Limit (LCL) = x̄ - Aσ/√n

Where:
x̄ = Mean
A = Constant from control chart constants table (for n=16 and 3σ, A=3)
σ = Standard deviation
n = Sample size

Given:
x̄ = 23 ounces
σ = 0.4 ounces
n = 16
A = 3

Putting the values in the formula:

UCL = 23 + 3(0.4)/√16 = 23.3 ounces
LCL = 23 - 3(0.4)/√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