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

To find the control limits, we need to use the formula:

Upper Control Limit (UCL) = x-bar + A3 * s/sqrt(n)
Lower Control Limit (LCL) = x-bar - A3 * s/sqrt(n)

where A3 is a constant value based on sample size, which can be found in a standard normal distribution table (A3 = 1.128 for n = 16).

Substituting the given values, we get:

UCL = 23 + 1.128 * 0.4/sqrt(16) = 23.30
LCL = 23 - 1.128 * 0.4/sqrt(16) = 22.70

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

If = 23 Ounces,σ = 0