You are developing an X-bar chart based on sample means. You know the standard deviation of the sample means is 4, the desired confidence level is 99 percent, and the average of the sample means is 20. Which of the following is your LCL?
A) 36
B) 24
C) 9.68
D) 16.79
E) 30.32

Question

Quizplus · Accepted Answer

To find the lower control limit (LCL) for an X-bar chart, we use the formula: 
LCL = X-double-bar - A2 * (sigma / sqrt(n)), where 
X-double-bar = average of the sample means (given as 20) 
A2 = a constant based on the sample size and desired confidence level (looked up from a table or calculated) 
sigma = standard deviation of the sample means (given as 4) 
n = sample size (not given, but assumed to be sufficient)

For a 99 percent confidence level and sample size of 25 or more, the A2 value is 2.78. Plugging in the values: 
LCL = 20 - 2.78 * (4 / sqrt(n))

Since sqrt(n) is not given, we cannot solve for the exact value of LCL. However, we can compare the answer choices to the equation and eliminate any that are clearly incorrect.

Eliminating A and E: 
A) LCL = 20 - 2.78 * (4 / sqrt(1)) = negative value, not possible 
E) LCL = 20 - 2.78 * (4 / sqrt(100)) = 17.68, too high

Eliminating B and D: 
B) LCL = 20 - 2.78 * (4 / sqrt(9)) = 15.12, too low 
D) LCL = 20 - 2.78 * (4 / sqrt(16)) = 18.84, too high

Therefore, the only answer choice that remains is C) LCL = 20 - 2.78 * (4 / sqrt(n)), which is the best choice for the lower control limit.

You Are Developing an X-Bar Chart Based on Sample Means