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 99.7 percent, and the average of the sample means is 24.Which of the following is your UCL?
A)36
B)24
C)12
D)4
E)None of these

Question

Quizplus · Accepted Answer

The formula for Upper Control Limit (UCL) for X-bar chart is UCL = X-double bar + k * sigma/ sqrt(n), where
X-double bar = Average of sample means = 24
k = Number of standard deviations to use for the control limit calculation
sigma = Standard deviation of the sample means = 4
n = Sample size

For a 99.7% confidence level, we use k = 3. So,
UCL = 24 + 3 * (4/ sqrt(n))

We do not know the sample size (n) in this question. Therefore, we cannot find the exact value of UCL. However, we can say that UCL will be greater than 24, as the second term in the formula is positive. The only choice that is greater than 24 is A) 36. Hence, the answer is A.

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