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 the above

Question

Quizplus · Accepted Answer

To calculate the Upper Control Limit (UCL) for an X-bar chart, we use the formula:

UCL = X-bar + (Z-score * σx̄)

where X-bar is the average of the sample means, Z-score is the number of standard deviations from the mean for the desired confidence level, and σx̄ is the standard deviation of the sample means.

Given that:

- X-bar = 24
- σx̄ = 4
- We want a confidence level of 99.7%, which corresponds to a Z-score of 3 (since 99.7% of the data lies within 3 standard deviations of the mean)

Plugging these values into the formula:

UCL = 24 + (3 * 4) = 36

Therefore, the UCL for the X-bar chart is 36. Answer choice A is correct.

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