Six Sigma Black Belt Certified Practice Exam

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Six Sigma Black Belt Certified Exam preparation with quizzes and multiple choice questions, complete with explanations. Enhance your skills and ensure success!

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For a process, X = 35.0 and σ = 5.00. If the subgroup size is n = 5, what is the value for the upper control limit for the process?

37.24
37.89
41.71
52.50

The correct answer is: 41.71

To calculate the upper control limit for the process, we use the formula for the control limits in a control chart. Specifically, the upper control limit (UCL) can be determined using the average of the process (X) plus a factor times the standard error of the mean. The formula for the upper control limit is: UCL = X + Z * (σ / √n) Where: - X is the process mean, - Z is the z-score that corresponds to the desired level of confidence (typically for a control chart, this is 3 for three sigma), - σ is the standard deviation of the process, - n is the size of the subgroup. In this case, we have: - X = 35.0 - σ = 5.00 - n = 5 First, we need to calculate the standard error of the mean (SEM): SEM = σ / √n = 5.00 / √5 ≈ 2.24 Next, applying the three-sigma control chart method, we use Z = 3. Therefore: UCL = 35.0 + (3 * 2.24) = 35.0 + 6.72 = 41.