Six Sigma Black Belt Practice Exam 2025 – Complete Prep Resource

Question: 1 / 400

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

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.

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