Six Sigma Black Belt Certified Practice Exam

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Prepare for the Six Sigma Black Belt exam with study materials, flashcards, and multiple choice questions. Each query comes with hints and explanations. Enhance your abilities and get ready for success!

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If a process produces nonconformities following a Poisson distribution with a mean of 25, what is the standard deviation?

2.5
5.0
12.5
25.0

The correct answer is: 5.0

In a Poisson distribution, the mean and variance are both equal to the parameter λ (lambda), which is the average rate at which events occur over a specified interval. In this case, the mean of the Poisson distribution is given as 25. The variance is also 25. The standard deviation is the square root of the variance. Therefore, to find the standard deviation, you take the square root of the mean (or variance, since they are the same in this distribution): Standard deviation = √variance = √25 = 5.0. Thus, the standard deviation for this Poisson distribution, which reflects the spread of the nonconformities around the mean, is 5.0. This provides a measure of the variability in the number of nonconformities produced, indicating that while the average is 25, the actual count can vary by about 5 around that mean in a typical case.