Six Sigma Green Belt Certification Practice Exam

What is the probability of finding four defects in a sample of 50 chips with a defect rate of 5% using the Poisson distribution?

1. 39.06%

2. 13.36%

3. 76.57%

4. 2.5%

The correct answer is: 13.36%

To determine the probability of finding four defects in a sample of 50 chips with a defect rate of 5%, the Poisson distribution can be applied. The Poisson distribution is particularly useful for scenarios involving a number of rare events occurring over a specified period or in a specific sample size. First, we find the average number of defects (λ) in our sample. This is calculated by multiplying the total number of chips by the defect rate: λ = 50 chips × 0.05 = 2.5 defects. Next, to find the probability of exactly four defects, we use the Poisson probability mass function formula: P(X = k) = (e^(-λ) * λ^k) / k! Where: - k is the number of events we want the probability for (in this case, 4 defects), - e is approximately 2.71828, - λ is the average number of occurrences (2.5 in this situation). By substituting our values into this formula, we calculate as follows: P(X = 4) = (e^(-2.5) * 2.5^4) / 4! Calculating this step-by-step: 1. e^(-