Six Sigma Green Belt Certification Practice Exam

A sample of 20 plastic bags is randomly taken from a continuous process. If 15% contain defects, what is the probability of finding two defective bags?

1. 77.06%

2. 85.00%

3. 15.00%

4. 22.94%

The correct answer is: 22.94%

To determine the probability of finding exactly two defective bags in a sample of 20 bags, we can use the binomial probability formula. This situation is a classic case where each bag has two possible outcomes: defective or not defective. In this case, the probability of finding a defective bag (success) is 15%, or 0.15, while the probability of finding a non-defective bag (failure) is 85%, or 0.85. Using the binomial probability formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n \) is the number of trials (20 bags), - \( k \) is the number of successes we are interested in (2 defective bags), - \( p \) is the probability of success (0.15). Substituting the values: \[ P(X = 2) = \binom{20}{2} (0.15)^2 (0.85)^{18} \] Calculating each component: - \( \binom{20}{2} = \frac{20!}{2!(20-2)!} = 190 \