Six Sigma Green Belt Certification Practice Exam

A sample of 20 plastic bags is taken from a continuous process where the population is 1000 plastic bags. Which option represents the probability of finding two defective bags?

1. 77.06%

2. 15.00%

3. 22.94%

4. 85.00%

The correct answer is: 22.94%

The probability of finding a certain number of defective items in a sample can often be modeled using the binomial distribution, particularly when dealing with a finite population. In this scenario, you're examining a sample of 20 plastic bags from a larger population of 1,000 bags. To find the probability of two defective bags, several factors need to be considered, including the total number in the population, the sample size, and the defect rate. Assuming a defect rate (let's denote it as 'p'), you can calculate the probability of exactly two defects in your sample of 20 bags. The binomial probability formula is used for this, which is given by: \[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \] where \( n \) is the sample size, \( k \) is the number of successes (defective bags, in this case), and \( p \) is the probability of finding a defect. The correct response, representing the probability of finding two defective bags, is provided as approximately 22.94%. This figure reflects a calculated probability outcome based on the assumption of the defect rate being factored correctly