Six Sigma Green Belt Certification Practice Exam

To approximate the normal distribution using the central limit theorem, the sample size should be:

1. Small

2. Medium

3. Large

4. Random

The correct answer is: Large

The central limit theorem (CLT) states that, given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution from which the sample is drawn. A common rule of thumb is that a sample size of 30 or more is generally considered large enough to invoke the central limit theorem and ensure that the distribution of the sample mean approaches a normal distribution. Using a large sample size helps mitigate the effects of population skewness and outliers, leading to more reliable statistical inferences when estimating population parameters. This is why the choice indicating that a large sample size is necessary is correct. While sample size is indeed important for invoking the central limit theorem, the other options suggest that a small or medium sample would suffice, which would not adequately satisfy the conditions of the theorem. Additionally, while random sampling is critical for making valid inferences about a population, it does not directly relate to the size of the sample needed for applying the central limit theorem.