1. The problem asks: What does the Central Limit Theorem (CLT) state? 2. The Central Limit Theorem is a fundamental result in probability theory and statistics. 3. It states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution, provided the samples are independent and identically distributed. 4. This means that if you take sufficiently large random samples from any population, the means of those samples will be approximately normally distributed. 5. Let's analyze the options: - a) The sum of independent random variables follows a binomial distribution — This is incorrect; sums of independent variables can have various distributions. - b) The distribution of sample means approaches a normal distribution as the sample size increases — This is the correct statement of the CLT. - c) The distribution of a population can always be approximated by a normal distribution — This is false; the population distribution can be any shape. - d) The sum of independent random variables follows a Poisson distribution — This is only true under specific conditions, not generally. Final answer: b) The distribution of sample means approaches a normal distribution as the sample size increases.