A company’s marketing team takes 50 samples of 10 recent clients to create a sampling distribution of sample means for the average amount spent per month on company products. Can the Central Limit Theorem be used to determine that the sampling distribution is normal?

• A. No
• B. Yes
• C. More information is required

Answer: (A)

Verified step by step guidance

1. Understand the Central Limit Theorem (CLT): The CLT states that the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large (typically n ≥ 30) or if the population itself is normally distributed.
2. Identify the sample size: In this problem, the sample size is 10 (n = 10), which is less than 30. This means the sample size alone does not guarantee that the sampling distribution will be normal.
3. Consider the population distribution: To apply the CLT for smaller sample sizes, the population distribution must be normal. However, the problem does not provide information about the shape of the population distribution.
4. Evaluate the given options: Since the sample size is small and the population distribution is unknown, we cannot definitively determine whether the sampling distribution is normal.
5. Conclude: The correct answer is 'More information is required' because we need additional details about the population distribution to apply the CLT in this scenario.