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 given information: The problem states that 50 samples of size 10 are taken, but it does not provide information about the shape of the population distribution or whether the population is normal.
3. Evaluate the sample size: Since the sample size is 10, which is less than 30, the CLT cannot guarantee that the sampling distribution of the sample mean will be normal unless the population itself is normal.
4. Determine if more information is needed: To conclude whether the sampling distribution is normal, we need to know if the population distribution is normal. This information is not provided in the problem.
5. Conclude: Based on the lack of information about the population distribution, the correct answer is 'More information is required.'