The question asks about the conditions under which the normality of the sampling distribution can be used. The options provided are:

A. The sample mean must be representative in the sample. B. The margin of error should be greater than or equal to 30. C. The sample should be sufficiently large. D. The population distribution should be normally distributed.

The correct answer is:

C. The sample should be sufficiently large.

Explanation: For the sampling distribution to approximate a normal distribution, especially when using the central limit theorem, the sample size needs to be large enough. This is typically considered to be a sample size of 30 or more. If the sample size is small, the underlying population needs to be normally distributed (which is option D) for the sampling distribution to be approximately normal.

Would you like further clarification or more details on the central limit theorem and its conditions?

Here are some related questions for deeper understanding:

1. What is the central limit theorem, and how does it apply to sample distributions?
2. Why is a sample size of 30 often used as a rule of thumb in statistical tests?
3. How does the normality of the population affect the sampling distribution when the sample size is small?
4. How can we determine if a sample is large enough to apply the normal distribution?
5. What are the consequences of using a small sample size when the population is not normally distributed?

Tip: Remember that for small sample sizes, it’s critical to know the shape of the population distribution to apply normality assumptions to the sampling distribution.