Which of the following best describes the Central Limit Theorem?
A)If the distribution of a random variable is non-normal, the sampling di stribution of the sample mean will be approximately normal for samples $n \geq 30$.
B) The sample mean is close to $0.50$.
C) The underlying population is normal.
D) All of these choices are correct.

Question

Which of the following best describes the Central Limit Theorem? 
A)If the distribution of a random variable is non-normal, the sampling di stribution of the sample mean will be approximately normal for samples $n \geq 30$.
B) The sample mean is close to $0.50$.
C) The underlying population is normal.
D) All of these choices are correct.

Quizplus · Accepted Answer

The Central Limit Theorem states that for large enough sample sizes ($n \geq 30$), the sampling distribution of the sample mean will be approximately normal, regardless of the underlying population distribution. Therefore, option A is the correct choice. Option B is incorrect because it makes a specific claim about the sample mean, which may or may not be true depending on the context. Option C is also incorrect because the Central Limit Theorem does not require the underlying population to be normal.

Which of the Following Best Describes the Central Limit Theorem n≥30n \geq 30n≥30

Which of the Following Best Describes the Central Limit Theorem $n \geq 30$