The Central Limit Theorem states that,if a random sample of size n is drawn from a population,then the sampling distribution of the sample mean $\bar { X }$ : A) is approximately normal if n 30. C) is approximately normal if the underlying population is normal. D) None of these choices.

Question

The Central Limit Theorem states that,if a random sample of size n is drawn from a population,then the sampling distribution of the sample mean $\bar { X }$ :
A) is approximately normal if n < 30.
B) is approximately normal if n > 30.
C) is approximately normal if the underlying population is normal.
D) None of these choices.

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal regardless of the underlying population distribution, as long as the sample size is sufficiently large (n > 30). This is because as sample size increases, the distribution of sample means becomes more and more normal in shape. If n < 30, the distribution may still be approximately normal, but it depends on the underlying population distribution and the amount of skewness or outliers present.

The Central Limit Theorem States That,if a Random Sample of Size