Which of the following is true regarding the sampling distribution of the mean for a large sample size?
A) It has a normal distribution with the same mean and standard deviation as the population.
B) It has a normal distribution with the same mean as the population but with a smaller standard deviation.
C) It has the same shape and mean as the population, but has a smaller standard deviation.
D) It has the same shape, mean, and standard deviation as the population.

Question

Quizplus · Accepted Answer

For a large sample size, the sampling distribution of the mean will have a normal distribution with the same mean as the population but with a smaller standard deviation. This is known as the central limit theorem, which states that as sample size increases, the distribution of sample means becomes more normal and the standard error (i.e. standard deviation of the sample mean) decreases.

Which of the Following Is True Regarding the Sampling Distribution