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

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that for large sample sizes (typically considered n>30) the sampling distribution of the mean will be approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (i.e. smaller than the population standard deviation). Therefore, choice D is correct as it reflects this concept.

Which of the Following Is True Regarding the Sampling Distribution