A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5.The sampling distribution of $\bar { X }$
____________________.
A)Cannot be determined
B)Is skewed to the left
C)Is approximately normal
D)Is skewed to the right

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of sample means 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. In this case, the mean is 50 and the standard deviation is 5/sqrt(36) = 5/6, which is not too different from the standard deviation we would expect if the sample size was much larger. Therefore, we can reasonably assume that the sampling distribution of sample means is approximately normal.

A Random Sample of Size 36 Is Taken from a Population