Question

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

Select one:

a. It has the same shape, mean, and standard deviation as the population.

b. It has the same shape and mean as the population, but has a smaller standard deviation.

c. It has a normal distribution with the same mean as the population but with a smaller standard deviation.

d. It has a normal distribution with the same mean and standard deviation as the population.

Answer 1

according to central limit theorem, when the sample size is larger the sampling distribution of the sample mean tend to be normal with the same mean as the population , and the standard deviation as follows:

mean of sampling distribtion ,               where is population mean

standard deviation of sampling distribution =             

so, correct answer is

C:

It has a normal distribution with the same mean as the population but with a smaller standard deviation