Question

The central limit theorem states that:

Populations with more than 30 observations are approximately normally distributed.

As the sample size increase, a sampling distribution will look more and more like the population.

As long as the sample size collected is at least 30, the variable of interest will always be approximately normally distributed.

A skewed-left population can never be a sampling distribution that is approximately normally distributed.

For sufficiently large random samples, the sampling distribution of the sample mean is approximately normal regardless of the shape of the population.

Which one?

Answer 1

Solution:

      The central limit is about sampling distribution of sample mean when sample size is sufficiently large, since option 1 , 2 , and 3 do not describe about sampling distribution. Thus option 1 , 2, 3 and 4 are incorrect. Also option 4 does not say about sample size. So option 4 is also incorrect.

Thus correct option is: 5^th option

Thus central limit states that:

For sufficiently large random samples, the sampling distribution of the sample mean is approximately normal regardless of the shape of the population.