Which of the following is true of the sampling distribution?

Question

A.  Sampling distribution approximate the normal curve 

 

B.  The mean of a sampling distribution is equal to the population mean 

 

C.  Standard deviation of a sampling distribution smaller than the standard deviation of the population 

 

D. All of the answers are correct

Answer 1

D. All of the answers are correct.

why all of them are correct

Option A: Approximates Normal Curve

For large sample sizes, the Central Limit Theorem ensures the sampling distribution of the mean approximates a normal curve, regardless of population shape.

Option B: Mean Equals Population Mean

The mean of the sampling distribution of the sample mean is always equal to the population mean

Option C: Smaller Standard Deviation

Sample averages bunch closer together around the true average than individual data points do, because averaging smooths out random ups and downs; bigger samples make this bunching even tighter.