Which of the following statements is true A The Central Limi

Which of the following statements is true?                                          
                                          
A.   The Central Limit Theorem states that a sampling distribution of means will not have the same shape as the population distribution from which it is taken.                                        
                                          
B.   The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.                                        
                                          
C.   The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with n > 1) will have a larger standard deviation as the population distribution from which it is taken.                                      
                                          
D.   None of A through C are true.                                      

Solution

Which of the following statements is true?                                          
                                          
A.   The Central Limit Theorem states that a sampling distribution of means will not have the same shape as the population distribution from which it is taken.                                        
                                          
B.   The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.                                        
                                          
C.   The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with n > 1) will have a larger standard deviation as the population distribution from which it is taken.                                      
                                          
D.   None of A through C are true.      

Answer D

The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough.