Which of the following statements are true? I. The sampling distribution of ¯ x x¯ has standard deviation σ √ n σn even if the population is not normally distributed. II. The sampling distribution of ¯ x x¯ is normal if the population has a normal distribution. III. When n n is large, the sampling distribution of ¯ x x¯ is approximately normal even if the the population is not normally distributed. I and II I and III II and III I, II, and III None of the above gives the complete set of true responses.

Complete Question

Which of the following statements are true?

I. The sampling distribution of has standard deviation even if the population is not normally distributed.

II. The sampling distribution of   is normal if the population has a normal distribution.

III. When  n is large, the sampling distribution of  is approximately normal even if the the population is not normally distributed.

A  I and II

B  I and III

C II and III

D I, II, and III

None of the above gives the complete set of true responses.

The correct option is  D

Step-by-step explanation:

Generally the mathematically equation for evaluating the standard deviation of the mean() of samples is    hence the the first statement is correct

   Generally the second statement is true, that is the sampling distribution of the mean () is  normal given that the population distribution is  normal

 Now  according to central limiting theorem given that the sample size is  large the distribution of the mean () is approximately  normal notwithstanding the distribution of the population

the answer is c. hope this !

step-by-step explanation: