Which of the following statements is true?

I.The Central Limit Theorem states that the standard deviation of the sampling distribution will be smaller when the sample size is larger.

II.The distribution of the weights of all guinea pigs is nearly normal. The Central Limit Theorem assures us that the means from samples of size 7 will also be nearly normal.

III.The Central Limit Theorem states that the larger the sample size, the more normal the shape of the population distribution.