Final answer:
The sampling distribution of the sample mean of a random sample has certain properties including the approximate equality of means, the normality of larger sample sizes, and the decreasing standard deviation with increasing sample size.
Step-by-step explanation:
The sampling distribution of the sample mean of a random sample has the following properties:
- True: The mean of the sampling distribution of the means is approximately the mean of the data distribution.
- True: According to the central limit theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
- True: The standard deviation of the sampling distribution of the means will decrease and become approximately the same as the standard deviation of X as the sample size increases.