Final answer:
The standard deviation of the sampling distribution of the means decreases as sample size increases, due to the central limit theorem and the law of large numbers.
Step-by-step explanation:
As the sample size gets larger, the standard deviation of the sampling distribution of the means will become smaller, indicating that the estimated sample mean value better approximates the population mean. This occurs because of the central limit theorem, which states that as the sample size increases, the distribution of the sample means becomes more normal and the standard deviation decreases. In addition, according to the law of large numbers, as you take larger samples from the population, the mean of these samples gets closer to the actual population mean.