Final answer:
The standard deviation of the sampling distribution is inversely proportional to the square root of the sample size N, known as the standard error of the mean.
Step-by-step explanation:
Mathematically, the standard deviation of the sampling distribution is inversely proportional to the square root of N (the sample size). This relationship is known as the standard error of the mean. To be more specific, if you have a population with a population standard deviation (σ), and you take random samples of size n, the standard deviation of the sampling distribution of the sample means (also called the standard error) is equal to the population standard deviation divided by the square root of the sample size (n).
Therefore, the correct answer to the student's question would be option A: Inversely proportional to the square root of N.