Final answer:
The mean of the sampling distribution of the sample mean X-bar is represented by the population mean, denoted as μ (mu). The central limit theorem assures that this distribution approaches normality as the sample size n increases. The correct answer to the question is A) μ (mu).
Step-by-step explanation:
In the context of population statistics, X-bar is the mean of a random sample of size n. When we consider the sampling distribution of the X-bar, we're looking at how the means of different samples of the same size n are distributed. This concept is based on the central limit theorem which states that the distribution of the sample means will approach a normal distribution as the sample size increases, regardless of the population's distribution.
The symbol μ (mu) represents the population mean, and in the case of the sampling distribution of the sample mean, X-bar is distributed with a mean of μ. This is because the expected value of the sample mean is equal to the population mean, assuming that the samples are taken randomly and the size n is sufficiently large.
Therefore, the correct option in this context is A) μ (mu). This signifies that the sampling distribution of the mean, for large n, is centered around the actual population mean. It is important to note that the standard deviation of the sampling distribution, denoted as sigma (σ), is the population standard deviation divided by the square root of the sample size, which is not an option provided in the question.
Final Answer: A) μ (mu) is the mean denoted for the distribution of X-bar.