What describes the distribution of means from all possible samples of size n?

What describes the distribution of means from all possible samples of size n?

• A. Distribution of Sample Means
• B. Random Sample
• C. p(A)
• D. Unit Normal Table

Answer: (A)

The main idea is the distribution of sample means. If you take every possible sample of a fixed size n from a population, compute each sample’s average, and look at how those averages are spread, you get the distribution of sample means (the sampling distribution of the mean). This distribution centers on the true population mean, and its spread—called the standard error—seems smaller as n grows (roughly sigma over sqrt(n), with a small finite-population correction if you’re sampling without replacement). The Central Limit Theorem adds that, as n increases, this distribution tends toward normal shape, even if the population isn’t normal. This concept is specifically about the means across all possible samples, not about the data in a single sample, not about the probability of an event, and not about a normal-table reference. That’s why describing it as the distribution of sample means is the best answer.

The main idea is the distribution of sample means. If you take every possible sample of a fixed size n from a population, compute each sample’s average, and look at how those averages are spread, you get the distribution of sample means (the sampling distribution of the mean). This distribution centers on the true population mean, and its spread—called the standard error—seems smaller as n grows (roughly sigma over sqrt(n), with a small finite-population correction if you’re sampling without replacement). The Central Limit Theorem adds that, as n increases, this distribution tends toward normal shape, even if the population isn’t normal. This concept is specifically about the means across all possible samples, not about the data in a single sample, not about the probability of an event, and not about a normal-table reference. That’s why describing it as the distribution of sample means is the best answer.