Which term is associated with the idea that the distribution of the mean from samples tends toward normality as the sample size grows?

Which term is associated with the idea that the distribution of the mean from samples tends toward normality as the sample size grows?

• A. Central Limit Theorem
• B. Normal Distribution
• C. Probability
• D. Unit Normal Table

Answer: (A)

Think about taking many samples from a population and looking at each sample’s average. As you increase how many observations go into each sample, the distribution of these sample means becomes more and more like a normal curve, centered at the true population mean, with spread shrinking as the sample size grows. This guiding principle is the Central Limit Theorem. It explains why normal-based methods work for inference about a population mean even when the original data aren’t perfectly normal, as long as the population has finite variance. The standard deviation of that sampling distribution is the population standard deviation divided by the square root of the sample size. The other terms describe either the shape of a distribution in general, a broad concept, or a specific lookup tool, rather than the behavior of sample means across repeated samples.

Think about taking many samples from a population and looking at each sample’s average. As you increase how many observations go into each sample, the distribution of these sample means becomes more and more like a normal curve, centered at the true population mean, with spread shrinking as the sample size grows. This guiding principle is the Central Limit Theorem. It explains why normal-based methods work for inference about a population mean even when the original data aren’t perfectly normal, as long as the population has finite variance. The standard deviation of that sampling distribution is the population standard deviation divided by the square root of the sample size. The other terms describe either the shape of a distribution in general, a broad concept, or a specific lookup tool, rather than the behavior of sample means across repeated samples.