What theorem states that with a sufficiently large sample, the sample's average can be treated as if it were drawn from a normal distribution?

The correct answer is the Central Limit Theorem. This theorem is fundamental in statistics and states that, regardless of the original distribution of the data, the distribution of the sample means will tend to be normally distributed as the sample size becomes sufficiently large. This means that as the size of the sample increases, the average of those samples will approximate a normal distribution.

This is particularly important in risk management and other fields that rely on statistical analysis since it allows practitioners to make inferences about population parameters using sample statistics, even when the population distribution is not normal. For example, it helps in estimating confidence intervals and conducting hypothesis tests about means.

The Law of Large Numbers relates to the expected value of sample averages converging to the expected value of the population mean as the sample size increases, but it does not specifically address the shape of the distribution of the sample means. Normal Distribution Theory focuses on the properties of normal distributions themselves rather than on the behavior of sample means. Lastly, the Sampling Distribution Theorem describes the distribution of a statistic based on a random sample from a population but does not specifically highlight the normal approximation aspect associated with larger sample sizes.