Yes, you are correct in assuming that the central limit theorem (CLT) is the basis for many statistical methods. The CLT is a fundamental theorem in probability theory that has important applications in statistics and many other fields.

One of the key applications of the CLT in statistics is that it allows us to use the normal distribution to make inferences about the population mean and variance based on a sample mean and variance. For example, if we have a sample mean and variance from a large sample, we can use the normal distribution to construct confidence intervals and perform hypothesis tests.

The CLT is also used in many other statistical methods, such as regression analysis, time series analysis, and Bayesian statistics. It is a cornerstone of modern statistical theory and underpins many of the tools and techniques used by statisticians and data scientists.
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