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# “If children typically look like their parents, parents must also typically look like their children.” , the child and parent analogy above is not strictly an example of the central limit theorem. Why

On page 128, Chapter 8, of the Wheelan textbook states, “The core principle underlying the central limit theorem is that a large, properly drawn sample will resemble the population from which it is drawn.” Let this wording be a definition of the Central Limit Theorem.On page 130 of the Wheelan textbook states, “If a sample usually looks like the population from which it’s drawn, it must also be true that a population will usually look like a sample drawn from that population.” Consider this sentence to be an inference of the Central Limit Theorem.Again, on page 130 the author provides an analogy to help clarify what the central limit theorem is about: “If children typically look like their parents, parents must also typically look like their children.” Refer to this statement as a teaching illustration.As a teaching illustration this analogy is fine. It can help people to learn about the central limit theorem, which is a key statistical idea. However, the child and parent analogy above is not strictly an example of the central limit theorem. Why? Explain. Provide your reasoning.