user: In which years did the Women's England cricket team win the world cup

assistant: 1973
1993
2009
2017

user: Why do cats lick themselves

assistant: Cats lick to show affection, to bond with you and other cats, and to groom themselves. Licking excessively can signal your cat has a medical issue, an allergy, or stress and anxiety. You may need to take your cat to the vet for evaluation and treatment if they develop bald spots from grooming too much

user: What is the central limit theorem

assistant: For example, suppose that a sample is obtained containing many observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic mean of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the probability distribution of the average will closely approximate a normal distribution.

The central limit theorem has several variants. In its common form, the random variables must be independent and identically distributed (i.i.d.). In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, if they comply with certain conditions.

The earliest version of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is the de Moivre–Laplace theorem.