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The fundamental prerequisite is that the underlying population distribution must have a calculable mean (finite expected value). If the mean is undefined, the Central Limit Theorem cannot be applied, as demonstrated by the Cauchy distribution.

Conditions: The population distribution must possess a finite expected value.; The Cauchy distribution is cited as a counterexample lacking a mean.; This condition overrides the $n \ge 30$ rule of thumb.

The fundamental prerequisite is that the underlying population distribution must have a calculable mean (finite expected value). If the mean is undefined, the Central Limit Theorem cannot be applied, as demonstrated by the Cauchy distribution.

Conditions: The population distribution must possess a finite expected value.; The Cauchy distribution is cited as a counterexample lacking a mean.; This condition overrides the $n \ge 30$ rule of thumb.