In the uncommon case where the distribution is extremely skewed or has more than one mode,you may need sample sizes larger than 30 to ensure normality.

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When the distribution is extremely skewed or has more than one mode, the Central Limit Theorem may not apply even for sample sizes of 30 or more. In such cases, other techniques such as non-parametric tests may be more appropriate.

In the Uncommon Case Where the Distribution Is Extremely Skewed