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The Central Limit Theorem states that the the distribution of \bar{X} approaches normality as n increases, regardless of what the distribution of X is.
Stated more formally, for samples of size n drawn from a distribution with mean \mu and finite variance \sigma^2, the distribution of the sample mean is approximately N\left(\mu, \frac{\sigma^2}{n} \right) for sufficiently large n.
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This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S1EstimationCentral Limit Theorem-
AQA A2 Further Maths 2017StatisticsCentral Limit Theorem - ExtraCentral Limit Theorem-
AQA AS/A2 Further Maths 2017StatisticsCentral Limit Theorem - ExtraCentral Limit Theorem-
CCEA A-Level (NI)S2EstimationCentral Limit Theorem-
CIE A-Level (UK)S2EstimationCentral Limit Theorem-
Edexcel A-Level (UK - Pre-2017)S3EstimationCentral Limit Theorem-
Edexcel A2 Further Maths 2017Further Statistics 1Central Limit TheoremCentral Limit Theorem-
Edexcel AS/A2 Further Maths 2017Further Statistics 1Central Limit TheoremCentral Limit Theorem-
I.B. Higher Level7EstimationCentral Limit Theorem-
Methods (UK)M15EstimationCentral Limit Theorem-
OCR A-Level (UK - Pre-2017)S2EstimationCentral Limit Theorem-
OCR A2 Further Maths 2017StatisticsHypothesis Tests and Confidence IntervalsCentral Limit Theorem-
OCR MEI A2 Further Maths 2017Statistics BSample Mean and Central Limit TheoremCentral Limit Theorem-
OCR-MEI A-Level (UK - Pre-2017)S3EstimationCentral Limit Theorem-
Universal (all site questions)EEstimationCentral Limit Theorem-
WJEC A-Level (Wales)S2EstimationCentral Limit Theorem-