S3.3.2 - Distribution of the sample mean

Know that the sample mean X̄ has mean μ and variance σ²/n; if X is normal, then X̄ ~ N(μ, σ²/n). Proofs are not required.

Use distribution of the sample mean to connect the rule to the data and decision in the question.

This matters because distribution of the sample mean determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply distribution of the sample mean to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Distribution of the sample mean is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.