Mathematics: Applications and Interpretation · Topic 4: Statistics and probability

AHL4.15 — Combining normal variables and the central limit theorem

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL4.15.1

   Linear combinations of normal variables

   A combination of independent normals is normal; the sample mean $\bar{X}\sim N(\mu,\sigma^2/n)$.

2. AIAHL4.15.2

   The central limit theorem

   For large $n$ the sample mean is approximately normal whatever the population.