(5) Central Limit Theorem

Sample mean of Normal distribution

Is continuity correction needed for sample mean?

No, whilst the underlying distribution may be discrete, the sample mean itself isn’t and can theoretically take non-integer values

What happens to the approximation as n increases?

Approximation improves/gets more accurate

What happens to the variance of the sample mean as n increases

Variance decreases

For a large sample, sample mean ≈ population mean

If X₁ ~ N(μ₁, σ²₁) and X₂ ~ N(μ₂, σ²₂) are both independent, what is X₁ + X₂?

X₁ + X₂ ~ N(μ₁ + μ₂, σ²₁ + σ²₂)