🎲
Central Limit Theorem
★★★★☆Undergraduate
📖Definition
The Central Limit Theorem states that with sufficient sample size, the distribution of sample means approaches a normal distribution regardless of the original distribution.
📐Formulas
\barX ∼ N(μ, (σ²)/(n))
Distribution of sample mean (large n)
\frac\barX - μσ / √n → N(0, 1)
Standardized sample mean
✏️Examples
예제 1
When rolling a die 100 times, find P(3.3 ≤ mean ≤ 3.7).
📜History
Discovered by: Pierre-Simon Laplace (1810)
Laplace discovered it while studying normal approximation to binomial distribution.
⚡Applications
Statistical Inference
Confidence intervals, hypothesis testing
Quality Control
Sampling inspection
Polling
Election prediction
🔗Related Documents
→Prerequisites
←Next Topics
↔Related
#중심극한정리#정규분포#central limit theorem#CLT