📘 Session 4.6 - Normal Approximation to Binomial & Poisson Distributions

🎯 When Can We Use Normal Approximation?

Binomial → Normal: Use when np > 5 and n(1-p) > 5
Poisson → Normal: Use when λ > 5
Use continuity correction: P(X ≤ x) → P(X ≤ x + 0.5)

🔢 Key Formulas

Standardization for binomial:
Z = (X - np) / sqrt(np(1 - p))

Standardization for Poisson:
Z = (X - λ) / sqrt(λ)

📌 Example 1: Binomial Approximation

n = 50, p = 0.1. What is P(X ≤ 2)?

📌 Example 2: Poisson Approximation

λ = 1000. What is P(X ≤ 950)?

📊 Binomial vs Normal Graph

🛠️ Example 3: Practical Question – Quality Control

A factory produces USB cables, and each has a 0.5% chance of being defective. If 2,000 cables are produced in a day, what is the probability that 15 or fewer are defective?