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Grade 12 Math Lab: Analysis & Inference FREE

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Normal Distribution & Statistics

50 min Grade 12 Math Lab: Analysis & Inference

Learning Objectives

  • Understand normal distribution
  • Apply 68-95-99.7 rule
  • Calculate z-scores

Key Concepts

Normal Distribution

Bell-shaped curve: f(x) = (1/σ√2π)e^(-(x-μ)²/2σ²)

Z-Score

z = (x - μ)/σ — number of standard deviations from mean

Theory

**Normal Distribution N(μ, σ²):** - μ = mean (center) - σ = standard deviation (spread) **68-95-99.7 Rule:** - 68% within ±1σ - 95% within ±2σ - 99.7% within ±3σ **Z-score:** z = (x - μ)/σ - z > 0: above mean - z < 0: below mean

Examples

Scores N(75, 10²). P(score > 85)?

Solution: z = (85-75)/10 = 1. P(z>1) ≈ 0.1587 = 15.87%