Normal Distribution Properties
The normal distribution N(μ, σ²) has: (1) a bell-shaped, symmetric probability density function; (2) mean μ, median, and mode are equal at the center; (3) approximately 68% of observations lie within μ ± σ, 95% within μ ± 2σ, 99.8% within μ ± 3σ; (4) inflection points occur at μ ± σ.
Real World
When Cadbury claims a Dairy Milk bar weighs 200g, quality control relies on the 68-95-99.8 rule: bars within 3σ of 200g are accepted, so fewer than 0.2% of bars are rejected as defective.
Exam Focus
Use symmetry to halve your working: P(μ - a < X < μ) = P(μ < X < μ + a) without extra calculation.
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