Module 3 · Distributions · Topic 6
The Normal Distribution. The normal (Gaussian) distribution is a continuous, symmetric, bell-shaped distribution defined by its mean (μ) and standard deviation (σ). It is the most important distribution in statistics.
Empirical Rule (68-95-99.7). About 68% of data falls within 1σ of μ, about 95% within 2σ, and about 99.7% within 3σ. This gives a quick way to assess probabilities for normal data.
f(x) = (1 / (σ√(2π))) × exp(−(x − μ)² / (2σ²))
P(X = k) = C(n,k)p^k(1-p)^(n-k) — Exact probability of k successes in n independent Bernoulli trials.z = (x - mu) / sigma — Standardizes a value by measuring standard deviations from the mean.Adult heights are approximately normal with μ = 170 cm and σ = 7 cm. By the empirical rule, about 68% of adults are between 163 and 177 cm tall.
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