Common distributions

Learning objectives

• Match garment data to normal, binomial, Poisson, t, chi-square or F distributions.
• State the support and key assumptions of each distribution.
• Recognise when empirical/non-parametric methods are safer.

Core idea

Normal models symmetric continuous variation; binomial counts successes in fixed independent trials with constant p; Poisson models rare event counts over exposure; t handles small-sample means with estimated sigma; chi-square and F describe variance-related statistics.

Selection lab

• Chest measurement (cm, continuous, symmetric) → Normal.
• Pass/fail per garment (fixed n, constant p) → Binomial.
• Loose threads per shirt (count per opportunity) → Poisson.
• Small-sample mean seam strength (n<30, unknown σ) → t.
• Comparing two shift variances → F.

Garment-factory example

Buttons attached per shirt (12) with per-button failure probability 0.01 → binomial(12, 0.01). Loose threads per garment averaging 0.4 per unit → Poisson(0.4).

Method

1. Identify data type (continuous vs count vs pass/fail).
2. Check support, independence and constant rate/p.
3. Choose the distribution or fall back to empirical methods.

Common mistakes

• Forcing normality on strongly skewed counts.
• Using Poisson when opportunity changes without a rate denominator.