Module 9 · Lesson 4 of 22
Common distributions
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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
- Identify data type (continuous vs count vs pass/fail).
- Check support, independence and constant rate/p.
- 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.
Knowledge check
Pick one answer per question. Explanations appear after you submit.
1. Twelve buttons per shirt, each with independent failure probability p, is best modelled by:
2. Loose threads per garment across an eight-hour shift are best modelled by:
Author: NOSK.life · Last reviewed: 2026-07-21