Binomial: Quality Control

Probability · Axiom Academy

EXAMPLE Binomial Distribution: Quality Control A factory produces items with a 5% defect rate. Find the probability of at most 2 defects in a sample of 20 items. Excellent work! You've completed this binomial distribution example. Here's what we learned: Binomial conditions: Fixed number of trials (n = 20), constant probability (p = 0.05), independent trials, and binary outcomes (defect or no defect). Cumulative probability: For "at most" problems, sum individual probabilities: P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2). Binomial formula: Use P(X = k) = C(n,k) × p^k × (1-p)^(n-k) to calculate each term. Practical interpretation: There's about a 92.5% chance of finding 2 or fewer defects in a sample of 20 items. This approach applies to any binomial scenario with fixed trials and constant probability. Practice with different values to build confidence!

This is the written version of the interactive lesson above. See the full Probability course.