Statistics (STAT 101) Probability Distributions Cheat Sheet: Normal, Binomial, and Poisson
University of California, Davis
Statistics (STAT 101) | Study Guide

Overview
A STAT 101 distributions quick sheet for exams: when to use binomial vs Poisson vs normal, the key formulas, and the condition checks that prevent wrong-model mistakes.

Key topics
•binomial model checklist (n, p, independence, two outcomes)
•Poisson rate model and when it approximates binomial
•normal model and standardization (z-scores)
•mean/variance for each distribution
•common calculator steps and probability interpretations

Suggested study tasks
•decide which distribution fits 20 short scenarios
•compute 10 binomial probabilities (exact and complement)
•compute 10 Poisson probabilities (including cumulative)
•standardize and compute 10 normal probabilities
•write a one-page checklist for model selection

Common pitfalls
•using Poisson when n is small
•mixing up rate lambda with probability p
•forgetting that binomial counts successes in fixed n trials
•standardizing with wrong mu or sigma
•using normal approximation without checking np and n(1-p)