AP Statistics — two-way tables, simulation and the normal model

This material trains the probability skills of Unit 2 of the AP Statistics course framework for 2026–27 that the exam uses most often with data: reading probabilities from two-way tables, conditional probability, estimating probabilities by simulation and calculating with the normal model. It is written at introductory college level for students preparing for the May 2027 exam, with a graphing calculator at hand.

The quiz starts from a two-way table of car owners by area and car type: you compute a joint relative frequency, a conditional probability given a row and the reverse conditional given a column, and you judge association by comparing conditional percentages rather than raw counts. It then applies the general multiplication rule, finds the probability of a positive screening result that can arise in two ways, reads a simulation result as an estimate that the law of large numbers makes more reliable with more trials, and assigns random digits correctly to model an event with probability 0.3. The last four questions use a normal model: the empirical rule, the probability of an interval, the boundaries that cut off the most extreme 10 percent split between the two tails, and the mean a filling machine needs so that only 15 percent of bags are underweight. Each explanation shows the working and says why every wrong answer is wrong.

The flashcards review joint, marginal and conditional relative frequencies, the probability rules, mutually exclusive and independent events, the law of large numbers and the normal-model techniques.

The written work is a printable sheet of eight free-response tasks: a full two-way-table analysis with a justified claim of association, the difference between mutually exclusive and independent events, a screening test with a low base rate, the design and reading of a simulation, three normal calculations, a misuse of the empirical rule on skewed data, a two-tailed boundary and a mean set from a percentile, and the misunderstanding that a win is 'due'. Handwritten answers are photographed and checked against model answers and key points.

The oral exam has an examiner ask one question at a time, starting from a two-way table and moving through conditional probability, simulation and the normal model, and it ends with short, precise feedback.

Probability rules, discrete random variables and binomial distributions are covered by another material of this category; the geometric distribution and combining random variables are no longer part of the 2026–27 framework and are not included. All scenarios are invented and all questions are original practice items written by Zestly, not released exam questions. The material follows the published course framework but is independent practice and does not predict an exam score.

• Compute joint, marginal and conditional relative frequencies and probabilities from a two-way table
• Justify a claim of association between two categorical variables by comparing conditional relative frequencies
• Apply the general multiplication rule and combine the routes to an event
• Design a simulation with random digits and use the law of large numbers to interpret its estimate
• Use the empirical rule and normal calculations for areas, percentiles and two-tailed boundaries
• Find a mean or cutoff from a stated percentile of a normal distribution

Practice material written by Zestly, based on the College Board AP Statistics course framework effective fall 2026 (Unit 2, Probability, Random Variables, and Probability Distributions, topics 2.1–2.7 and 2.11). Original questions, not released exam items.