Chapter 7 · Simulations

Section 7.1Setting Up a Simulation

When a real-world process is too complex, costly, or time-consuming to study directly, a simulation lets you model it using randomness. In this section, you will learn how to design and run a simulation — identifying the problem, assigning probabilities, generating random outcomes, and repeating trials to build reliable estimates.

Summary

SimulationA model that imitates a real-world process using randomness to predict outcomes. Simulations are used when direct experimentation is impractical or impossible.

ComponentThe smallest part of a simulation, representing one occurrence of an event — for example, buying one cereal box or spinning a spinner once.

TrialA full execution of the simulation from start to finish, producing one possible outcome — for example, buying boxes until all three toys are collected.

Multiple trialsRunning the simulation many times to reduce the effect of chance on any single outcome. More trials produce more reliable estimates of the true expected value.

Assigning probabilitiesMapping outcomes to values (such as digits 0–9) so that each value appears with the correct frequency — for example, assigning 0–2 to a 30% outcome and 3–8 to a 60% outcome.

Random number generatorA tool used to introduce randomness into a simulation. A random number generator produces unpredictable integers within a range you define, so each trial reflects genuine chance rather than a pattern. You can use the generator built into this page to run your simulation trials.

Simulations are a powerful bridge between theoretical probability and real-world data — a theme developed further throughout Chapter 7.

The Real World Statistics Learning Progression

Each section follows the same learning progression: understand the concept, practice the skill, think like a statistician, then apply your learning to authentic data.

Learn This Section

Whether learning independently or teaching a class, the learning path below is designed to help students master the concepts in this section. Page references correspond to the Real World Statistics instructional system.

Read the sectionRead pages 213–217 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on page 218-219. Check your work using the Answer Key, then review and correct any questions you missed before moving on.

Think like a statisticianExplore Enrichment: Role-Based Statistical Analysis Tasks and the Chapter Dataset to apply statistical thinking in real-world contexts.

Need Extra Support? If you'd like additional guidance while working through the practice questions, explore the Worked Solutions Manual for step-by-step solutions and explanations.

From Learners to Statisticians

Examples of authentic statistical work supported by this section include:

Designing a simulation to estimate how many customers a coffee shop must serve before one orders every item on a limited promotional menu, assigning random digits to each item based on its historical order frequency (e.g., a business analyst modeling promotional campaign outcomes).
Running repeated simulation trials to estimate the probability that a medical screening test flags at least one false positive in a batch of 20 patients, using the known false-positive rate to assign outcomes to random digits (e.g., a public health researcher evaluating testing protocols).
Using a simulation with a random number generator to model how many at-bats a baseball player with a .300 batting average needs before recording three consecutive hits, and comparing the simulated average to the theoretical expectation (e.g., a sports analyst preparing a performance report).

You may use these ideas to design your own investigations or explore the Real World Statistics System.

Enrichment: Role-Based Statistical Analysis Tasks

Enrichment tasks place students in the role of a statistician working on real research problems, where they evaluate data, justify decisions, and communicate findings clearly. Each section includes multiple enrichment tasks, including one with a model response that demonstrates statistical reasoning in context, showing how evidence is evaluated, decisions are justified, and conclusions are communicated. This serves as a bridge to working with authentic datasets and independent statistical investigation within each chapter.

Available in the Interactive eBook at the end of the section (page 219) and in the Appendix of the Print Book (page 401).

Teaching with Real World Statistics?

These structured learning paths — including Enrichment tasks and Chapter Datasets — can be adapted or copied directly into Canvas, Google Classroom, Schoology, and other learning management systems to simplify lesson planning and student assignments.

Part of the Real World Statistics instructional system — bringing together print, interactive learning, videos, datasets, enrichment, worked solutions, and teacher resources.