Simulation Basics
A free Statistics and Data Analysis lesson from the “Collecting Data” unit, with a worked example and practice problems including step-by-step solutions.
A simulation imitates a random process many times to estimate long-run behavior. It is useful when exact probability is difficult or when the process is easier to model than calculate directly. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Use random digits or technology to model chance
- Run repeated trials
- Estimate probability from simulated outcomes
Worked example
Problem. A student uses random digits to model whether a free throw is made, repeats 100 trials, and records the percent of makes. What is the simulation estimating?
- A simulation repeats a random process.
- Many trials estimate long-run behavior.
Answer: long-run chance of the outcome
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: A simulation models one game at a time. What is one trial?
Choices: the final average only · the population parameter · the treatment group · one run of the random process being modeled
Show solution
- A trial is one repetition of the process.
- Many trials are combined to estimate long-run behavior.
Answer: one run of the random process being modeled
2. Practice case B: Why do simulations use repeated trials?
Choices: to estimate long-run behavior more reliably · to guarantee the next outcome · to avoid defining outcomes · to prove causation
Show solution
- More repetitions reduce the noise in the estimate.
- Simulation estimates long-run patterns.
Answer: to estimate long-run behavior more reliably
3. Practice case C: A spinner lands on red 30% of the time. Which random digits could model red?
Choices: no digits represent success · digits 0, 1, and 2 represent success · only digit 0 represents success · digits 0 through 8 represent success
Show solution
- Three out of ten digits represent 30%.
- The assignment should match the probability.
Answer: digits 0, 1, and 2 represent success
4. Practice case D: A simulation counts whether at least one of two attempts works. Which result is a success?
Choices: only the first trial · the sample size · any trial meeting the event being estimated · every possible random digit
Show solution
- The success definition comes from the event of interest.
- Each trial is checked against that event.
Answer: any trial meeting the event being estimated
5. Practice case E: A useful simulation needs random rules that match:
Choices: the longest answer choice · the graph color · the sample mean only · the chance process in the question
Show solution
- The model should represent the real random process.
- Bad assumptions lead to poor estimates.
Answer: the chance process in the question
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