Explanation 1
Estimated time: 44 minutes.
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Lesson 9 of 11
Build a transparent bounded scenario from minimum, most-likely, and maximum values.
Lesson 7.8
Build a transparent bounded scenario from minimum, most-likely, and maximum values. Business question: Estimate the mean.
Explanation 1
Estimated time: 44 minutes.
Explanation 2
Prior knowledge: complements, algebra, probability notation, and careful unit conversion.
Explanation 3
Calculate and simulate a triangular scenario from valid parameters.
Explanation 4
Explain when triangular assumptions are more transparent than uniform or normal assumptions.
Explanation 5
Interpret a optional: triangular distribution for what-if analysis result in business context with consistent units.
Explanation 6
Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
Core explanation
Minimum a: The lowest credible scenario value. Mode b: The single most-likely scenario value. Maximum c: The highest credible scenario value.
Explanation 1
A probability is an area over an event, not an unexplained curve height.
Explanation 2
State the random variable, support, units, and assumptions before using a formula.
Explanation 3
Connect every numerical answer to a practical decision and limitation.
Terminology
The lowest credible scenario value.
Earliest completion.
The single most-likely scenario value.
Most likely duration.
The highest credible scenario value.
Latest completion.
Notation and formulas
mu=(a+b+c)/3; Var=(a^2+b^2+c^2-ab-ac-bc)/18
Symbols: a is the minimum, b is the mode, and c is the maximum with a<=b<=c. All three parameters and the mean use the scenario variable's units. Use: apply this relationship only after defining the model and event. Plain-text equivalent: mu=(a+b+c)/3; Var=(a^2+b^2+c^2-ab-ac-bc)/18.
Worked example
Scenario
Experts give 20, 45, and 90 days.
R check
The custom rtri() function generates scenario values; simulation proportions estimate probabilities and must be checked for Monte Carlo error.The triangular mean is 51.67 days.
Guided practice
Scenario
Low, likely, high demand are 1,000, 1,600, 2,800.
R check
The custom rtri() function generates scenario values; simulation proportions estimate probabilities and must be checked for Monte Carlo error.The long upper range creates right skew.
Interactive Mission
Interval probability
0.3983
Interpretation: Parameters (20, 45, 90) are scenario judgments; test how the decision changes when they move.
Independent practice
Scenario
Only bounds 20 and 90 are defensible.
R check
The custom rtri() function generates scenario values; simulation proportions estimate probabilities and must be checked for Monte Carlo error.No; use a transparent range model or collect evidence.
Independent practice
Scenario
Stakeholders revise the high duration from 90 to 120.
R check
The custom rtri() function generates scenario values; simulation proportions estimate probabilities and must be checked for Monte Carlo error.The mean and upper-tail risk rise; document the elicitation change.
R connection
The custom rtri() function generates scenario values; simulation proportions estimate probabilities and must be checked for Monte Carlo error. Run the original starter code, inspect every printed intermediate value, then modify one assumption and explain the decision impact. Keep code, formulas, function names, column names, and numerical output left-to-right.
Live R Lab
Use bounded minimum, most-likely, and maximum values for transparent scenarios.
Ready to run
Common mistakes and model safeguard
Triangular inputs are scenario judgments unless supported by data; sensitivity analysis is required. Also check tail direction, parameter units, support, and whether software returned density, cumulative probability, a quantile, or generated data.
Originality and provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Reflection
Name the assumption, the evidence you would seek, and how the recommendation could change.
Lesson summary
Build a transparent bounded scenario from minimum, most-likely, and maximum values. The reliable workflow is: define X and units, justify the model, state the event, calculate, verify, interpret, and disclose limitations.
Explanation 1
Minimum a: The lowest credible scenario value.
Explanation 2
Mode b: The single most-likely scenario value.
Explanation 3
Maximum c: The highest credible scenario value.
Assistant
Coach me through Optional: Triangular Distribution for What-if Analysis one decision at a time. Before submission, give hints only and do not reveal quiz answers or complete my recommendation.
Resource
Download an original, accessible STATLAB Academy reference and practice sheet.
DownloadExit check
Use the short exit check after instruction and practice. Reach 70% to complete this lesson; explanations appear only after submission.
Checkpoint
Question 1 of 4. Answered 0/4. Passing score: 70%.