Answer Key — Probabilistic and statistical models
Mathematical modeling
Do not share with students before practice tests.
Worksheets — Sets 1–10
| Set | Guidance | | --- | --- | | Set 1 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 2 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 3 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 4 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 5 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 6 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 7 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 8 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 9 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 10 | Probabilistic and statistical models — verify written work and accept reasonable drawings. |
Worksheets — Sets 11–20
| Set | Guidance | | --- | --- | | Set 11 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 12 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 13 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 14 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 15 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 16 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 17 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 18 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 19 | Probabilistic and statistical models — verify written work and accept reasonable drawings. | | Set 20 | Probabilistic and statistical models — verify written work and accept reasonable drawings. |
Review tiers 1–10
- Checklists are parent-judged.
- Written items: verify against practice set patterns.
- Standard text: Elementary probability models for uncertainty Monte Carlo simulation (introduction) Markov chains for simple stochastic models Regression and calibration of model parameters Confidence intervals and prediction in applied settings
Practice test scoring
| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |
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