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23-Ind-B1 Reliability and Maintainability: December 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Joint Probability Distribution — Marginals, Mean/SD, Covariance, Correlation, Independence
  2. Question 2 Beer Fermentation — Correlation, Confidence Interval, Prediction Interval
  3. Question 3 Piecewise Probability Density Function — Normalization, Mean, Variance
  4. Question 4 Aeration and Fermentation Time — Two-Sample t -Test Against a Claimed Reduction
  5. Question 5 Blood-Collection Shakers — Variance, Mean, and One-Sample Tests, CI, Anomaly Check
  6. Question 6 BMI vs. Age — Simple Linear Regression, ANOVA F -Test, Prediction Interval
  7. Question 7 Power Outages — Poisson Goodness-of-Fit Test
  8. Question 8 Frozen-Pie Fill Mass — Two-Way ANOVA with Interaction
  9. Question 9 Running-Shoe Comparison — One-Way ANOVA and Tukey's HSD
  10. Question 10 Marathon Time — Multiple Regression via $(X'X)^{-1}$
  11. Question 11 Machine-Tool Life — $2^3$ Factorial Design

Start with Question 1 →

National Exams — December 2016 — 98-Ind-B1 Applied Probability & Statistics. Three-hour, closed-book exam; one of two permitted calculators (Sharp or Casio), one 8.5″×11.0″ aid sheet (both sides), statistical tables supplied. Format: three sections — Section A: do 2 of 4 (30 marks); Section B: do 2 of 3 (30 marks); Section C: do 2 of 4 (40 marks) — a 6-question, 100-mark paper as printed. All eleven questions across the three sections are solved below for completeness.

Reference texts: Montgomery & Runger, Applied Statistics and Probability for Engineers (7th ed., Wiley) — joint distributions and covariance (ch. 5), point/interval estimation (ch. 8), hypothesis testing incl. two-sample and goodness-of-fit tests (ch. 9–10), simple linear regression (ch. 11), design and analysis of single-factor and factorial experiments (ch. 13–14). Montgomery, Peck & Vining, Introduction to Linear Regression Analysis (6th ed., Wiley) — multiple regression by matrices, confidence/prediction intervals (ch. 2–3). Montgomery, Design and Analysis of Experiments (9th ed., Wiley) — two-way factorial ANOVA and $2^k$ designs (ch. 5, 6–7).