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23-Ind-B1 Reliability and Maintainability: December 2014

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

  1. Question 1 Probability Density Function — Validity, Mean, and Variance
  2. Question 2 Joint Distribution — Covariance and Correlation
  3. Question 3 Binomial and Poisson Probabilities
  4. Question 4 Multiple Linear Regression — Pull Strength on Wire Length and Die Height
  5. Question 5 Simple Linear Regression — Marathon Time vs. Race Number
  6. Question 6 Sample-Size, One-Sample $t$-Test, and Confidence Intervals for IBU
  7. Question 7 Two-Sample $F$- and $t$-Tests — Marathon Shoe Comparison
  8. Question 8 Two-Factor ANOVA — Line Speed and Repair Policy on Throughput
  9. Question 9 One-Way ANOVA, Bartlett's Test, and Tukey's Test — Packing Times

Start with Question 1 →

National Exams — December 2014 — 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: four sections — Section A: do 2 of 3 questions (20 marks); Section B: do 1 of 2 (25 marks); Section C: do 1 of 2 (25 marks); Section D: do 1 of 2 (30 marks) — a 5-question, 100-mark paper as printed. All nine questions across the four sections are solved below for completeness. Page 1's own NOTES list is mis-numbered (two items both labelled "4."), transcribed as printed.

Reference texts: Montgomery & Runger, Applied Statistics and Probability for Engineers (7th ed., Wiley) — point/interval estimation (ch. 8–9), hypothesis testing (ch. 9–10), simple/multiple linear regression (ch. 11–12), single- and two-factor ANOVA (ch. 13). Montgomery, Peck & Vining, Introduction to Linear Regression Analysis (6th ed., Wiley) — multiple regression by matrices, confidence/prediction intervals (ch. 2–3).