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23-Ind-B1 Reliability and Maintainability: December 2018

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

  1. Question 1 Normal-Distribution Assembly Times
  2. Question 2 Two-Sample $t$-Test for a Process Design Change
  3. Question 3 Comparing Two Shipping Companies — Two-Sample $t$-Test
  4. Question 4 Continuous-Random-Variable PDF — Validity, Mean, Variance
  5. Question 5 Simple Linear Regression — Age vs. BMI
  6. Question 6 Comparing Two Marathon Routes — Variance and Mean Tests
  7. Question 7 Edison Motors — Bartlett's Test, One-Way ANOVA, Tukey's Test
  8. Question 8 Multiple Linear Regression by Matrices
  9. Question 9 $2^2$ Factorial Design — Hospital Patient-Flow Screening Experiment

Start with Question 1 →

National Exams — December 2018 — 17-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 (20 marks); Section B: do 2 of 3 (40 marks); Section C: do 1 of 2 (20 marks) — a 9-question, printed-total-80-mark paper as actually structured (the front page's own summary line states “Exam: 5 Questions. Total marks: 100”, but 20+40+20=80 by the section instructions and per-question mark values printed beside each question — the front page's 100 is internally inconsistent with its own section table; the 80-mark reading is used throughout, consistent with the section-by-section split printed on pages 2, 4 and 6). All nine questions across the three sections are solved below for completeness.

Reference texts: Montgomery & Runger, Applied Statistics and Probability for Engineers (7th ed., Wiley) — normal distribution and sums of normals (ch. 4–5), point/interval estimation (ch. 8), two-sample hypothesis testing (ch. 9–10), simple linear regression (ch. 11), single-factor ANOVA and multiple comparisons (ch. 13). 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) — Bartlett's test, $2^k$ factorial designs (ch. 3, 6).