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23-Ind-B1 Reliability and Maintainability: May 2015

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

  1. Question 1 Joint Probability Function — Correlation Coefficient and Independence
  2. Question 2 Exploratory Oil Wells — Binomial, Geometric, and Large- n Binomial Probability
  3. Question 3 Class-Average Sampling Distribution — Normal Probability and a One-Observation z -Test
  4. Question 4 Proportion of Female Engineering Students — CI and Two-Proportion Tests
  5. Question 5 Marathon Training — Simple Linear Regression, ANOVA, Intervals
  6. Question 6 Class-Mark Variability at Université de Quimper — CI for Variance, Ratio of Variances, and a Mean Test
  7. Question 7 Deflection Temperature of Plastic Pipe — Variance Test, Two-Sample t -Test, Sample-Size Design
  8. Question 8 Bearing Wear vs. Viscosity and Load — Multiple Linear Regression by Matrices
  9. Question 9 Hop-Plant Yields — Bartlett's Test, One-Way ANOVA, Tukey's Test, and a Single-df Contrast
  10. Question 10 2³ Factorial Design — Design Matrix, Effects, Sums of Squares, and ANOVA

Start with Question 1 →

National Exams — May 2015 — 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 questions (10 marks); Section B: do 2 of 3 (20 marks); Section C: do 1 of 3 (20 marks) — a 5-question, 50-mark paper as printed. All ten 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 (ch. 5), binomial/geometric probability (ch. 3), normal distribution and sampling distributions (ch. 4–7), point/interval estimation (ch. 8–9), hypothesis testing incl. sample-size design (ch. 9–10), simple linear regression and ANOVA (ch. 11–13), Bartlett's and Tukey's tests, single-degree-of-freedom contrasts and 23 factorial designs (ch. 13–14). Montgomery, Peck & Vining, Introduction to Linear Regression Analysis (6th ed., Wiley) — multiple regression by matrices, confidence/prediction intervals (ch. 2–3).