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04-BS-2: December 2015

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

  1. Question 1 Tire Life — Normal Distribution
  2. Question 2 Binomial and Poisson Approximations
  3. Question 3 Poisson and Hypergeometric Distributions
  4. Question 4 Continuous Probability Density Function
  5. Question 5 Confidence Intervals and Hypothesis Tests on Young's Modulus
  6. Question 6 Large-Sample Tests — Mean, Variance, and Proportion
  7. Question 7 Two-Sample Tests — Comparing Two Processes
  8. Question 8 Correlation and Simple Linear Regression

Start with Question 1 →

National Examinations, December 2015 — 04-BS-2 Probability and Statistics (2 hours, closed book except one hand-written information sheet and an approved calculator). Statistical tables of the Normal, t, chi-square and F distributions are supplied with the exam. The rubric states "Any 5 questions constitute a complete paper"; every question is answered.

Reference texts: Walpole, Myers, Myers & Ye, Probability & Statistics for Engineers and Scientists, 9th ed. (Pearson) — used throughout for normal/binomial/Poisson/hypergeometric probability, confidence intervals, hypothesis tests, and simple linear regression.

Check — source defect in Question 4. As literally printed, K/y cannot integrate to a finite value over (1, ∞), so the density as given is not valid. This solution reconstructs the intended density as f(y) = 1/y² for y > 1 — the unique minimal correction (recovering one dropped exponent) that makes the function integrate to 1 on the stated domain, and it is the standard "infinite mean" example from this course's own textbook (Walpole). This choice is disclosed here rather than presented as certain.