Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Examinations, December 2014 — 04-BS-2, Probability and Statistics (2 hours; closed book except one hand-written information sheet and an approved calculator; any 5 of 8 questions constitute a complete paper — all 8 are solved below as a complete study resource).
Reference texts: Walpole, Myers, Myers & Ye, Probability & Statistics for Engineers and Scientists, 9th ed.