MA272 Exam (2).pdf - MA272 Engineering Mathematics IV...

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MA272: Engineering Mathematics IV Faculty of Science, Technology & Environment School of Computing, Information & Mathematical Sciences Final Examination Semester II, 2019 Mode: Face to Face Duration of Exam: 3 hours + 10 minutes Reading Time: 10 minutes Writing Time: 3 hours Total marks: 100 INSTRUCTIONS: 1. There are 8 questions and all are compulsory. 2. There are 7 pages in this exam paper (including this cover page). 3. Write your answers in the answer booklet provided. 4. Start each question on a new page. 5. Show all necessary working. Partial marks will be awarded for partially correct answers. 6. Only non-programmable calculators are allowed. 7. Formulas and statistical table are provided on pages 5-7. 8. This exam is worth 50% of the overall mark. The minimum exam mark is 40/100.
MA272 Final Exam, Semester 2, 2019 Page 2 of 7 Question 1 Start on a new page [4+3+4=11 marks] (a) The time to failure of the cathode ray tube has the following probability density function ( ) , 0 t f t e t where 0 is a constant known as failure rate. Find the probability that the tube lives at least 100 hours. (4 marks) (b) An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates?

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