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MidTerm exam, fall 2013, solution

MidTerm exam, fall 2013, solution - Qatar University...

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Qatar University College of Engineering First Mid-Term Exam – GENG 200 Probability and Statistics for Engineers Instructor Dr. A.Sleptchenko Date: November 6, 2013 Exam Duration: 70 minutes CLOSED BOOK, CLOSED NOTES Notes: 1 - Answer all questions 2 - Provide as many details as possible, unclear answer might lead to lower mark Question #1: A machine produces certain parts in batches of size 50. Length of each produced part is exponentially distributed with expected length 20cm. Part is considered as not satisfying quality control (failed) if its length exceeds certain limit. (a) Failure length is set to 32cm. 13 points What is the probability for a part to fail? P(fail) = P(X>32) = 1-P(X<=32) = 1-(1-exp(-1/20 * 32)) = 0.2019 (b) Assume now that probability for a part to fail is 0.2. 12 points The parts from the batch are inspected until one failed is found. What is probability to discard the batch after inspecting not more than 4 parts? Geometric distribution with p=0.2 should be used P(discard) = P(X<=4) = p + (1-p)p + (1-p) 2 p + (1-p) 3 p = 0.2 + 0.8 * 0.2 + 0.8 2 * 0.2 + 0.8 3 * 0.2 = 0.5904 (c) Assume now that probability for a part to fail is 0.2.
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