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2008 3 - Stat 230 Spring 2008 STAT 230 Spring 2008 Test 3...

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Stat 230 Spring 2008 STAT 230 - Spring 2008 - Test 3 SOLUTIONS 1. [18 marks] Flaws occur in glass for widescreen TVs according to a Poisson process with an average of 2 flaws per 1000 in 2 . (a) [6 marks] List the three conditions for a general Poisson process and what they mean (in words or mathematically.) Property Name Meaning 1 Independence The number of events in non-overlapping time intervals are independent 2 Individuality Events occur one at a time OR P (2 or more events in ( t, t + Δ t )) = o t ) 3 Uniformity/ Events occur according to a constant rate λ OR Homogeneity P (1 event in ( t, t + Δ t )) = λ Δ t + o t ) (b) [3 marks] A 42-in widescreen TV needs 750 in 2 of glass. The TV is rejected at the factory if it has 2 or more flaws. Find the probability a TV is rejected. λ = 2, t = 0 . 75 so μ = λt = 1 . 5 Let X = number of flaws in 750 in 2 of glass. X Poi (1 . 5) P ( reject ) = P ( X 2) = 1 - P ( X = 0) - P ( X = 1) = 1 - e - 1 . 5 - 1 . 5 e - 1 . 5 = 0 . 4422 (c) [3 marks] What is the probability that after 30 such TVs are produced by the factory, exactly 8 are rejected?
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