Quiz3Solutions - X represent the number of containers in a...

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STA 3032 - Section 7661 - Fall 2011 - Quiz 3 Please write your name and UF ID number and answer all questions on the paper that is provided to you. Do not write on the quiz sheet. Anything you write on the quiz sheet will not be graded. Show all work. Discrete Uniform f ( x ; a,b ) = 1 N ,x ∈ { a,a + 1 ,...,b - 1 ,b } where N = b - a + 1 Bernoulli f ( x ; p ) = p x (1 - p ) 1 - x ,x ∈ { 0 , 1 } Binomial f ( x ; n,p ) = ( n x ) p x (1 - p ) n - x ,x ∈ { 0 , 1 ,...,n } Poisson f ( x ; λ ) = e - λ λ x x ! ,x ∈ { 0 , 1 , 2 ,... } Geometric f ( x ; p ) = p (1 - p ) x - 1 ,x ∈ { 1 , 2 ,... } Negative Binomial f ( x ; r,p ) = ( x - 1 r - 1 ) p r (1 - p ) x - r ,x ∈ { r,r + 1 ,... } 1. In a test of weld strength, 80% of tests result in a fracture in the weld, while the other 20% result in a fracture in the beam. Let X denote the number of tests up to and including the third beam fracture. Find P ( X = 8) . (7 points) Answer: X NegBin ( r = 3 ,p = 0 . 2). P ( X = 8) = ( 8 - 1 3 - 1 ) (0 . 2) 3 (1 - 0 . 2) 8 - 3 = ··· = 0 . 05505024 2. Suppose that 0.03% of plastic containers manufactured by a certain process have small holes that render them unfit for use. Let
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Unformatted text preview: X represent the number of containers in a random sample of 10,000 that have this defect. Find P ( X = 3). (6 points) Answer: X Poisson ( = 10000 * . 0003) P ( X = 3) = e-(10000 * . 0003)(10000 * . 0003) 3 3! = 0 . 2240418 3. In testing a certain kind of truck tire over a rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, nd the probability that from 3 to 5 have blowouts; (7 points) Answer: X Bin ( n = 15 ,p = 0 . 25) P (3 X 5) = P ( X = 3) + P ( X = 4) + P ( X = 5) = 15 3 (0 . 25) 3 (1-. 25) 12 + 15 4 (0 . 25) 4 (1-. 25) 11 + 15 5 (0 . 25) 5 (1-. 25) 10 = 0 . 2251991 + 0 . 2251991 + 0 . 1651460 = 0 . 6155441 . 2...
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Quiz3Solutions - X represent the number of containers in a...

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