Explanation It is given that the rate of teeth lost per year from 1987-2001 is same as in 1987, whereas the rate of teeth lost per year from 2002–2016 is half the 1987 rate. Let X 1 is the number of teeth lost over the first 15 years follows a Poisson distribution with the mean λ 1 = 0.176 ( 15 ) = 2.64 . Let X 2 is the number of teeth lost over second 15 years follows a Poisson distribution with the mean λ 2 = 0.176 2 ( 15 ) = 0.088 ( 15 ) = 1.32 . The required probability can be obtained as follows: Pr ( X ≥ 3 ) = 1 − Pr ( X ≤ 2 ) { ∵ X = X 1 + X 2 } = 1 − { Pr ( X = 0 ) + Pr ( X = 1 ) + Pr ( X = 2 ) } Consider, Pr ( X = 0 ) = Pr ( X 1 = 0 ) × Pr ( X 2 = 0 ) = e − λ 1 × e − λ 2 = e − 2.64 × e − 1.32 = e − 3.96 = 0.0191 Pr ( X = 1 ) = Pr ( X 1 = 1 ) × Pr ( X 2 = 0 ) + Pr ( X 1 = 0 ) × Pr ( X 2 = 1 ) = ( λ 1 e − λ 1 × e − λ 2 ) + ( e − λ 1 × λ 2 e − λ 2 ) = ( 2.64 e − 2.64 × e − 1.32 ) + ( e − 2.64 × 1.32 e − 1.32 ) = ( 2.64 e − 3.96 ) + ( 1.32 e − 3.96 ) = e − 3.96 ( 2.64 + 1.32 ) = e − 3.96 ( 3.96 ) = 0

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ISBN: 9781305268920

Author: Bernard Rosner

Publisher: Cengage Learning

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Chapter 4, Problem 88P

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Find the probability that a man will need dentures under different assumptions.

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Chapter 4, Problem 87P

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