a. Explanation Given info: The parameter, λ = 6.3 . Calculation: The probability P ( X = 7 ) The Poisson distribution formula is, P ( X = x ) = e − λ λ x x ! Where, x is the number occurrences of the event in a given interval, λ is the mean occurrences of the event, and e is a constant Substitute x as 7, λ as 6.3 and e as 2.71828 P ( X = 7 ) = e − 6.3 6.3 7 7 ! = ( 2.71828 ) − 6.3 × ( 6.3 ) 7 7 × 6 × 5 × 4 × 3 × 2 × 1 = 0.14351 Rounding off to three decimal places,the probability P ( X = 7 ) = 0.144 . The probability P ( 5 ≤ X ≤ 8 ) The required probability is the sum of the probabilities P ( X = 5 ) , P ( X = 6 ) , P ( X = 7 ) and P ( X = 8 ) . The Poisson distribution formula is, P ( X = x ) = e − λ λ x x ! Substitute λ as 6.3 and e as 2.71828 P ( 5 ≤ X ≤ 8 ) = [ P ( X = 5 ) + P ( X = 6 ) + P ( X = 7 ) + P ( X = 8 ) ] = [ e − 6.3 6.3 5 5 ! + e − 6.3 6.3 6 6 ! + e − 6.3 6.3 7 7 ! + e − 6.3 6.3 8 8 ! ] = [ ( 2.71828 ) − 6.3 × ( 6.3 5 ) 5 × 4 × 3 × 2 × 1 + ( 2.71828 ) − 6.3 × ( 6.3 6 ) 6 × 5 × 4 × 3 × 2 × 1 + ( 2 b. To determine To find: The mean, standard deviation of the random variable X.

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ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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Chapter 5.4, Problem 98E

To determine

The probabilities P(X=7),P(5≤X≤8),P(X≥2) and to round off the answers to three decimal places.

To determine

To find: The mean, standard deviation of the random variable X.

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Chapter 5.4, Problem 97E

Chapter 5.4, Problem 99E

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The probabilities P ( X = 7 ) , P ( 5 ≤ X ≤ 8 ) , P ( X ≥ 2 ) and to round off the answers to three decimal places.

Solution Summary: The author explains the Poisson distribution formula, where x is the number occurrences of the event in a given interval, lambd