Explanation Given information: f ( x ) = 2 k e − k x , 0 ≤ x ≤ 10 , k = ( ln 2 ) / 10 . Formula used: P ( a ≤ X ≤ x ) = ∫ a x f ( x ) d x . Calculation: Let X be the age of cell and the possible values of X range between 0 and 10 And the density function of X is f ( x ) = 2 k e − k x , where k = ( ln 2 ) / 10 The probability that X is at most 5 equals the probability that X is between 0 and 5 Thus, P ( 0 ≤ X ≤ 5 ) = ∫ 0 5 2 k e − k x d x = 2 ( k e − k x − k ) | 0 5 =</

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 12.2, Problem 31E

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To calculate: The probability that a cell is at most 5 days old. Where, the density function f(x)=2ke−kx , 0≤x≤10, k=(ln2)/10.

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Chapter 12.2, Problem 30E

Chapter 12.2, Problem 32E

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Calculus & Its Applications (14th Edition)

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The probability that a cell is at most 5 days old. Where, the density function f ( x ) = 2 k e − k x , 0 ≤ x ≤ 10 , k = ( ln 2 ) / 10 .

Solution Summary: The author calculates the probability that a cell is at most 5 days old.

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To calculate: The probability that a cell is at most 5 days old. Where, the density function f(x)=2ke−kx , 0≤x≤10, k=(ln2)/10.

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Chapter 12 Solutions