Explanation Given information: X : Lifetime (in hours) of a certain type of flashlight battery. The probability density function is given by f ( x ) = 1 20 , 30 ≤ x ≤ 50 and Pr ( X ≥ 35 ) . Formula used: 1) Power rule of integration : ∫ x n d x = x n + 1 n + 1 , n ≠ − 1 2) Area under the graph of f ( x ) is given by a definite integral P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x Calculation: The probability that X lies between the endpoints of the given interval [ a , b ] is given by the area under the graph of a function f ( x ) from a to b . So, area under the graph of f ( x ) is given by a definite integral P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x At least 35 hours is written in symbolic form as X ≥ 35 As the function f ( x ) is defined for interval 30 ≤ x ≤ 50 , Pr ( X ≥ 35 ) = Pr ( 35 ≤ X ≤ 50 )

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 19E

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To calculate: The probability, Pr ( X≥ 35) with the density function as f(x)= 120, 30≤x≤50.

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Chapter 12.2, Problem 18E

Chapter 12.2, Problem 20E

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Chapter 12 Solutions

Calculus & Its Applications (14th Edition)

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The probability, Pr ( X ≥ 35 ) with the density function as f ( x ) = 1 20 , 30 ≤ x ≤ 50 .

Solution Summary: The author calculates the probability that X lies between the endpoints of the given interval [a,b].

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To calculate: The probability, Pr ( X≥ 35) with the density function as f(x)= 120, 30≤x≤50.

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Chapter 12 Solutions

The probability, Pr ( X ≥ ​ 35 ) with the density function as f ( x ) = 1 20 , 30 ≤ x ≤ 50 .

Solution Summary: The author calculates the probability that X lies between the endpoints of the given interval [a,b].

Concept explainers

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To calculate: The probability, Pr ( X≥​ 35) with the density function as f(x)= 120, 30≤x≤50.

Want to see the full answer?

Chapter 12 Solutions

The probability, Pr ( X ≥ 35 ) with the density function as f ( x ) = 1 20 , 30 ≤ x ≤ 50 .

To calculate: The probability, Pr ( X≥ 35) with the density function as f(x)= 120, 30≤x≤50.