Explanation Given Information: The probability density function of the product, f ( t ) = 0.1 e − 0.1 t . Formula used: The idea that lifetime of the product should be more than a years but not more than b years can be related to a variable x , which lies in the interval [ a , b ] . Then the probability that x lies in [ a , b ] , i.e. the probability that lifetime of product is more than a years and less than b years is, P ( c ≤ x ≤ d ) = ∫ c d f ( x ) d x The anti-derivative of the exponential function can be written as, ∫ a c c x d x = a c e c x + c 1 According to the fundamental theorem of calculus, if f ( x ) is a function that is continuous in [ a , d ] and f ( x ) is the anti-derivative of the function f ( x ) , Then, ∫ a b f ( x ) d x = f ( x ) | a b = f ( b ) − f ( a ) Calculation: Consider the function f ( t ) = 0.1 e − 0.1 t . The probability that x lies in 2 ≤ x ≤ 4 is, P ( 2 ≤ x ≤ 4 ) = ∫ 2 4 f ( x ) d x = ∫ 2 4 0

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 9.2, Problem 5CP

To determine

To calculate: The probability that the life time of randomly selected unit will have more than

2 years, but no more than 4 years.

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Chapter 9.2, Problem 4CP

Chapter 9.2, Problem 1SWU

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Chapter 9 Solutions

Calculus: An Applied Approach (Providence College: MTH 109)

Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CP Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1SWU Ch. 9.1 - Prob. 2SWU Ch. 9.1 - Prob. 3SWU Ch. 9.1 - Prob. 4SWU

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The probability that the life time of randomly selected unit will have more than 2 years , but no more than 4 years .

Solution Summary: The author explains how the probability of life time of a randomly selected unit is 0.148 based on the fundamental theorem of calculus.

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To calculate: The probability that the life time of randomly selected unit will have more than

2 years, but no more than 4 years.

Want to see the full answer?

Chapter 9 Solutions

The probability that the life time of randomly selected unit will have more than 2 years , but no more than 4 years .

Solution Summary: The author explains how the probability of life time of a randomly selected unit is 0.148 based on the fundamental theorem of calculus.

Concept explainers

Videos

To calculate: The probability that the life time of randomly selected unit will have more than 2 years, but no more than 4 years.

Want to see the full answer?

Chapter 9 Solutions

To calculate: The probability that the life time of randomly selected unit will have more than

2 years, but no more than 4 years.