   Chapter 9.2, Problem 5CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# For the function in Example 5. find the probability that a randomly selected unit will have a lifetime of more than 2 years, but no more than 4 years.

To determine

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

2years, but no more than 4years.

Explanation

Given Information:

The probability density function of the product, f(t)=0.1e0.1t.

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(cxd)=cdf(x)dx

The anti-derivative of the exponential function can be written as,

accxdx=acecx+c1

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,

abf(x)dx=f(x)|ab=f(b)f(a)

Calculation:

Consider the function f(t)=0.1e0.1t.

The probability that x lies in 2x4 is,

P(2x4)=24f(x)dx=240

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