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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Product life The useful life of a car battery t (in years) is given by the probability density function

f ( t )   =   0.2 e 0.2 t ,     t 0

Find the probability that a battery chosen at random lasts

(a) 2 years or less. (b) between 4 and 6 years.

(c) more than 4 years given that it lasts less than 6 years.

(a)

To determine

To calculate: The probability that a battery chosen at random lasts 2 years or less if the useful life of a car battery where time t in years is given by the probability density function f(t)=0.2e0.2t, t0 .

Explanation

Given Information:

The probability density function f(t)=0.2e0.2t.

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral eaxdx=eaxa where a is constant and x is variable.

Calculation:

Consider the probability density function f(t)=0.2e0.2t.

Since, a battery chosen at random lasts 2 years or less probability is the definite integral from 0 to 2.

Thus, probability that the battery takes 3 years or less is the integral 02(0.2e0.2t)dt.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Consider the expression (0.2t).

Differentiate with respect to t.

d(0.2t)dt=0.2d(0.2t)=0.2dt

Thus, d(0.2t)=0.2dt.

Simplify the integral using d(0.2t)=0.2dt.

02(0

(b)

To determine

To calculate: The probability that a battery chosen at random lasts between 4 and 6 years if the useful life of a car battery where time t in years is given by the probability density function f(t)=0.2e0.2t, t0 .

(c)

To determine

To calculate: The probability that a battery chosen at random lasts more than 4 years given that it lasts less than 6 years if the useful life of a car battery where time t in years is given by the probability density function f(t)=0.2e0.2t, t0 .

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Chapter 13 Solutions

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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