Chapter 13.2, Problem 68E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Product life** The useful life of a car battery

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

Explanation

**Given Information:**

The probability density function

**Formula used:**

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

The value of the integral *a* is constant and *x* is variable.

**Calculation:**

Consider the probability density function

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

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

Consider the expression

Differentiate with respect to *t*.

Thus,

Simplify the integral using

**(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

**(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

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