Chapter 13.3, Problem 2YT

YOUR TURN Repeat Example 2 for a flashlight battery with a useful life given by the probability density function $f\left(t\right)=\frac{1}{25}{e}^{-t/25}\text{ for }t\ge 0$.

EXAMPLE 2 Flashlight Battery

Suppose the useful life (in hours) of a flashlight battery is the random variable T, with probability density function given by the exponential distribution

$f\left(t\right)=\frac{1}{20}{e}^{-t/20}\text{ for }t\ge 0.$

(a) Find the probability that a particular battery, selected at random, has a useful life of less than 100 hours.

(b) Find the expected value and standard deviation of the distribution.

(c) What is the probability that a battery will last longer than 40 hours?