The Life Span of Car Stereos Manufactured by a Certain $$f ( x ) = \left\{ \begin{array} { l l } 0.2 e ^ { - 0.2 x } & \text { if } x \geq 0 \\0 & \text { if } x < 0\end{array} \right.$$

Short Answer

The life span of car stereos manufactured by a certain company is measured by a random variable X that is exponentially distributed with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } 0.2 e ^ { - 0.2 x } & \text { if } x \geq 0 \\0 & \text { if } x < 0\end{array} \right.$$ where x is the life span in years of a randomly selected stereo. What is the probability that the life span of a randomly selected stereo is between 1 and 15 years? Round to the nearest hundredth.