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

Question

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.

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The Answer of 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.

The Life Span of Car Stereos Manufactured by a Certain f(x)={0.2e−0.2x if x≥00 if x<0f ( 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.f(x)={0.2e−0.2x0​ if x≥0 if x<0​

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