Suppose the Length of Time, X, That It Takes a Chimpanzee

Multiple Choice

Suppose the length of time, x, that it takes a chimpanzee to solve a simple puzzle is measured by a random variable X that is exponentially distributed with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } \frac { 2 } { 3 } e ^ { - 2 x / 3 } & \text { if } x \geq 0 \\0 & \text { if } x < 0\end{array} \right.$$ where x is in minutes. Find the probability that a randomly chosen chimpanzee will take more than 12 minutes to solve the puzzle.

A) $e ^ { - 8 }$
B) $e ^ { 8 }$
C) $e ^ { 8 } - 1$
D) $e ^ { - 8 } + 1$