The Time Interval Between the Arrivals of Successive Trains at a Certain

Multiple Choice

The time interval between the arrivals of successive trains at a certain station is measured by a random variable X with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } 0.35 e ^ { - 0.35 x } & \text { for } x \geq 0 \\0 & \text { for } x < 0\end{array} \right.$$ where x is the time (in minutes) between the arrivals of a randomly selected pair of successive trains. What is the probability that two successive trains selected at random will arrive within 4 minutes of one another? Round to the nearest hundredth.

A) 0.25
B) 0.56
C) 0.38
D) 0.75