The time it takes a ski patroller to respond to an accident call has an exponential distribution with an average response time of 5 minutes. As part of ski patrollers' commitment to prevent an accident related fatalities, the ski patrollers' association has committed that ski patrollers would respond within 5 minutes.
a. What is the probability that it will take a ski patroller between 2 minutes to 4 minutes to respond to an accident call?
b. What is the probability that the ski patrollers' association fails to honor its commitment?
c. What is the probability that a ski patroller takes at most 2 minutes to respond to an accident call?