The time it takes a worker on an assembly line to finish task is exponentially distributed with a mean of 10 minutes. Please answer the following questions and list out every step used to solve each of the questions:
a. What is the probability density function for the time it takes to finish the task?
b. What is the probability that it will take a worker less than 5 minutes to finish the task?
c. What is the probability that it will take a worker between 6 and 12 minutes to finish the task?