The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 17 minutes.

(a)What is the probability density function for the time it takes to change the oil?

f(x) = for x 0

(b)What is the probability that it will take a mechanic less than 18 minutes to change the oil? (Round your answer to four decimal places.)

(c)What is the probability that it will take a mechanic between 15 and 17 minutes to change the oil? (Round your answer to four decimal places.)

(d)What is the variance of the time it takes to change the oil?