Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at2,300 stores.Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time tojust24seconds.(a)Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket.

f(x) =

,	x0
,	elsewhere

(b)What is the probability that a customer will have to wait between30and45seconds? (Round your answer to four decimal places.) (c)What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)