Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 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 to just 26 seconds.

(a)

Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket.

f(x) =

,	x 0
,	elsewhere

(b)

What is the probability that a customer will have to wait between 30 and 45 seconds? (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.)