Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at 2300 stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 26 seconds (information Week website and the Wall Street Journal website, January 5, 2015).
a. Assume that Kroger waiting times are exponentially distributed. Show the probability density function of waiting time at Kroger.
b. What is the probability that a customer will have to wait between 15 and 30 seconds?
c. What is the probability that a customer will have to wait more than 2 minutes?