The United Airlines security station for Terminal C in Indianapolis has 3 X-ray machines. During the busy early morning hours, an average of 400 passengers per hour arrive at Terminal C (with exponential interarrival times). Each X-ray machine can handle an average of 150 passengers per hour (with exponential service times for X-ray machines). After going through security, 90% of the customers are free to go to their flight, but 10% must be "wanded." Three people are available to do the wanding. Wanding requires a mean of 4 minutes, with a standard deviation of 2 minutes.
a. How long does it take the average passenger to pass through security?
b. If there were no wanding, how long would it take the average passenger to pass through security?
c. Which would improve the situation more: adding an X-ray machine or adding an additional person to perform wanding?