The next question is On average, does it take more or less time for a passenger to go through the whole process now? Please show calculations to justify your answer.Please explain each step! It was a bit hard for me to learn in class :)

2. We model the security process at an airport as follows: A single queue for all random screenings departure C p 1 random screener 1-P A single queue for all departure passengers Security checkpoint 4 lanes Let's examine the process during a typical time period. Arrival to the checkpoint follows a Poisson distribution and averages 3 arrivals per minute. Four lanes are open during this time period. The time it takes to go through each lane of the security checkpoint is exponentially distributed with an average of 1 minute. After each person has gone through the checkpoint, s/he has a 20% chance (p=20% in the picture) of being selected for random screening. There is only one random screener (the security officer who does the random screenings). Moreover, the selection of passengers for screening is completely random and independent of whether the random screener is busy (i.e. it's possible for someone to be selected even when the screener is busy). The random screening time is again assumed to be exponential with an average of 1/2 minute. In answering the following questions, you can safely assume that the checkpoint and the random screening are two independent queueing systems. Moreover, we know that the arrival to the screener, which is a random subset of a Poisson process, is again a Poisson process, albeit with a smaller rate. (a) What is the average time for a passenger to go through the whole process The Transportation Security Administration (TSA) announced changes to the airport security procedure and updates to the prohibited items list. In particular, small tools and scissors will be permitted onboard aircraft. This will clearly speed up the security process. As a result, we expect that the checkpoint time will be reduced to an average of 2/3 minute (but still exponential). On the other hand, TSA also announced that more random screenings will be conducted. Assume that the probability p will increase from 20% to 30%