7. Get Me to Class on Time (20 Points) Mabel has class at 9:30am, and she doesn't have any breakfast foods at home, so she needs to go out to buy something to eat. She's considering going to Spot's, a coffee shop a couple of blocks from her home. The coffee and pastries are pretty good, but it's also usually pretty busy, and the service isn't very predictable. At this time of morning, she estimates that customers will arrive at a rate of 26 customers per hour, and the cashier takes an average of 2 minutes to serve each customer. She thinks that both inter-arrival times and service times are exponentially distributed. a) points) Calculate the utilization and coefficient of variation for arrivals and service for the checkout line at Spot's. pa CA Cs= b) (3 points) What is the expected amount of time (in minutes) that Mabel will spend waiting in line (before being served by the cashier)? Expected time waiting in line minutes c) (3 points) What is the probability that Mabel will find the cashier idle at the moment she arrives at the coffee shop? Probability of idle cashier d) (3 points) Suppose Mabel is also considering another option - a new Cuban-Swiss fusion breakfast place called The Havana Yodeler that sells breakfast wraps. This place is even more popular, but their service is a little faster and more reliable. At this time of day, Mabel thinks that customers will arrive at a rate of 30 customers per hour, and arrivals are Poisson. The average cashier service time here is 90 seconds, with a standard deviation of 30 seconds. If Mabel chooses this restaurant, what is the expected amount of time (in minutes) that she will spend waiting in line and being served by the cashier? Expected time at The Havana Yodeler minutes e) (4 points) Mabel has decided that she doesn't care which kind of food she eats - what matters most is getting to class on time. It is currently 8:30pm. She can eat either kind of food while she walks back home, but The Havana Yodeler is a little farther away. To walk there and back will take 35 minutes, while it will only take 25 minutes to walk to Spot's and back. Which place should she choose, and what is the probability that she will be late for class? Restaurant she should choose: Probability she is late for class: 1) (4 points) Do the following: Give an example of something that either restaurant might do to help Mabel's wait seem shorter, and identify the associated "psychology of waiting" principle: Identify some aspect of either of the restaurants that is an example of something that is typical of a service operation