17. *A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and 10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5. What is the expected amount paid to the company under this policy during a one-year period? (7,231)

6. Consider a coffee shop that uses a single-server queue. The inter-arrival time is exponentially distributed with a mean of 10 minutes and the service time is also exponentially distributed with a mean of 8 minutes. Calculate the: (i) mean wait in the queue (2) (ii) mean number in the queue (2) (iii) the mean wait in the system (2) (iv) mean number in the system (2) (v) proportion of time the server is idle. (2) [10] 7. The arrival of customers at a bank follows a Poisson distribution with a mean arrival rate of 10 customers per hour. The service time at the bank follows an exponential distribution with a mean service rate of 6 minutes per customer. Calculate the average number of customers in the system (including those being served and waiting) and the average time a customer spends in the system. How is the system performing? [8]

5.6. The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 8 minutes to land and clear the runway (exponentially distributed). Planes arrive at the airport at the rate of 5 per hour (Poisson distributed). a. Determine the average number of planes that will stack up waiting to land. b. Find the average time a plane must wait in line before it can land. c. Calculate the average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land. d. The FAA has a rule that an air traffic controller can, on the average, land planes a maximum of 45 minutes out of every hour.

Officer Thompson of the Bay Ridge Police Department works the graveyard shift. He averages 4.5calls per shift from this dispatcher. Assume the number of calls follows a Poisson distribution. Find theprobability that Officer Thompson get fewer than 2 calls in a shift.