(Answered) : Q59 Villa Hotel Enough Space Six Taxicabs Load Passengers Line Wait Guests Entrance Cabs A Q30676872

Q59

The Villa Hotel has enough space for six taxicabs to loadpassengers, line up, and wait for guests at its entrance. Cabsarrive at the hotel every 10 minutes and if a taxi drives by thehotel and the line is full it must drive on. Hotel guests requiretaxis every five minutes on average and then it takes a cab driveran average of 3.5 minutes to load passengers and luggage and leavethe hotel (exponentially distributed). [2 Marks] (a) What is theaverage timing a cab must wait for a fare? (b) What is theprobability that the line will be full when a cab drives