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Jesse Atkinson, the only mechanic at the service center of New York Taxicab Company (NYTC). provides automotive services for NYTC taxis. Jesse services taxicabs at an average rate of five per hour, with service times being negatively exponentially distributed. Taxicabs arrive at the NYTC service center independently and randomly following a Poisson distribution throughout the day at a rate of one every 15 minutes. Taxis are serviced on a FCFS basis. NYTC is the city's largest taxi company and the number of NYTC taxis is large enough to be considered infinite for probability purposes). a) What percentage of time is the mechanic busy? b) What is the average number of taxis waiting in line at the NYTC service center? c) On average, how long will an NYTC taxi spend at the service center, including the times waiting in line and being serviced? d) What the probability that three or more taxis are at the NYTC service center? e) Suppose now that the arrival of taxis for servicing at NYTC's service center has significantly increased to 11 taxicabs per hour. Two additional mechanics have been hired at the NYTC service center, each having the same service rate of 5 taxis per hour. e-1) How many taxis, on average, are at the service center, including those waiting in line and being serviced? e-2) If the NYTC service center were to hire a fourth mechanic, with all four mechanics expected to have identical service rates of 5 taxis per hour, how many taxis will be waiting in line to be served with these four identical mechanics? It costs NYTC $20.00 per hour that a taxi is at the service center, and a mechanic's wage is $30.00 per hour. Should the NYTC service center hire a fourth mechanic instead of having only the current three mechanics? (Must show your work. A simple YES/NO answer will receive zero marks!)