(b) A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8 –hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find i. The probability of there being no customer in the system (4 Marks) ii. The average number of customers in the system (3 Marks) iii. Average number of customers waiting to be served (2 Marks) iv. Average time a customer spends in the system (2 Marks) v. Average waiting time for a customer

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26-06-2024
Mathematics

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(b) A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8 –hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find i. The probability of there being no customer in the system (4 Marks) ii. The average number of customers in the system (3 Marks) iii. Average number of customers waiting to be served (2 Marks) iv. Average time a customer spends in the system (2 Marks) v. Average waiting time for a customer

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