A small software company hired a Customer Service Representative (CSR) to handle technical support questions. It is estimated that during peak periods, the CSR would receive four alls per hour and follow a Poisson distribution. Based on past experience, a CSR can handle an average of five (5) calls per hour during the same time period and follow an exponential distribution.
a. Determine the probability that the CSR is idle.
b. Determine the probability that three customers are in the system, waiting or being served.
c. Determine the average number of callers waiting for service (on hold).
d. Determine the average number of callers in the system.
e. Determine the average time a caller spends waiting for service (on hold).
f. Determine the average time a caller spends in the system (waiting time plus service time).
g. Determine the probability that an arriving call will have to wait for service.

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The Answer of A small software company hired a Customer Service Representative (CSR) to handle technical support questions. It is estimated that during peak periods, the CSR would receive four alls per hour and follow a Poisson distribution. Based on past experience, a CSR can handle an average of five (5) calls per hour during the same time period and follow an exponential distribution.
a. Determine the probability that the CSR is idle.
b. Determine the probability that three customers are in the system, waiting or being served.
c. Determine the average number of callers waiting for service (on hold).
d. Determine the average number of callers in the system.
e. Determine the average time a caller spends waiting for service (on hold).
f. Determine the average time a caller spends in the system (waiting time plus service time).
g. Determine the probability that an arriving call will have to wait for service.

A Small Software Company Hired a Customer Service Representative (CSR)