A single public health worker is inoculating children against measles at a local clinic. An average of 8 children per hour is expected to arrive according to a Poisson distribution. He serves the children at a rate of 10 per hour. Assume that the service-time distribution is approximately exponential.

(a) For the ‘inoculation system’, find:

i) the utilization of the health worker.

ii) the average time spent by a child in the system.

iii) the average number of children in the system.

iv) the average number of children in line.

v) the average number of children in the system if another health worker is added to the system who has the same service rate as the existing one.

(b) At what rate must children be served by the single public health worker so that the average time that a child spends in the system can be reduced by 50%?