3. The employee performing final assembly of electric generators at Electro can produce generators at the Poisson rate of 10 generators per hour. The generators are then conveyed on a belt to an employee in the inspection department for final testing. The belt can hold a maximum of 7 generators (plus the final assembly department has an area to work on one generator). An electric sensor will automatically stop the conveyor once it is full, preventing the final assembly department from assembling more units until a space becomes available. The time to inspect generators is exponential with a mean of 15 minutes.

a) What is the probability that the final assembly department will stop production?

b) What is the average number of generators on the conveyor belt?