Question: Observations gathered by the plant engineer of a large manufacturing concern revealed that the number of stoppages of the production line follows the Poisson law with an average of 3.2 stoppages per 300 hours of operation.

(a) Compute the probability that more than one but fewer than five stoppages occur in 300 hours of operation.

(b) Compute the probability that at most 3 stoppages occur in 600 hours of operation.

(c) Compute the probability that exactly 3 stoppages occur in a period of 300 hours of operation followed by 4 stoppages in a subsequent, non-overlapping, period of 300 hours of operation.

(d) Compute the probability that more than 50 but fewer that 70 stoppages occur in 6,000 hours of operation.