Silver-coated nylon fiber is used in hospitals for its anti-static electricity properties, as well as for antibacterial and antimycotic effects. In the production of silver-coated nylon fibers, the extrusion process is interrupted from time to time by blockages occurring in the extrusion dyes. The time in hours between blockages, T, has an exponential E(λ) distribution, where λ is the rate parameter. Required:
Suppose λ = 1/5, find the probabilities that (i) a run continues for at least 5 hours. (ii) a run lasts less than 10 hours.