Assume the capacity of a pile supporting a transmission tower is modeled with a log-normal random distribution with a mean of 250 tons and a c.o.v. of 20%.
a) What is the probability that the pile will survive a load of 275 tons?
b) What will be the probability that the pile will survive a load of 275 tons if during the installation of the pile, a pile load test indicated that the pile can support at least a load of 200 tons?
c) What will be the probability that the pile can carry a load of 275 tons if the pile has survived a recent tornado during which the load transmitted to the pile is estimated to be 220 tons.