A student has submitted a concrete cylinder to the "strength contest" in Engineering Open House. Suppose the strength of her concrete cylinder is lognormally distributed with mean and standard deviation of 100 kips and 20 kips, respectively. She was schedules to be the last contestant for load testing. Immediately prior to her cylinder being tested, the two highest strengths in the contest thus far are 120 and 80 kips.
(a) What is the probability that she will be the first place winner?
(b) What is the probability that she will be the second-place winner?
(c) Suppose her cylinder is being tested, and it has not shown any sign of distress at a load of110 kips. What is the probability that she will win the first place?