An article in Applied Mathematics and Computation [“Confidence Intervals for Steady State Availability of a System with Exponential Operating Time and Lognormal Repair Time” (2003, Vol.137(2), pp. 499-509)] considered the long-run availability of a system with an assumed lognormal distribution for repair time. In a given example, repair time follows a lognormal distribution with θ = ω = 1. Determine the following:

(a) Probability that repair time is more than five time units

(b) Conditional probability that a repair time is less than eight time units given that it is more than five time units

(c) Mean and variance of repair time