As in the case of the Weibull and Gamma distributions, the lognormal distribution can be modified by the introduction of a third parameter g such that the pdf is shifted to be positive only for x . g. The article cited in Exercise 4.39 suggested that a shifted lognormal distribution with shift (i.e., threshold) 5 1.0, mean value = 2.16, and standard deviation = 1.03 would be an appropriate model for the rv X = maximum-to-average depth ratio of a corrosion defect in pressurized steel.
a. What are the values of m and s for the proposed distribution?
b. What is the probability that depth ratio exceeds 2?
c. What is the median of the depth ratio distribution?
d. What is the 99th percentile of the depth ratio distribution?