5. It is assumed that the distribution of a crack size a in a pipeline can be described by the following lognormal PDF 2 2 ln 0.2 1 exp 0.5 2 T a f a a where T is the age of the pipeline in years and =1.2 and =0.35 are the distribution parameters. (a) What is the probability based on this PDF that the crack size after 6 years will exceed 10 mm? (b) After 6 years the pipeline is inspected for cracks using a device whose probability of detection (POD) is given by the exponential distribution with a mean crack detection size of 6 mm. If no crack has been detected by the inspection, what is the probability that there is, in fact, a crack exceeding 10 mm? Use Excel for the calculations