Question

Insurance losses L in a given year have a lognormal distribution with L=e^X, where X is a normal random variable with mean 3.9 and standard deviation 0.8. If a $100 deductible and a $50 benefit are imposed, what is the probability the insurance company will pay the benefit limit given that a loss exceeds the deductible?

Answer 1

The question seems to be what is the probability that L > 150.

ln L = X

mean (ln L) = 3.9
s.d. (ln L) = 0.8

ln (150) = 5.0

find the normal distribution probability that 5.0 or more occurs when mean = 3.9 and s.d =0.8 this is same as z-score >= (5.0-3.9)/0.8

I must leave. Good luck.