SOA Exam P Question 129 | Conditional Joint Distribution

The cumulative distribution function for health care costs experienced by a policyholder
is modeled by the function
F(x)=1-e^-(x/100) for x greater than 0
The policy has a deductible of 20. An insurer reimburses the policyholder for 100% of
health care costs between 20 and 120. Health care costs above 120 are reimbursed at
50%.
Let G be the cumulative distribution function of reimbursements given that the
reimbursement is positive.
Calculate G(115).
(A) 0.683
(B) 0.727
(C) 0.741
(D) 0.757
(E) 0.777

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