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#1




SOA Sample Question #284
Hello,
I am somewhat struggling with this question: Losses incurred by a policyholder follow a normal distribution with mean 20,000 and standard deviation 4,500. The policy covers losses, subject to a deductible of 15,000. Calculate the 95th percentile of losses that exceed the deductible. The answer is 27,700. I really don't know how to start this question and the solution provided confuses me. Any help is appreciated! Thank you! 
#2




Losses exceed the deductible with probability Pr(Z > [1500020000]/4500) = 0.8665.
I would draw a picture of the normal distribution, then identify the point where losses exceed the deductible and try to graphically reason what percentile of the normal distribution equates to the 95th percentile of the claim distribution (i.e. the distribution where losses exceed the deductible). Last edited by R2Capital; 07142018 at 03:04 PM.. 
#3




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because you’re restricting your distribution to values exceeding the deductible of 15,000. So you need to solve for the value of that makes the equation hold by using the standard normal table in reverse and then solve for x. I hope that helps. 
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Tags 
deductible, loss, normal distribution, percentiles 
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