Losses covered by an insurance policy are modeled by a uniform distribution on the interval [0, 1000]. An insurance company reimburses losses in excess of a deductible of 250.

Calculate the difference between the median and the 20th percentile of the insurance company reimbursement, over all losses.

• 225
• 250
• 300
• 375
• 500

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

Before applying the deductible, the median is 500 and the 20th percentile is 200. After applying the deductible, the median payment is 500 – 250 = 250 and the 20th percentile is max(0, 200 –250) = 0. The difference is 250.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.