For a certain health insurance policy, losses are uniformly distributed on the interval [0, b]. The...

For a certain health insurance policy, losses are uniformly distributed on the interval [0, b]. The policy has a deductible of 180 and the expected value of the un-reimbursed portion of a loss is 144.

Calculate b. (A) 236 (B) 288 (C) 388 (D) 450 (E) 468

Expert Solution

expected value of the un-reimbursed portion of a loss = xf(x) dx+180*- f(x)dx =(x/b) dx +180* (1/b) dx

=x²/(2b) |¹⁸⁰₀ +(x/b) |^b₁₈₀=16200/b +(180-32400/b) =180-16200/b =144

16200/b =36

b=16200/36=450

option D is correct

orchestra answered 2 years ago

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