Question

For a certain health insurance policy, losses are uniformly distributed on the interval [0, 450]. The policy has a deductible of d and the expected value of the unreimbursed portion of a loss is 56. Calculate a (A) 60 (B) 87 (C) 112 (D) 169 (E) 224

Answer 1

Here the losses $\fn_jvn X$ are uniformly distributed. $\fn_jvn X\sim U\left ( 0,450 \right )$ . The expected value of the reimbursed loss is

$\fn_jvn E\left ( X \right )-d=56$. Or we can write,

$\fn_jvn d=E(X)-56\\ d=\frac{450}{2}-56\\ {\color{Blue} d=169}$

Correct choice is (D).

From the given table, the probability that the model year of the automobile involved in accident is

$\fn_jvn \frac{0.16\times 0.05}{0.16\times 0.05+0.18\times 0.02+0.2\times 0.03+0.46\times 0.04}=0.2222$

Correct choice is (A).