I am not for sure if it is that I am misunderstanding the problem statement here or that the problem is just poorly stated -


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An insurance policy reimburses dental expense, X, up to a maximum benefit of 250. The
probability density function for X is

f(x) =   ce^−0.004x for x >= 0,
           0 otherwise,

where c is a constant. Calculate the median benefit for this policy.
(A) 161 (B) 165 (C) 173 (D) 182 (E) 250


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My question is -

When the question states the maximum benefit is 250 units, shouldnt the benefit density function be the value for f(x) only until 250 and 0 beyond?

I ask as this changes the answer. With benefit density limited to 250 (as the question states), my median calculation is around 94. Withouth the 250 unit limitation, the median works out to be 173 (Option - C) which matches the solution in my textbook.

Why is the solution not accounting for 250 unit limit? Any ideas?

THANKS IN ADVANCE BOBBYM!!!

- G