Expected Value of Insurance Payment

#1
Hi everyone, it's me again...

Here is my current struggle and what I've done.
Insurance.JPG

First, i found the expected value of the amount of damage which is ($1,410 + $284)/2 because it is uniform. This is $847. There is a $532 deductible, so the expected payment is $847-$532 = $315. The problem is this isnt a possible answer (multiple choice). The answers are $410.77, $359.43, $342.31,$393.66, and $376.54.

So since my first answer is obviously wrong I thought maybe to take the deductible into consideration I needed to change the range of the interval...which didnt feel right but I didn't know what else to do, so I said the real range was 0 to $878 (1410 minus the deductible) and then divded by two to get $439. This isn't an answer either. I feel like there are only so many ways to add and subtract and divide these numbers, and my logic makes sense to me, so I really don't know what else to attempt right now...I appreciate your help.
 

Dason

Ambassador to the humans
#2
What would a plot look like if you were to plot amount of damage on the x axis and insurance payout on the y axis?
 
#3
I'm also interested in this question. I had thought:

E(I) = 0 * P[d is in (284,532)] + (E(D) - 532) * P[d is in (532,1410)]

but this doesn't result in any of the answer choices. So, I don't know.