Answer:
35.35%
Step-by-step explanation:
If there were no deductibles, the expected claim payment would be:
[tex]E(X) = \frac{10,000 +1,000}{2} \\E(X) =\$5,500[/tex]
If the collision insurance claim is under $2,000, then the insurer would not pay anything, but if X > $2,000, then the insurer would pay X - $2,000. The new expected value is:
[tex]E_2(X)=\frac{2,000-1,000}{10,000-1,000} *0+\frac{10,000-2,000}{10,000-1,000}*\frac{(2,000-2,000)+(10,000-2,000)}{2} \\E_2(X)=\frac{8}{9}*\frac{0+8,000}{2}\\ E_2(X)=\$3,555.56[/tex]
The percentage reduction on the claim payment is:
[tex]P=(1-\frac{E_2(X)}{E(X)})*100 \\P=(1-\frac{3,555.56}{5,500})*100\\P=35.35\%[/tex]
There was a 35.35% reduction.
