Question

select the correct answer.
acasa insurance company offers several plans for home insurance.

• plan a has a $700 yearly premium with a $3,000 deductible.
• plan b has a $1,200 yearly premium with a $1,000 deductible.

the average payout by the insurance company for a fire claim is $27,000. suppose 5% of the claims were for fire damage. what would acasa’s expected value (loss or gain) be per customer who chooses plan a?
a. $-25,300
b. $-1,350
c. $850
d. $-500

Explanation:

Step1: Calculate payout per claim

The insurance pays the claim minus the deductible. For Plan A, deductible is $3,000, average claim is $27,000.
$\text{Payout per claim} = 27000 - 3000 = 24000$

Step2: Find expected payout per customer

5% of customers file a claim, so expected payout is 5% of the per-claim payout.
$\text{Expected payout} = 0.05 \times 24000 = 1200$

Step3: Calculate net expected value

Acasa gains the premium, minus the expected payout. Premium for Plan A is $700.
$\text{Expected value} = 700 - 1200 = -500$

Answer:

D. -$500