Question

the table shows claims and their probabilities for an insurance company. use the table to answer parts a through c.

amount of claim (to the nearest $50,000)	probability
$50,000	0.23
$100,000	0.06
$150,000	0.04
$200,000	0.01
$250,000	0.01

a. calculate the expected value.
$square$
b. how much should the company charge as an average premium so that it breaks even on its claim costs?
$square$
c. how much should the company charge to make a profit of $50 per policy?
$square$

Explanation:

Step1: Recall expected - value formula

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ is the value of the random variable and $p_i$ is its corresponding probability.

Step2: Calculate the product for each row

For $x_1 = 0$ and $p_1=0.65$, the product $x_1p_1=0\times0.65 = 0$.
For $x_2 = 50000$ and $p_2 = 0.23$, the product $x_2p_2=50000\times0.23=11500$.
For $x_3 = 100000$ and $p_3 = 0.06$, the product $x_3p_3=100000\times0.06 = 6000$.
For $x_4 = 150000$ and $p_4 = 0.04$, the product $x_4p_4=150000\times0.04=6000$.
For $x_5 = 200000$ and $p_5 = 0.01$, the product $x_5p_5=200000\times0.01 = 2000$.
For $x_6 = 250000$ and $p_6 = 0.01$, the product $x_6p_6=250000\times0.01=2500$.

Step3: Sum up the products

$E(X)=0 + 11500+6000 + 6000+2000+2500=28000$.

Step4: Answer part b

To break even on claim costs, the company should charge a premium equal to the expected value of the claims. So the premium should be $\$28000$.

Step5: Answer part c

To make a profit of $\$50$ per policy, the company should charge the expected - value of the claims plus the desired profit. So the premium should be $28000 + 50=\$28050$.

Answer:

a. $28000$
b. $28000$
c. $28050$