based on historical data, an insurance company estimates that a particular customer has a 3.7% likelihood of…

based on historical data, an insurance company estimates that a particular customer has a 3.7% likelihood of having an accident in the next year, with the average insurance payout being $1500. if the company charges this customer an annual premium of $160, what is the companys expected value of this insurance policy? $

based on historical data, an insurance company estimates that a particular customer has a 3.7% likelihood of having an accident in the next year, with the average insurance payout being $1500. if the company charges this customer an annual premium of $160, what is the companys expected value of this insurance policy? $

Answer

Explanation:

Step1: Define the two - case scenarios

There are two cases: accident occurs and accident does not occur.

Step2: Calculate the value when accident occurs

If the accident occurs (probability $p_1 = 0.037$), the company receives a premium of $$160$ and pays out $$1500$. So the net value to the company is $160 - 1500=- 1340$.

Step3: Calculate the value when accident does not occur

If the accident does not occur (probability $p_2=1 - 0.037 = 0.963$), the company only receives the premium of $$160$. So the net value to the company is $160$.

Step4: Calculate the expected value

The expected value $E(X)$ is calculated using the formula $E(X)=p_1x_1 + p_2x_2$, where $x_1=-1340$ and $x_2 = 160$. $E(X)=0.037\times(- 1340)+0.963\times160$ $E(X)=-49.58 + 154.08$ $E(X)=104.5$

Answer:

$104.5$