Question

If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?

Answer 1

In order to calculate the expected value of one policy, we can use the formula below:

`E(x)=\sum x\cdot p(x)`

When the holder of the policy dies before 70 years old (probability of 3%), the company will earn $765 but will lose $27400. If the holder dies after 70 years old, the company will earn $765.

So the expected value is:

`\begin{gathered} E(x)=0.03\cdot(765-27400)+0.97\cdot765\\ \\ E(x)=0.03\cdot(-26635)+742.05\\ \\ E(x)=-799.05+742.05\\ \\ E(x)=-57 \end{gathered}`

Since the expected value is negative, that means the company should expect to have a loss of $57 for each insurance policy sold.

Therefore the correct option is the second one, and the expected loss is $57 per policy.