Question

Student Life Insurance Company wants to offer an insurance plan with a maximum claim amount of $5,000 for dorm students to cover theft of certain items. Past experience suggests that the probability of a maximum claim is .01.
1. What premium should be charged if the company wants to make a profit of $25 per policy?

Answer 1

Answer:

$25 = 0.01*5000 - X* 0.99$

And now if we solve for X we have this:

$0.99 X = 50-25 =25$

$X= \frac{25}{0.99}=25.25$

So then we conclude that they should be charge $25.25 for the insurance in order to have a profit of $25.

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

For this case we can use the definition of expected value given by:

$E(X) =\sum_{i=1}^n X_i P(X_i)$

Solution to the problem

For this case we know that the probabiity of maximum claim is 0.01, so then the probability of no maximum claim by the complement rule is 1-0.01=0.99

And we know that the plan with maximum claim gives an amount of $5000

Let X the charge for the premium insurance

We also know that the profit or the expected value would be 25 for the company

If we apply the concept of expected value we have this:

$25 = 0.01*5000 - X* 0.99$

And now if we solve for X we have this:

$0.99 X = 50-25 =25$

$X= \frac{25}{0.99}=25.25$

So then we conclude that they should be charge $25.25 for the insurance in order to have a profit of $25.