# Struggling Stats Word Problem

1. May 28, 2009

### war485

1. The problem statement, all variables and given/known data

Suppose that one year, an insurance company incurred dollar damages,
X, in four different amounts with probabilities, p(x), shown below:

X
0
1000
5000
10000

p(x)
0.7
0.2
0.08
0.02

If the company offers a $500 deductable and wants and wants an expected profit of$150, how much should it charge for the premium?

2. Relevant equations

Not even sure what's relevant here. Maybe the expected value is involved somehow:
E(x) = sum ( x*p(x) ) = 800

3. The attempt at a solution

How would I even go about with a problem like this?

2. May 28, 2009

### Redbelly98

Staff Emeritus
If the premium is P, what is the company's profit when damages = $0? How about when damages =$1000?

3. May 28, 2009

### war485

company's profit is $500 for 0 damage and -$500 profit for 1000 damage.

4. May 29, 2009

### Redbelly98

Staff Emeritus
You're not including the premium P, the amount the customer pays for the insurance policy.

First the customer pays the insurance company an amount P. Then later, the company pays back to the customer an amount depending on what the damages are.

5. May 29, 2009

### war485

I think I'm getting it.
So overall, if I made up an equation, would this seem right?
Premium = profit + (damages - deductable)
so then my answer should be \$800

6. May 30, 2009

### Redbelly98

Staff Emeritus
That's right.

(Of course, whenever damages are less than the deductible, no payment is made, but it looks like you realize that.)

7. Jun 1, 2009

thanks! ^.^