An insurance policy sells for $800. Based on past data, an average of 1 in 50 policyholders will file a $15,000 claim, an average of 1 in 100 policyholders will file a $30,000 claim, and an average of 1 in 400 policyholders will file a $70,000 claim. Find the expected value (to the company) per policy sold. If the company sells 20,000policies, what is the expected profit or loss?

The expected value is $
The profit is $

The expected value is $375

The profit is $6,500,000

Step-by-step explanation:

15000, 30000, 70000

1/100, 1/200, 1/400

So the expected value of the claim is:

15000 × (1/100) + 30000 × (1/200) + 70000 × (1/400) = 475

Given that an insurance policy sells for $800 and the expected value of the claim is $475.

So, the expected value of the companies profit is = $(800 – 475) = $325.

If the company sells 20,000 policies then the expected profit is = $(20000 × 325) = $6,500,000

Thus, The expected value (to the company) per policy sold is $375 and the expected profit is $6,500,000.

-TheUnknownScientist 72

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify