Question 1032264: An insurance company has determined that in a certain region the probability of lightning striking a house in a given year is about 0.0004, and the average cost of repairs of lightning damage is $7000 per incident. The company charges $20 per year for lightning insurance.
(a) What is the company's expected value for the net income from each lightning insurance policy in one year?
$
(b) If the company has 450,000 lightning damage policies, what is the company's expected yearly income from lightning insurance?
$
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! expected value per customer = 20 - .0004 * 7000 = 17.2
with 450,000 customers, this comes out to 450,000 * 17.2 = 7,740,000 dollars of net income per year.
look at it from another angle.
450,000 customers * 20 per customer = gross income of 9,000,000 per year.
an average of .0004 * 450,000 customers will experience a lightning strike each year.
that equals 180 customers per year.
they receive an average of 7000 each in compensation.
that's 180 * 7,000 = 1,260,000 per year is spent in compensation.
9,000,000 minus 1,260,000 equals net income of 7,740,000 per year.
their expected value is 7,740,000 per year.
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