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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

APPLICATIONS

Lightning Insurance An insurance company has determined that in a certain region the probability of lightning striking a house in a given year is about 0.0003 , and the average cost of repairs of lightning damage is $ 7500 per incident. The company charges $ 25 per year for lightning insurance.

(a) Find the company’s expected value for each lightning insurance policy.

(b) If the company has 450 , 000 lightning damage policies, what is the company’s expected yearly income from lightning insurance?

To determine

(a)

The expected value for each lightning insurance policy.

Explanation

Approach:

The compliment of the probability is given as,

p=1p(1)

Here, p is the compliment of the probability and p is the probability.

The expected value is given as,

E=a1p1+a2p2++anpn(2)

Here, a1,a2,,an is the amount of payout and p1,p2,,pn is the probability of payout.

Given:

The probability of lightning striking a house in a year is 0.0003, the average cost of repairs of lightning damage is $7500 per incident. And, the company charges $25 per year for lightning insurance.

Calculation:

Calculate the probability of lightning not striking the house.

Substitute 0

To determine

(b)

The company’s expected yearly income from lightning insurance.

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Chapter 14 Solutions

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