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There is a 0.9988 probability that a randomly selected 31-year-old male lives th

ID: 3322476 • Letter: T

Question

There is a 0.9988 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charges $152 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit. Complete parts (a) through (c) below. 9. a. From the perspective of the 31-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is $ The value corresponding to not surviving the year is $ (Type integers or decimals. Do not round.) b. If the 31-year-old male purchases the policy, what is his expected value? The expected value is $ (Round to the nearest cent as needed.) c. Can the insurance company expect to make a profit from many such policies? Why? (1)- because the insurance company expects to make an average profit of $ 31-year-old male it insures for 1 year. Round to the nearest cent as needed.) on every (1) O No, Yes,

Explanation / Answer

A.

The value corresponding to surviving the year = 152*.9988 = $151.8176

The value corresponding to surviving the year = 100000 * 0.0012 = $120

B.

X

- 100,000

152

P(X)

0.0012

0.9988

Lets say X is the amount that person will pay

Thus, 152 is positive as it is premium and 100000 is negative as it is death benefit

Thus, E(X) = 0.0012(-100000) + 0.9988(152)

E(X) = -120+151.8176 = 31.8176

Thus, Expectation is person will pay $31.8176 to company

C. Insurance com pany makes profit

Yes, because the insurance company expects to make an average profit of $31.82 (151.82-120) on every 31 year old male it insures for 1 year

X

- 100,000

152

P(X)

0.0012

0.9988

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