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

Question

There is a 0.9988 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charges $193 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

a) From the perspective of the 31-year old male, what are the monetary values corresponding to the two events of survivng the year and not survivng?

The value corresponding to survivng the year is $

The value corresponding to not survivng the year is $

b) if the 31 year old male purchases the policyt, what is his expected value?

The expected value is $

c) Can the insurance company expect to make a profut from many such policies? Why?

Yes/no because the insurance company expects to make an average profit of $ on every 31 year old male it insures for 1 year.

Explanation / Answer

a. From the perspective of the 31 yr old male:

Value of surviving the year = -193 $

Value of not surviving the year = 100000 $

b. Expected value = P(Survival) * (-193) + P(Death) * 100000

= 0.9988 * (-193) + (1-0.9988)*100000

= -72.7684

c. Yes. The insurance company expects to make a profit on such policies.

Because average expected profit per policy is positive, and is equal to:

Average profit per policy = $ 72.7684

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