There is a 0.9987 probability that a randomly selected 31​-year-old male lives through the year. A life insurance company charges ​$186 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.

Parts a through c is missing and it is;

a) From the perspective of the 33-year-old male, what are the monetary values corresponding to the two events of surving the year and not surviving?

The value corresponding to surviving the year is $_____.

The value corresponding to not surviving the year is $_____.

b) If the 33-year-old male purchases the policy, what is his expected value?

The expected value is $_____.

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

_____ because the insurance company expects to make an average profit of $_____ on every 33-year-old male it insures for 1 year.

Answer:

A) the value that corresponds to surviving the year = - $186

The value corresponding to not surviving the year = $99814

B) μ = -$56

C) Yes, the company can make a profit from many such policies because it makes an average profit of $56 on every 31 year old male it insures for 1 year.

Step-by-step explanation:

A) The company charges $186 for insuring. Thus;

Amount paid out = - $186

Therefore, the value that corresponds to surviving the year = - $186

Therefore, the value corresponding to not surviving the year = $100000 - $186

The value corresponding to not surviving the year = $99814

B) since probability that a 31 year old male survives is 0.9987, then;

Probability that a male doesn't survive is;

P(doesn't survive) = 1 - 0.9987

P(doesn't survive) = 0.0013

The expected value is calculated from;

μ = Σx•P(x) = (0.0013 × 99814) + (-186 × 0.9987)

μ = -$56

C) Yes, the company can make a profit from many such policies because it makes an average profit of $56 on every 31 year old male it insures for 1 year.

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