The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
There is a 0.9986 probability that a randomly selected 27-year-old male lives through the year. A life insurance company charges $174 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below.
a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 27 -year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why? From the point of view of the insurance company, the expected value of the policy is
Answer:
a. The life insurance company charges $174 for insuring if the male survives
Value(survive) = -$174
The life insurance company pays $90,000 for insuring if the male does not survive.
Value(not survive) = $89,826
b. The expected value for a 27-year-old male is
E(x) = -$48
c. The expected value for the insurance company is
E(x) = $48
Step-by-step explanation:
The probability that a randomly selected 27-year-old male survives is given by
P(survive) = 0.99864
The probability that a randomly selected 27-year-old male does not survive is given by
P(not survive) = 1 - P(survive)
P(not survive) = 1 - 0.99864
P(not survive) = 0.0014
a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
If 27-year-old male survives:
The life insurance company charges $174 for insuring if the male survives
Value(survive) = -$174
If 27-year-old male does not survive:
The life insurance company pays $90,000 for insuring if the male does not survive.
Value(not survive) = $90,000 - 174
Value(not survive) = $89,826
b. If the 27-year-old male purchases the policy, what is his expected value?
The expected value for a 27-year-old male is given by
E(x) = P(survive)×Value(survive) + P(not survive)×Value(not survive)
E(x) = 0.9986×-174 + 0.0014×89,826
E(x) = -$48
The negative sign indicates that it is a loss from the perspective of the 27-year-old male.
c. Can the insurance company expect to make a profit from many such policies? Why? From the point of view of the insurance company, the expected value of the policy is
The expected value for the insurance company is given by
E(x) = 0.9986×174 + 0.0014×-89,826
E(x) = $48
The positive sign indicates that it is a profit from the perspective of the insurance company.
