A man wishes to purchase a life insurance policy that will pay the beneficiary $20,000 in the event that the man's death occurs during the next year. Using life insurance tables, he determines that the probability that he will live another year is 0.92. What is the minimum amount that he can expect to pay for his premium

The minimum amount that he can expect to pay for his premium is $1600

Step-by-step explanation:

Let the minimum amount he can expect to pay for his premium be $P.  The minimum premium occurs when the insurance company expected profit is zero.

If the man lives for one years the gain would be $P and the probability of the man living for one year = 0.92.

If the man dies during one year the gain is $(P - 20000) and the probability of him dying within one year is (1 - 0.92 = 0.08)

Therefore insurance company expected profit is:

0.92P + 0.08(P - 20000)

Since The minimum premium occurs when the insurance company expected profit is zero,

0.92P + 0.08(P - 20000) ≥ 0

0.92P + 0.08P - 1600 ≥ 0

P - 1600 ≥ 0

P ≥ 1600

Therefore the minimum amount that he can expect to pay for his premium is $1600

(a) the volume of the cone is 20/3 in3

hence, option a is correct.