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1. A man wishes to purchase a 5-year term life insurance policy that will pay the beneficiary $20,000 in the event that the man's death occurs during the next five years. Using life insurance tables, he determines that the probability that he will live another five years is 0.96. What is the minimum amount that he can expect to pay for his premium? (Hint: The minimum premium occurs when the insurance company's expected gain is zero.)

1. A man wishes to purchase a 5-year term life insurance policy that will pay the beneficiary $20,000 in the event that the man's death occurs during the next five years. Using life insurance tables, he determines that the probability that he will live another five years is 0.96. What is the minimum amount that he can expect to pay for his premium? (Hint: The minimum premium occurs when the insurance company's expected gain is zero.)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Analyzing Decisions Use expected value to analyze the following. 1. A man wishes to purchase a 5-year term life insurance policy that will pay the beneficiary $20,000 in the event that the man's death occurs during the next five years. Using life insurance tables, he determines that the probability that he will live another five years is 0.96. What is the minimum amount that he can expect to pay for his premium? (Hint: The minimum premium occurs when the insurance company's expected gain is zero.) 2. As a fringe benefit, Mrs. Taylor receives a $25,000 life insurance policy from her employer. The probability that Mrs. Taylor will live another year is 0.9935. If she purchases the same coverage for herself, what is the minimum amount that she can expect to pay for the policy? 3. The proprietor of Midland Construction Company has to decide between two projects. He estimates that the first project will yield a profit of $180,000 with a probability of 0.7 or a profit of $150,000 with a probability of 0.3; the second project will yield a profit of $220,000 with a probability of 0.6 or a profit of $80,000 with a probability of 0.4. Which project should the proprietor choose if he wants to maximize his expected profit? 4. The management of Multi-Vision, Inc., a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.2, the estimated profit over the next ten years is $10 million; if the company obtains the rights to city B, the probability of which is 0.3, the estimated profit over the next ten years is $7 million. The cost of submitting a bid for rights in city A is $250,000 and that of city B is $200,000. By comparing expected profits for each venture, determine whether the company should bid for the rights in city A or city B.
Transcribed Image Text:Analyzing Decisions Use expected value to analyze the following. 1. A man wishes to purchase a 5-year term life insurance policy that will pay the beneficiary $20,000 in the event that the man's death occurs during the next five years. Using life insurance tables, he determines that the probability that he will live another five years is 0.96. What is the minimum amount that he can expect to pay for his premium? (Hint: The minimum premium occurs when the insurance company's expected gain is zero.) 2. As a fringe benefit, Mrs. Taylor receives a $25,000 life insurance policy from her employer. The probability that Mrs. Taylor will live another year is 0.9935. If she purchases the same coverage for herself, what is the minimum amount that she can expect to pay for the policy? 3. The proprietor of Midland Construction Company has to decide between two projects. He estimates that the first project will yield a profit of $180,000 with a probability of 0.7 or a profit of $150,000 with a probability of 0.3; the second project will yield a profit of $220,000 with a probability of 0.6 or a profit of $80,000 with a probability of 0.4. Which project should the proprietor choose if he wants to maximize his expected profit? 4. The management of Multi-Vision, Inc., a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.2, the estimated profit over the next ten years is $10 million; if the company obtains the rights to city B, the probability of which is 0.3, the estimated profit over the next ten years is $7 million. The cost of submitting a bid for rights in city A is $250,000 and that of city B is $200,000. By comparing expected profits for each venture, determine whether the company should bid for the rights in city A or city B.
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