An insurance company pays 90% of the amount that exceeds a deductible of 200$, with a maximum payment of 1,800$. The company loads the expectation ofthis random variable by 20%, and charges this premium to the policyholder. Ifthe losses are exponentially distributed with a mean of 950$, what is theprobability that a claim surpasses the premium?

of the amount exceeding a deductible of is paid by the insurance company.The maximum paymentThe…

Answered: An insurance company pays 90% of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Along with interest rates, life expectancy is a component in pricing financial annuities. Suppose that you know that last year average life expectancy was 77 years for your annuity holders. Now you want to know if your clients this year have a longer life expectancy, on average, so you randomly sample n=20 of your recently deceased annuity holders to see actual age at death. Using a 5% level of significance, test whether or not the new data shows evidence of your annuity holders now live longer than 77 years, on average. The data below are the sample data (in years of life): (78,75,83,81,81,77,78,79,79,81,76,79,77,76,79,81,73,74,78,79) Does this sample indicate that life expectancy has increased? Test an appropriate hypothesis and state your conclusion (use a 5% level of significance). Be sure to check the necessary assumptions and conditions before conducting your test. Construct A 90% confidence interval for the true average age of death for the…
A certain model phone costs $599. The probability of the phone breaking over the course of a year is .07. What is the maximum amount you could pay for phone replacement insurance and still have a non-negative expected value on the policy? In other words, for what price or below would it be worth it to get the insurance?
The probability that a 29-year old female will die within 1-year is 0.000594. If an insurance company sells a 1-year, $50000 life insurance policy to a 29-year old female for $77, what is the expected value for the insurance company? Round your answer to the nearest cent.
The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
A company estimates that 0.7% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $50.If they offer a 2 year extended warranty for $4, what is the company's expected value of each warranty sold?
A company estimates that 0.6% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $250. If they offer a 2 year extended warranty for $39, what is the company's expected value of each warranty sold?
A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
The probability that a 30-year-old male in the U.S. will die within one year is about 0.00142. An insurance company is preparing to sell a 30-year-old male a one-year, $45,000 life insurance policy. How much should it charge for its premium in order to have a positive expectation for the policy? (Round your answer to the nearest dollar.)
An insurance company sells a one year term life insurance policy to an 80 year old woman. The woman pays a premium of $1000. If she dies within one year, the company will pay $18,500 to her beneficiary. According to the company's statistics department, the probability that an 80 year old woman will be alibve one year later is 0.9581. Find the expected value of the insurance company's profit.
A company estimates that 0.6% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $42, what is the company's expected value of each warranty sold?
A company estimates that 0.1% of their product will fail after th original warranty period but within 2 years of the purchase, with a replacement cost of $350. If they offer a 2 year warranty for $18 , what is the company's expected value of each warranty sold?
Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 88.9%. If BIC charges a premium of 8,240 silver coins and would pay a death benefit of 56,881 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC? Round to the nearest silver coin as needed. If the expected value is a loss to BIC, enter your answer as a negative number. Phil Dunphy, a real estate agent, is considering whether he should list an unusual $303,402 house for sale. If he lists it, he will need to spend $3,848 in advertising, staging, and fresh cookies. The current owner has given Phil 6 months to sell the house. If he sells it, he will receive a commission of $23,557. If he is unable to sell the house, he will lose the listing and his expenses. Phil estimates the probability of selling this house in 6 months to be 73%. What is the expected…

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