Probability of Annual Profit in Insurance Company
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Questions and Answers

What is the percentage of reimbursement of health care costs above 120?

  • 100%
  • 50% (correct)
  • 25%
  • 75%

    • What is the minimum value of health care costs that will be reimbursed at 50%?

  • 100
  • 110
  • 130
  • 120 (correct)

    • What is the probability function of N1 and N2 in terms of n1 and n2?

  • 1 - e^(-n1) * 1 - e^(-n2)
  • e^(n1 + n2)
  • e^(n1 - n2)
  • 3/4 * e^(-n1) * e^(-n2) (correct)

    • What is the expected number of claims that will be submitted to the company in May, given that exactly 2 claims were submitted in April?

    <p>3e/16</p> Signup and view all the answers

    What is the probability that a modem selected from Source A is defective?

    <p>0.20</p> Signup and view all the answers

    What is the total number of modems in the store's inventory?

    <p>80</p> Signup and view all the answers

    What is the amount that the life insurance policy will pay if the man dies before his 50th birthday?

    <p>5000</p> Signup and view all the answers

    What is the probability that exactly two out of a sample of five modems selected without replacement from the store's inventory are defective?

    <p>0.105</p> Signup and view all the answers

    What is the mean of the number of claims filed by a policyholder under a vision care insurance policy during one year?

    <p>2</p> Signup and view all the answers

    What is the standard deviation of the lifetime of a brand of light bulb?

    <p>1</p> Signup and view all the answers

    What is the expected value of a single claim in thousands?

    <p>4</p> Signup and view all the answers

    What is the probability that the average of 25 randomly selected claims exceeds 20,000?

    <p>0.27</p> Signup and view all the answers

    Approximately how many contributions does the charity receive?

    <p>2025</p> Signup and view all the answers

    What is the approximate 90th percentile for the distribution of the total contributions received?

    <p>6,343,000</p> Signup and view all the answers

    What is the probability that there is a total of between 2450 and 2600 claims during a one-year period?

    <p>0.68</p> Signup and view all the answers

    What is the expected value of the largest of the three claims?

    <p>3232</p> Signup and view all the answers

    What percentage of policyholders file fewer than two claims during a given year?

    <p>40%</p> Signup and view all the answers

    What is the probability that a random policyholder will file more than three claims during a given year?

    <p>0.27</p> Signup and view all the answers

    What is the deductible for each loss reported to an insurance company?

    <p>5,000</p> Signup and view all the answers

    What is the probability that the total payout on 200 reported losses is between 1,000,000 and 1,200,000?

    <p>0.1799</p> Signup and view all the answers

    What percentage of the clients have none of the three products (auto insurance, homeowners insurance, and renters insurance)?

    <p>17%</p> Signup and view all the answers

    What is the percentage of the agent's clients that have both auto and renters insurance?

    <p>16%</p> Signup and view all the answers

    What is the cumulative distribution function for health care costs experienced by a policyholder?

    <p>F(x) = 1 - e^(-x/100), x &gt; 0</p> Signup and view all the answers

    What is the deductible for the policy modeled by the cumulative distribution function?

    <p>20</p> Signup and view all the answers

    Which of the following events satisfies the condition that the probability of their union equals the sum of their probabilities?

    <p>Events B, C, and E</p> Signup and view all the answers

    What is the probability that at least one letter ends up in its accompanying envelope?

    <p>27/256</p> Signup and view all the answers

    What is the probability that a policyholder had exactly five office visits, given that costs exceed the deductible?

    <p>0.050</p> Signup and view all the answers

    What is the probability that part B works for one year, given that part A works for one year?

    <p>5/8</p> Signup and view all the answers

    What is the probability that part A works for one year?

    <p>0.8</p> Signup and view all the answers

    What is the probability that at least one part works for one year?

    <p>0.9</p> Signup and view all the answers

    What is the probability that a policyholder has exactly two visits in a year?

    <p>0.10</p> Signup and view all the answers

    What is the annual deductible on the policy?

    <p>350</p> Signup and view all the answers

    What is the probability that the annual profit does not exceed 2000?

    <p>0.7642</p> Signup and view all the answers

    What is the cumulative distribution function of the loss L on an automobile claim?

    <p>f(x) = 3(l/3)^3, 0 ≤ l ≤ 3</p> Signup and view all the answers

    What is the probability that exactly one of the two independent events E and F occurs?

    <p>0.546</p> Signup and view all the answers

    What is the probability that the number of claims received in a month is n, for n = 0, 1, 2, ...?

    <p>P[N = n] = (n + 1)^(-3)</p> Signup and view all the answers

    What is the probability that more than three claims will be received during a consecutive two-month period, given that fewer than two claims were received in the first of the two months?

    <p>0.3</p> Signup and view all the answers

    What is the value of the insured’s automobile?

    <p>V</p> Signup and view all the answers

    What is the probability that the annual profit does not exceed 3000?

    <p>0.9066</p> Signup and view all the answers

    Are events E and F independent?

    <p>Yes</p> Signup and view all the answers

    Study Notes

    Health Insurance Policy

    • An insurer reimburses 100% of health care costs between 20 and 120.
    • Health care costs above 120 are reimbursed at 50%.
    • The cumulative distribution function of reimbursements is G.

    Claim Submissions

    • The joint probability function of the number of claims submitted in April and May is given by a formula involving exponential functions.
    • The expected number of claims submitted in May, given that exactly 2 claims were submitted in April, is a function of e.

    Probability of Defective Modems

    • A store has 80 modems from two sources, A and B, with 30 from A and 50 from B.
    • The probability of a defective modem from A is 20% and from B is 8%.
    • The probability that exactly two out of a sample of five modems are defective is calculated.

    Life Insurance Policy

    • A policy pays 5000 if the policyholder dies before age 50 and 0 otherwise.
    • The probability that a policyholder will file more than three claims during a year is calculated.

    Automobile Losses

    • The amounts of automobile losses are mutually independent and uniformly distributed between 0 and 20,000.
    • The insurer covers each loss subject to a deductible of 5,000.
    • The probability that the total payout on 200 reported losses is between 1,000,000 and 1,200,000 is calculated.

    Insurance Profile

    • An insurance agent offers auto, homeowners, and renters insurance.
    • The purchase of homeowners and renters insurance is mutually exclusive.
    • The profile of the agent's clients is given by probabilities of having different products.
    • The percentage of clients with both auto and renters insurance is calculated.

    Cumulative Distribution Function

    • The cumulative distribution function for health care costs is modeled by a function involving exponential functions.
    • The policy has a deductible of 20.
    • A random variable X has a cumulative distribution function involving a different formula.
    • The expected value of the largest of three claims is calculated.

    Charity Contributions

    • A charity receives 2025 contributions with a mean of 3125 and standard deviation of 250.
    • The approximate 90th percentile for the distribution of the total contributions is calculated.

    Claims Distribution

    • Claims filed under auto insurance policies follow a normal distribution with mean 19,400 and standard deviation 5,000.
    • The probability that the average of 25 randomly selected claims exceeds 20,000 is calculated.

    Poisson Distribution

    • The number of claims filed by a policyholder under a vision care insurance policy is a Poisson random variable with mean 2.
    • The approximate probability that there is a total of between 2450 and 2600 claims during a one-year period is calculated.

    Light Bulb Lifetime

    • The lifetime of a light bulb is normally distributed with mean 3 and variance 1.
    • The probability that at least one light bulb lasts for more than 3 months is calculated.

    Independent Events

    • Four events are given, and the probability that their union equals the sum of their probabilities is calculated.

    Envelope Probability

    • Four letters to different insureds are prepared along with accompanying envelopes.
    • The probability that at least one letter ends up in its accompanying envelope is calculated.

    Health Insurance Policy

    • A health insurance policy covers visits to a doctor's office with a cost of 100.
    • The annual deductible is 350.
    • The probability that a policyholder had exactly five office visits, given that costs exceed the deductible, is calculated.

    Machine Parts

    • A machine has two parts, A and B, with different probabilities of working for one year.
    • The probability that at least one part works for one year is given.
    • The probability that part B works for one year, given that part A works for one year, is calculated.

    Profit Distribution

    • The annual profit of a life insurance company is normally distributed.
    • The probability that the annual profit does not exceed 2000 and 3000 is given.
    • The probability that the annual profit does not exceed 1000 is calculated.

    Automobile Claim

    • The loss on an automobile claim is a random variable with a cumulative distribution function involving a formula.
    • The probability that the loss is between 0.5V and 1.0V is calculated.

    Independent Events

    • Two events, E and F, are independent with given probabilities.
    • The probability that exactly one of the two events occurs is calculated.

    Flood Insurance

    • The number of claims received in a month is a random variable with a given probability distribution.
    • The probability that more than three claims will be received during a consecutive two-month period, given that fewer than two claims were received in the first month, is calculated.

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    Description

    Calculate the probability that the annual profit of a life insurance company does not exceed a certain amount, given the probabilities of profits not exceeding other amounts.

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