Unit Activity Unit: Sequences, Induction, and Probability This activity will help you meet these educational goals: Mathematical PracticesYou will make sense of problems and solve them and reason abstractly and quantitatively. Introduction The insurance industry deals with random variables and expected values. In this investigation, you may need to talk with an insurance agent. Insurance information is available online as well. Most people will purchase several types of insurance in their lifetime, such as homeowner's or renter's insurance, life insurance, health insurance, and long-term care insurance. Insurance companies deal with random variables as risks and are in the business to help individuals deal with the risks as well. This assignment requires using terms studied in this unit and citing data to back up the various differences one sees in the insurance industry. This assignment also requires that you do some online research. Please list your information sources (such as Internet URLs) in the Resources section of this document. __________________________________________________________________________ Directions and Analysis Task 1: Investigating Vehicle Insurance All states except one require car insurance, but not all states require the same coverage. Each state defines the minimum insurance coverage that is required. According to the Minnesota minimum coverage requirements, for example, all licensed vehicles are required to have coverage for: personal injury protection (PIP) liability uninsured motorist underinsured motorist a. Find the website for your state's department of motor vehicles (DMV). Investigate the minimum coverage requirements established by your state, and list these coverage requirements: Injury or death to one person Injury or death to more than one person Damage to property Type your response here: 1 2014 EDMENTUM, INC. b. If you own or regularly drive a vehicle, check the insurance policy and report which required coverages you have and what the coverage value is for each one of them. Note which coverages are at the minimum value prescribed by the state. If you do not own or drive a vehicle, review your state's minimum coverage requirements and describe which coverages would you like to have if you did regularly drive a vehicle. Type your response here: c. What are some variables that can affect your premium? How do these variables affect your premium? Check your state's DMV website or conduct an Internet search to get an idea of the variables that affect your premium. Type your response here: d. What is your deductible amount? How does changing to a higher or lower deductible affect the premium? Type your response here: e. What other variables do you have some control over? Type your response here: f. Of the variables affecting your insurance, are any of them truly random variables? Type your response here: g. Suppose that you head an insurance company. Your most popular insurance policy has a premium of $600 and a deductible of $1,000. This insurance policy provides your state's minimum coverage of $30,000 for injury or death to one person, $50,000 for injury or death to two or more people, and $10,000 for damage to property, which is called 30/50/10 coverage. Assume that, on average, 2 of your 100 customers have an accident every year. One of the accidents causes damage to property and the other causes injury or death to one person. Both drivers file for the maximum claims. After paying the claims, will your company still profit from the premiums collected in a year? Type your response here: h. Now assume that you are one of the customers purchasing this popular insurance policy with the company. Considering only your premiums, deductible, and claims, what is the 2 break-even period after which you could make a $10,000 claim for property damage without the insurance company suffering a loss? Type your response here i. How would the break-even period in this scenario change if you lived in another state? Research another state's minimum coverage requirement and calculate the break-even period you calculated above for that state's minimum coverage requirements. Assume that all other variables (premium, deductible, etc.) are the same. Type your response here: j. Do some research and define what \"usage-based,\" or \"pay as you go,\" insurance is. What variables are being measured in this form of insurance? Type your response here: k. Describe and explain whether you think there should be penalties for people who do not have auto insurance. Research the topic, and cite some data to back up your opinion. Type your response here: Task 2: Investigating Other Types of Insurance Apart from vehicle insurance, there are several other types of insurance such as life insurance, homeowner's insurance, etc. The coverages for these types of insurances are mostly the same. a. Why do banks require home insurance? Type your response here: b. If you owned your home outright, would you pay for insurance? Why or why not? Type your response here: c. Should states have no pay, no play laws for health insurance? Why or why not? Type your response here: d. Explain how an insurance company can pay a large benefit even if it hasn't collected that amount from an individual's premiums. 3 Type your response here: __________________________________________________________________________ Resources Document any references you used for this project below. At minimum, include a title and URL for any Internet resource: __________________________________________________________________________ 4 Evaluation Your teacher will use this rubric to evaluate the completeness of your work as well as the clarity of thinking you exhibit. Total Points: 10 Task 1: Investigating Vehicle Insurance a-f. Understand the concepts of minimum coverages, premiums, deductibles, and variables that affect premium rates. Task points: 7 3 g-i. Solve insurance policy problems. 3 j-k. Analyze usage-based insurance and penalties for uninsured motorists. 1 Task 2: Investigating Other Types of Insurance a-b. Understand home insurance and related terms. Task points: 3 1 c. Understand health insurance. 1 d. Understand damage claim payoffs. 1 5