1.According to the National Association of Insurance Commissioners (NAIC), the average premium for homeowner's insurance in the United States in a recent year was $1,034. Suppose these premium rates are uniformly distributed across the country from $535 to $1,533. What percentage rates are between $800 and $1,200? What percentage are more than $1,350?

2.A study by Quadrant Information Services commissioned byInsure.comcalculated auto insurance rates for each of the 50 states; and as a result, the average annual rate for the United States was $1,317. Suppose annual rates of auto insurance in the United States are normally distributed with a standard deviation of $324. Based on these data, what is the probability that a randomly selected auto insurance rate in the United States would be greater than $1,750? What percentage of auto insurance rates would be less than $1,200? What percentage of auto insurance rates would be between $1,100 and $1,500?

3.Homeowners do not make insurance claims very often. In fact, the Oregon Insurance Division says that, on average, a homeowner makes one claim every 9 years. Suppose such homeowner claims are Poisson distributed. What is the probability that it would be 15 years or more between claims for a homeowner? What percentage of the time would it be less than 5 years between claims? According to data released by the Insurance Information Institute, the claim frequency for automobile collisions is 5.59 per 100 car years (a car year is equal to 365 days of insured coverage for one vehicle). What is the average "interarrival time" for auto collisions in car years? What do you think this average means? Assume that auto collisions are Poisson distributed.