Adams College has a self-insured employee health care plan. Each employee pays a monthly premium of $100. Adams pays the rest of the health care costs. The number of covered employees is 1,000 this year. Each year, the number of employees who have major health claims follows a continuous uniform distribution between 10% and 15%, and the number of employees who have minor health claims follows a continuous uniform distribution between 60% and 65%. The rest have no health claims. Round off all numbers of claims to integers.
For this year, major health claims are expected to follow a normal distribution, with a mean of $5,000 and a standard deviation of $1,000. Minor health claims are expected to follow a normal distribution, with a mean of $1,500 and a standard deviation of $300. For purposes of simulating this model, assume that every minor health claim is the same amount simulated above. Assume likewise for major health clams. Use N replications of a simulation model to answer each of the following questions.
(a) What is the probability that Adams College’s total out-of-pocket cost will exceed $300,000 this year?
(b) The number of employees from year to year follows a continuous uniform distribution between a 3% decrease and a 4% increase. Round off all numbers of employees to integers. Also, due to rising health costs, the mean of minor health claims is expected to rise in a discrete uniform manner between 2% and 5% each year, and the mean of major health claims is expected to rise in a discrete uniform manner between 4% and 7% each year. What is the probability that Adams College’s total out-of pocket cost will exceed $2,000,000 over the next five years?