Health insurance claims
A large manufacturing company self-insures its employee health insurance claims. That is, it collects a fixed amount each month from every employee for healthcare costs, and then it pays the entire claim amount using its own funds to make up the difference. It would like to estimate its total healthcare payments for the coming year.
The total number of employees at the start of the year is 11,124. The firm expects the number of employees to change each month over the coming year by a percentage that is uniformly distributed between -2 and 5 percent. Employees contribute $125 each per month toward their healthcare costs, while the average claim is $250 per month. The average claim itself is expected to grow by an amount given by a normal distribution with a mean of 1 percent and a standard deviation of 2 percent.
a. What is the expected cost to the company of covering employee healthcare costs in the coming year?
b. What is the maximum cost to the company of covering employee healthcare costs in the coming year?
c. What is the probability that costs will not exceed $20 million?