You have just been hired by XZU's financial planning department. Your first job is to help XZU

determine how much money XZU should accrue on a monthly basis to pay for its employees'

health insurance claims. As a large multi$-$campus private university, it is self$-$insured, which

means that it pays health insurance claims with its own money $($although it contracts with

$B\frac{C}{B}S$ to handle the administrative details of processing claims and handling checks$).$

The money XZU uses to pay claims comes from two sources: employee contributions $($or

premiums deducted from employees' paychecks$),$ and university funds $($XZU must pay whatever

costs are not covered by employee contributions$).$ Each employee who is covered by the health

plan contributes $$475$ per month; however, the number of employees covered changes from

month to month as employees are hired, fired, quit, or simply drop health insurance coverage.

Historically, the month to month change in covered employees is given in the table below:

A total of $22,000$ employees are currently covered by the plan. The average monthly

health claim per covered employee is normally distributed with a mean of $$625$ and a standard

deviation of $$20.$

Determine within a margin of error of $1\%$ the average amount of money XZU should set

aside each month to cover the balance of employee health cost claims. XZU prefers to plan a

fixed monthly amount to set aside each month with the expectation that at the end of the year

they will have covered their health care liabilities.

$[$HINT: set up a simulation table with each row representing a month. Assume that during the

first month of the simulation you have $22,000$ employees covered. The last column should

contain the net amount that XYZ will have to pay that month $($EMPLOYEE CONTRIBUTIONS $-$

HEALTH COST CLAIMS, which is a negative number$).$ Then estimate the true average of that

amount within $1\%.$