A small private college self$-$insures its staff and faculty by maintaining its own fund to cover

health insurance claims. Under a new upcoming contract negotiated by the union and the

administrators, each employee is expected to contribute $$200\mathrm{.}00$ at the beginning of each

month that gets deducted automatically from pay stubs. The total current number of

employees at the beginning of the new contract year is $600,$ however, this number may

increase through additional hiring or decrease through early retirement incentives. Assume

that in each subsequent month, the change in the number of employees is uniformly

distributed between $-1\%$ and $2\%($use Excel's ROUNDUP function to round up the number of

employees to the next digit$).$ Each employee$$s claim averages about $$300$ per month and is

expected to increase each subsequent month by a uniformly distributed amount that ranges

between a minimum of $1\%$ and a maximum of $5\%.$

a$.$ Create a model in Crystal Ball to compute the average yearly cost at the end of the year

incurred by the college to cover its employees$$ health care costs. Use $5000$ simulation runs.

b$.$ Assume that the college plans to set aside a budget of $$800,000$ during the new contract year

to cover its employees$$ healthcare costs. What is the probability that this budget is inadequate

to cover its employees$$ health care costs?