S$1\mathrm{.}37$ State University has three health care plans for its faculty and staff to choose from, as follows.

Plan one $-$ Monthly cost of $$32$ with a $$500$ deductible: The participants play the $1$st $$500$ of medical payments for the year, The insurer pays $90\%$ of all remaining expenses.

Plan $2-$ Monthly cost of $$5\mathrm{.}00$ but a deductible of $$1200,$ with the insurer paying $90\%$ of medical expenses after the insured pays the first $$1200$ in a year.

Plan $3-$ Monthly cost of $$24\mathrm{.}00$ with no deductible; the participants pay $30\%$ of all expenses, with the remainder paid by the insurer.

Tracy McCoy, an administrative assistant, in the management department, estimates that her annual medical expenses are defined by the following probability definition:

Determine which medical plan Tracy should select