PLEASE SHOW ALL YOUR WORK! So I can follow along. Thanks.

Tech has three health care plans for its faculty and staff to choose from, as follows: Plan 1-monthly cost of $32, with a $500 deductible; the participants pay the first $500 of medical costs for the year; the insurer pays 90% of all remaining expenses. Plan 2monthly cost of $5 but a deductible of $1,200, with the insurer paying 90% of medical expenses after the insurer pays the first $1,200 in a year. Plan 3monthly cost of $24, 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 science department, estimates that her annual medical expenses are defined by the following probability distribution: Annual Medical Expenses $ 100 Probability .15 500 .30 .35 .10 1,500 3,000 5,000 10,000 .05 .05 Determine which medical plan Tracy should select