I need help soon, please!!!

the question goes,

Joe is the breadwiner for her family, and it is Dec. 1 of the current year. The amount N of uninsured medical expenses that her family will incur druing next year is uncertain.

US tax law allows Joeto prepay any amount q of her medical expense in a way that can save money by reducing federal and state income tax. His marginal income tax rate is 40%. Joe's uninsured medical expense X for the forthcoming year is uncertain. Based on past experience, Joe estimates that X is normally distributed.Its distribution is normal with mean of $3500 and SD of $1200. Joe can declare an amount q of uninsured prepaid medical expense. His salray for the year is reduced by q dollars. Joe's company reimubrses him for the first q dollars. He pays any excess (X-q)+ out of after-tax income. Prepaying q dollars of medical expenses saves Joe 0.4q in after -tax income because he does not pay taxes on the amount reduced from his salary. But there is a donwside. The law requires Joe's employer to keep any excess (q-X)+ of Joe's prepaid medical expenses over his actual medical expense. Joe's goal is to prepay the amount q* that maximizes the expectation of his after-tax income.

(a) What amount q* should Joe choose? Justify.

(b) for q* selected compute

(1) prob. that joe will need to pay for any uninsured emdical expense with after-tax dollars.

(2) prob. that joe's company will pay fewer than q* dollars toward Joe's uninsured medical expense.

(3) expectation of amount of uninsured medical expense that Joe will pay with after-tax dollars.

(4) expectation of amount by which q* exceeds amount of Joe's uninsured medical expense that his company will pay.

(5) expectation of increase in after-tax income that Joe garners from prepaying q* dollars of medical expense.