The education required to become a state trooper varies by state, but in general at least a year of post-high school education is required. In some states, if you have served in the military the post-high school educational requirement is waived because of your experience.
You can enroll in Medicare Part D coverage once you meet both of the above requirements. Your Initial Enrollment Period for Part D is when you're first eligible to sign up for prescription drug benefits, and this period usually coincides with when you're first eligible for Medicare coverage.
Although initially it is not a large amount, the penalty grows quickly. Example: John was first eligible to enroll in Medicare Part D during the Initial Enrollment Period that began on October 15, 2013. Despite his eligibility for drug coverage, John did not enroll in Part D. John waits until November 2014 to enroll for 2015 coverage (1 year)