Final answer:
The Centers for Medicare & Medicaid Services (CMS) is the federal agency responsible for the administration of Medicare, as part of the Department of Health and Human Services.
Step-by-step explanation:
The federal agency responsible for the administration of the Medicare programs is the Centers for Medicare & Medicaid Services (CMS). CMS is part of the Department of Health and Human Services (HHS), which oversees a vast array of health-related programs and services, including those aimed at providing health care for various populations such as seniors, low-income individuals, and children. The availability of Medicare is particularly significant for those eligible for Social Security benefits, as it ensures access to health insurance coverage for the elderly and certain individuals with disabilities.