Sample Free Response Question

The AP Exam is made up of a section containing Multiple Choice (MC) questions and a section containing Free Response (FR) questions. Each section counts toward 50% of your overall grade on the exam. Below is a sample FR question from a past AP Exam (one you will complete as part of your Exam Prep next spring!)

A department supervisor is considering purchasing one of two comparable photocopy machines, A or B. Machine A costs $10,000 and machine B costs $10,500. This department replaces photocopy machines every three years. The repair contract for machine A costs $50 per month and covers an unlimited number of repairs. The repair contract for machine B costs $200 per repair. Based on past performance, the distribution of the number of repairs needed over any one-year period for machine B is shown below.

(Number of Repairs, Probability)
(0, 0.50)
(1, 0.25)
(2, 0.15)
(3, 0.10)

You are asked to give a recommendation based on overall cost as to which machine, A or B, along with its repair contract, should be purchased. What would your recommendation be? Give a statistical justification to support your recommendation.