Sample Responses Q3.pdf

The 2021 AP Statistics Scoring Guidelines provide instructions for scoring student responses to a free-response question focusing on probability and sampling distributions. The question has three parts: (a) defining a random variable and calculating a probability, (b) calculating the expected value of the random variable, and (c) interpreting Agatha's experience in the context of the problem.

For part (a), a response is considered essentially correct (E) if it defines the random variable as the number of gift cards received in a 52-week year, describes the distribution as binomial with n = 52 and p = 0.005, identifies the event of interest, and provides supporting work to calculate the probability of 0.2295.

For part (b), a response is considered essentially correct (E) if it correctly calculates the expected value of 0.26 and provides a reasonable interpretation, including concepts such as repeating the selection process, averaging, and the context of receiving gift cards.

The guidelines provide additional notes and examples to help scorers evaluate student responses, including what constitutes a correct calculation of the expected value and how to interpret the results in context.