High school students’ reasoning when facing a binomial distribution

The aim of this study we to analyze the students’ intuitive understanding of the binomial distribution. We analyze the responses by 127 students to a task where students should provide four values of the binomial distribution and justify the values provided. We analyze the mean, rank of the four values in the response, and classify the arguments using content analysis. Most students provided values with mean and rank in the acceptable interval suggesting a distributional reasoning. Among the correct arguments, the correct estimation of probability stood out (56.7% of students), as well as the observation of convergence and variability of the distribution (40.2%) and some students provide more than an argument. We also found biases, such as the equiprobability bias or erroneous beliefs about randomness. Finally, 22% of students were unable to provide a justification