<s>[INST] I am working with a group of students in an introductory statistics course, and we are exploring the concept of probability. We are using the Free Throw Probability Experiment to explore the idea of probability in a real-world way. We have been recording shots and noting successes and failures of making shots. We are also calculating the percentage of successes and comparing that to our probability predictions. Now that we have some data, we need to discuss the concept of sampling distributions. We have the following data for our experiment:
Number of Trials: 25
Number Baskets Made: 15
Probability of Making a Shot: .60
P Value: 0.00016
We are trying to understand how the data we have collected relate to the concept of a sampling distribution. The students are having difficulty understanding how the data we have collected fit into the concept of the binomial distribution, and how that relates to a sampling distribution. Can you help us understand this relationship?[/INST]