Central High School is curious about how many ninth-grade students in the district participate in band, choir, and athletics. Based on previous years, the statistics class came up with a model that shows 62% of ninth-grade students who participate in extracurricular activities will be in athletics. The data collected from this year is shown in the table. School Name Band Choir Athletics Total
Valley High 41 18 91 150
Central High 31 16 45 92
Logan High 27 12 64 103

Part A Identify the theoretical probability of participation in athletics, based on the model created by the statistics class. Then calculate the experimental probability that ninth graders will be in athletics for each of the three schools in the district.

Part B Compare the theoretical probability of the event with each experimental probability from part A. In each instance, are they the same? If they are different, which one is higher? By how much do they differ?

Part C Is this a valid model? Consider the differences in probability from part B. Are these differences significant enough to question the validity of the model? If so, explain some of the potential problems with this model.