In Part D, we return to the statistics question in Part A, based on the game of Push Penny: "After several practices of Push Penny, have you developed skill in playing the game?"
One approach is to compare the data (the 100 scores of a player) to the expected scores of a "random" player (one with no particular skill, who is making "random" pushes). This strategy requires a model for a "random" player, which must be based on probabilities, because there is randomness in the outcomes of the games.
A game consists of four pushes. First, you consider the probability that a single random push will hit a line. Experiment with a quarter on the Push Penny board to investigate this. The key is to discover that the lines are uniformly spaced (the distance between lines is equal to two times the diameter of a quarter). By moving a quarter perpendicularly to the lines, you'll discover that the coin is touching a line half of the time and not touching a line half of the time.
<< back to Part D: Are You a Random Player?