You've been hired by the Nevada Gaming Commission to look into a suspicious roulette wheel. This roulette wheel has 2 green slots among its 38 slots, and patrons have complained that green occurs too often. You plan to observe many spins and record the number of times that green occurs.
Your goal is to form a 95% confidence interval for the proportion of times green occurs with a margin of error no bigger than 0.005. How many spins do you plan to observe? Write a brief summary explaining your calculations.