1. The PM2.5 is an important index for air pollution. A PM2.5 index of over 100 is harmful. To decide if the air over an industry zone is harmful, one took PM2.5 readings at 35 randomly picked spots in the zone. The readings are
119, 120, 102, 94, 79, 119, 92, 85, 96, 120, 101, 84, 97, 115, 107, 125, 117, 98, 91, 80, 122, 108, 122, 111, 109, 90, 83, 101, 118, 107, 99, 80, 102, 97, 96.
Is the air in the industry zone harmful? Assume $\alpha=0.02$.
2. You are given a coin. You do not know if it is a fair coin or not. You want to figure out a way so that you can make a sound statement about the fairness of the coin.