A model in herding cats results in cats herding easily, herding mostly in the right direction, and not herding at all. Based on previous experiments, the proportion of cats that herd easily should be about .05, those that herd mostly in the right direction should be about .15, and those that just will not herd at all about .80. In the most recent experiment, conducted with 82 randomly selected cats, about 8 of cats herded easily, 12 herded mostly in the right direction, and 62 did not herd at all. Carry out a test to determine whether the previous cat herding model seems to hold in this setting. (8 points)

A company claims that its mixed nuts canisters contain 20% Brazil nuts, 20% cashews, 20% almonds, and 20% hazelnuts, and 20% peanuts. After discovering what seemed like 50% peanuts in a canister, a disgruntled customer counted the nut and sorted them by type. There were 512 nuts in the canister, which the following distribution: 185 peanuts, 75 Brazil nuts, 119 almonds, 60 hazelnuts and 73 cashews. Perform a goodness of fit test of the company's reported distribution and report your results. (8 points)