In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 26 out of 855 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.
a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p.
b) Find a 99% confidence interval for p, and give a brief explanation of the meaning of the interval.
c) Is the normal approximation to the binomial justified in this problem? Explain.