Question

The sizes of animal populations are often estimated by using a capture-tag-recapture method. In this method k animals are captured, tagged, and then released into the population. Some time later n animals are captured, and Y, the number of tagged animals anong the n, is noted. The probabilities associated with Y are a function of N, the number of animals in the population, so the observed value of Y contains information on this unknown N. Suppose that k 4 animals are tagged and then released. A sample of n 3 animals is then selected at random from the same population. Find P(Y 1) as a function of N. What value of N will maximize P(Y = 1)? (a) Over the past year, a fertilizer production process has shown an average daily yield of 60 tons with a variance in daily yields of 100. If the yield should fall to less than 40 tons tomorrow, should this result cause you to suspect an abnormality in the process? (Calculate the probability of obtaining less than 40 tons.) What assumptions did you make concerning the distribution of yields? (b) The discharge of suspended solids from a phosphate mine is normally distributed with mean daily discharge 27 milligrams per liter (mg/L) and standard deviation 14 mg/L. In what proportion of the ays will the daily discharge be less than 13 mg/L?

Answer 1

Let