It is thought that there are 900 moose in the Yellowstone Park moose population

Question

It is thought that there are 900 moose in the Yellowstone Park moose population Last year 25 moose were captured and tagged. Six months later 100 moose are captured. Define the RV to be the number of tagged moose in the group of 100 most recently captured moose. We will assume that all moose are still living and that the population total has not changed. a. Name the probability distribution that can be appropriately used to find probabilities of Ax Be sure to specify values of any parameters b. What is the probabilit ty that 5 of the most recently captured moose are tagged? Leave your answer in formula form

Explanation / Answer

Solution:

(a) X follows Binomial(n = 100, p = 25/900 = 0.0277)

P(X = x) = 100Cx*(0.0277^x)*(1-0.0277)^(100-x), for x=0,1,2,...,300

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(b) So the probability is

P(X = 5) = 100C5*(0.0277^20)*(1-0.0277)^(100-5)

= 0.0851

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