(24) POISSON DISTRIBUTION (3 pts each),. Consider a situation in which a researc
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Question
(24) POISSON DISTRIBUTION (3 pts each),. Consider a situation in which a researcher has set up an automated camera that records endangered ocelots as they pass the camera at night (they are nocturnal so filming them is otherwise difficult). Long term data indicates that the mean number of ocelots that pass by the camera each night is 3. Use a value of e-2.7 for your calculations and provide all answers to the nearest 0.001 (a) What is the probability that the camera does not record an ocelot during a given night? prob- (b) What is the probability that the camera records 3 ocelots during a given night? prob = (b) What is the probability that the camera records more than 5 ocelots during a given night? prob =Explanation / Answer
For Poisson:
P(x) = e- * x/x!
Where = 3 and e = 2.7
(a) P(0) = 2.7-3 * 30/0! = 0.051
(b) P(3) = 2.7-3 * 33/3! = 0.229
(c) P(X > 5) = 1 - [P(0) + P(1) + P(2) + P(3) + P(4)]
We have P(0) = 0.051 and P(3) = 0.229
P(1) = 2.7-3 * 31/1! = 0.152
P(2) = 2.7-3 * 32/2! = 0.229
P(4) = 2.7-3 * 34/4! = 0.171
Therefore P(X > 5) = 1 - [0.051 + 0.152 + 0.229 + 0.229 + 0.171] = 1 - 0.796 = 0.204
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