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Mathematics, 18.12.2021 04:00 Shybaby5019

A large lab has thousands of mice that are housed in cages with four mice each. The weights of a single randomly chosen mouse is 32 grams with a standard deviation of 4 grams. Of course mice in different cages are independent of each other. However, the correlation between the weights of two mice in the same cage is -0.2 (the correlation within a cage is slightly negative because when one mouse eats more others will then eat less). A random sample of 20 cages is selected. What is the expected value and standard deviation of the total weight of the 80 mice in t hose cages?

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