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1) The dormouse is the animal that has the longest hibernation. They sleep on average 210 days (around 7 months) at one time with a standard deviation of 6 days. The duration of the hibernation is normally distributed. Which values adopt and o in the formula of the standard distribution? a.) Calculate the probability that a dormouse sleeps less than 200 days. b.) Calculate the probability that a dormouse sleeps between 207 and 212 days. c.) Calculate the probability that the hibernation of a dormouse is unusally long or short. (20 days deviation from the standard value.) 2) In a study about beavers the scientists noticed that the beavers prefer birch trees over ash trees to build their dams. A beaver chooses a birch tree with the probability of 0.65, and an ash tree with p 0.35. a.) Which typ is the random variable that determines exactely how many birch trees the beaver chooses for the dam. b.) Assuming the beaver chops down 200 trees for its dam. Calculate the probability that at least 120 of them are birch trees using the central limit theorem. c.) How many trees does the beaver have to chop down so that we can be sure with the probability of 95% that at least 280 birch trees were felled. 3) Paleontologists assemble 5 fossils of an extinct animal. For each of them they measure the length of the humerus X and the femur Y in cm. a.) Complete the following table and then determine Var(X), Var(Y) and Cov(X,Y). i 3% VA (x.)2 (ar) 1 44 40 2 62 57 3 71 59 4 73 65 5 87 77 i. b.) After having determined dopt and bopt, determine the fuction for the optimal regression line given by y aspeX bopt. c.) Calculate the coefficient of the correlation between X and Y given by P and comment on the result. d.) Calculate the length which the model of the regression finds at point b) where the femur of an animal measures 53cm.

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