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A statistician wants to estimate the mean height h (in meters) of a population, based on n independent samples X1,...,Xn, chosen uniformly from the entire population. He uses the sample

mean M = (X1+... + Xn)/n as the estimate of h, and a rough guess of 1.0 meters for the standard deviation of the samples X. ) (5 points) How large should n be so that the standard deviation of Ma is at most 1 centimeter? (5 points) How large should n be so that Chebyshev's inequality guarantees that the estimate is within 5 centimeters from h, with probability at least 0.99? (5 points) The statistician realizes that all persons in the population have heights between1.4 and 2.0 meters, and revises the standard deviation figure that he uses based on the bound of Example 5.3 (pg. 268 in the textbook, the derivation that was emailed out to everybody last week.) How should the values of n obtained in parts (a) and (b) be revised?

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