Define X as the height in meters of a randomly selected Canadian, where the selection prob-
ability is equal for each Canadian, and denote E[X] by h. Bo is interested in estimating h.
Because he is sure that no Canadian is taller than 3 meters, Bo decides to use 1.5 meters as
a conservative (large) value for the standard deviation of X. To estimate h, Bo averages the
heights of n Canadians that he selects at random; he denotes this quantity by H.
(a) In terms of h and Bo’s 1.5 meter bound for the standard deviation of X, determine the
expectation and standard deviation for H.
(b) Help Bo by calculating a minimum value of n (with n > 0) such that the standard
deviation of Bo’s estimator, H, will be less than 0.01 meters.
(c) Say Bo would like to be 99% sure that his estimate is within 5 centimeters of the true
average height of Canadians. Using the Chebyshev inequality, calculate the minimum
value of n that will make Bo happy.
(d) If we agree that no Canadians are taller than three meters, why is it correct to use 1.5
meters as an upper bound on the standard deviation for X, the height of any Canadian
selected at random?
 
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