March 31, Tuesday
Question 1: A statistician wants to estimate the mean height h (in meters) of a population, based on n independent samples X_1,X_2,...,X_n, chosen uniformly from the entire population. He uses the sample mean M_n = (X_1+X_2+...+X_n)/n as the estimate of h. It is also given that the standard deviation of the height of the population is 1 meter.
How large should n be so that the standard deviation of the sample mean M_n is at-most 1 centimetre?
The minimum value of 'n' so that the Chebyshev's inequality guarantees that the estimate is within 5 centimetres from 'h', with probability of at least 0.99.
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