1. You are trying to determine the melting point of a new material, of which you have a large number of sam- ples. For each sample that you measure you ?nd a value close to the actual melting point c but corrupted by measurement error. We model this with random variables Mi = c + Ui where Mi is the measured value in degrees Kelvin, and Ui is the occurring random error. It is known that E[Ui] = 0 and Var(Ui) = 3, for each i, and that we may consider the random variable M1,M2,... to be independent. According to Chebyshev's inequality, how many samples do you need to measure to be 90% sure that the average of the measurements is within half a degree of c?