You want to determine the melting point c of a newmaterial. You have n specimens on each of which you make ameasurement of the melting point in degrees Kelvin, giving you adataset m1,…,mn. We model this withrandom variablesMi=c+Ui, whereUi is the random measurement error. It is knownthat E[Ui]=0 andVar(Ui)=9467 for each i, and that we mayconsider the random variables M1,M2,… asindependent.

A) According to Chebyshev's inequality, how many measurements do youneed to perform to be 90% sure that the average of the measurementsis within 28 degrees of c?

B) Continuing on fromthe previous question, now use the normal approximation (centrallimit theorem rule of thumb) to find a less conservative value forn. You can use that the 0.95 quantile of the standardnormal distribution is q(0.95)≈1.645.