Measurements on the weight of a lump of metal are believed to be independent and identically dis- tributed; each measurement has mean 12 grams and standard deviation 1.1 gram. a) Find the chance that a single measurement is between 11.8 and 12.2 grams, assuming that individual measurements are normally distributed. b) Estimate the chance that the average of 100 measurements is between 11.8 and 12.2 grams. For this calculation, is it necessary to assume that individual measurements are normally distributed? Explain.

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