Question: Antonio measures the alcohol content of whiskey for his Chemistry 101 lab. He actually measures the mass of 5 milliliters of whiskey—a chemical calcu­lation then finds the percent alcohol from the mass. The standard deviation of students' measurements of mass is \(\sigma \) = 10 milligrams (mg). Antonio repeats the measurement 3 times and records the mean x of his 3 measurements.

(a) What is the standard deviationof Antonio's mean result?

(b) How many times must Antonio repeat the measurement to reduce the standard deviation ofto 5 mg? Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.