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.

1. What is the standard deviation \({{\sigma }_{{\bar{X}}}}\) of Antonio's mean result?
2. How many times must Antonio repeat the measurement to reduce the standard deviation of \(\bar{X}\) to 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.

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