Question: Measurements in the lab. Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is \(\sigma=10\) milligrams. Juan repeats the measurement 3 times and records the mean \(\bar{x}\) of his 3 measurements.

1. What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 3 measurements and averaging them, what would be the standard deviation of all his \(\bar{x}\) 's?)
2. How many times must Juan repeat the measurement to reduce the standard deviation of \(\bar{x}\) to 5? 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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