Averages of several measurements are less variable than individual measurements. The true mass of the whiskey sample is 4.6 grams, or 4600 milligrams(mg). Antonio’s measurements have the normal distributionwith mean4600 mg and standard deviation10mg. In this case, the mean of his 3 measurements also has a normal distribution.
(a) Sketch on the same graph the two normal curves, for individual measurements and for means of 3 measurements.
(b) What is the probabilitythat Antonio misses the true mass by more than 10 mg in either direction if he makes one measurement?
(c) What is the probability that the mean of three independent measurements misses the true mass by more than 10 mg?
The solution uses a normally distributed statistic relating to whiskey to show that an average number of measurements is better than an individual measurement.