Supplementary Exercise 5.14 of IPS7e
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Measurements of alcohol content in whiskey with sigma=10 (mg). 
Let Xmean = mean (or average) of 3 measurements.

(a) The rule for the standard variation of a mean says that
sd(Xmean) = sigma/sqrt(3) = 10/1.73 = 5.8 (mg).

Note that the terminology used in the exercise is the standard deviation
of the mean, but we could also have referred to this quantity as the 
standard error (of the mean).

(b) The standard deviation for the mean (or average) of n measurements 
is sigma/sqrt(n). Therefore, n=4 measurements are needed to obtain a
standard deviation of 5 (because 10/sqrt(4)=5). Formally, we
solve, with respect to n, the equation: 
  sigma/sqrt(n) = 5, or
  sqrt(n) = sigma/5, or
  n = (sigma/5)^2 = 2^2 = 4.

The average of several measurements has less random variation than a
single measurement, and is therefore a more precise (and in this sense, 
better) estimate of the population mean than a single measurement.

Our calculation in (b) will later on be one of our methods for sample
size calculation (Session 12).