Supplementary Exercise 5.14 of IPS7e
------------------------------------

Measurements of alcohol content in whiskey with sigma=10 (mg). 
X = average of 3 measurements.

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

(b) The standard deviation for the average X 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.

Our calculation in (b) will later on be one of our methods for sample
size calculation (Session 8).