An investigator collects data on the expenditure in a given week of each of 300 households. He rounds off the figures to the nearest pound and takes the average. Assuming that for any one household the error he thus makes is equally likely to have any value between plus and minus 10 shillings, find the standard deviation of the departure of his answer from the true average.
A factory makes components in the form of a rectangle whose length is intended to be twice its breadth. There is, however, a random error with standard deviation 0.1\% in the lengths; similarly, the breadths are distributed independently about a certain value with standard deviation 0.1\%. Find the percentage standard deviations of the perimeters and of the areas of the components produced.