The concentration of a certain active agent in a liquid form of a pesticide must not exceed 12 parts per million. The pesticide is made up in batches in which the concentration varies normally between batches, with mean 8 parts per million and standard deviation 1-5 parts per million. What proportion of batches exceeds the permitted maximum? If two batches are mixed equally by volume the resulting concentration is the average of the two concentrations in the constituent batches. What proportion of such mixed samples exceeds the permitted maximum? What proportion falls below 3 parts per million (the level at which the pesticide cecases to have any effect)?

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