At one stage of a water treatment process the number of particles of foreign matter per litre present in the water has a poisson distribution with mean 10. The water then enters a filtration bed which should extract 75% of foreign matter. The manager of the treatment works orders a study into the effectiveness of this filtration bed. 20 samples, each of 1 litre, are taken from the water and 64 particles of foreign matter are found. Using a suitable approximation test, at the 5% level of significance, weather or not there is evidence that the filter bed is failing to work properly.