at one stage of a water treatment process the number of particles of foreign matter per litle in the water has a poisson distribution with a 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. twenty 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, whether or not there is evidence that the filter bed is failing to work properly
but what i don't get is, under h0, what is the mean of the poisson distribution? isn't it 200? but then that's to big to use the normal approximation...
I know what to do after that, I just can't seem to get the mean of the poisson distribution...