Hypothesis

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Hi,
The question i was working on:
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 percent of foreign matter.

The Manager of the Treatment works orders a study into the effectiveness of this filtration bed. Twenty samples each of one litre, are taken from the water and 64 particles of foreign matter are found.
Using a suitable approximation test, at the 5 perecent level of significance, whether or not there is evidence that the filter bed is failing to work properly.

I understand you use a normal but im just wondering in X is distributed poisson with mean 2.5 to represent water after filtering and you do 64/20 to find the mean in the samples which comes to 3.2. Is the reason you cannot see if the probability that X is greater than or equal to 3.2 is less than 0.05 the fact that in this case X is actaully a continous variable and you cannot just equate it to x being greater than or equal to four.

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