probability distribution

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I would really be grateful if someone could answer me promptly. I believe i should use the poisson distribution model because that is the suitable one however i cannot satisfy the condition of 'specified interval' which is the case for poisson. I cannot also find the average mean and calculate probability. so i thought of binomial but again the same probability condition is not satisfied.

I am very much sure that this is related to Probability distribution but which model that i am not finding out.

Can anyone help me out?

thank you in advance

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The number $X$ of dust particles in the filters is a discrete random variable that counts number of occurances (dust particles) in a specified interval (filter). Thus, it is a reasonable assumption that it can be probabilistically described by the Poisson distribution.