The requirements are that there are repeated trials of the same experiment, that each trial is independent and that the probability of success remains the same.
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is median a chafractoristic of population
For the binomial, it is independent trials and a constant probability of success in each trial.For the Poisson, it is that the probability of an event occurring in an interval (time or space) being constant and independent.
No, in general is not. It is only symmetric if the probability of success in each trial is 0.5
It models the outcome of a number of independent trials in which each trial has only one outcome [that is of interest] with a constant probability of that outcome. There are random processes that meet these requirements exactly as well as others that may be approximated by the distribution.
The binomial distribution can be approximated with a normal distribution when np > 5 and np(1-p) > 5 where p is the proportion (probability) of success of an event and n is the total number of independent trials.