One would use binomial distribution if and only if the experiment satisfies the following conditions
1. There is a fixed number of trials.
2. Each trial is independent of one another.
3. There are only two possible outcomes (a Success or a Failure).
4. The probability of success, p, is the same for every trial. An example of an experiment that has a binomial distribution would be a coin toss.
1. You would toss the coin a n (a fixed number) times.
2. The result of a a previous toss does not affect the present toss (trials are independent).
3. There are only two outcomes - Heads or Tails.
4. The probability of success (whether a head is considered a success or a tail is considered a success) is constant at 50%.
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It is necessary to use a continuity correction when using a normal distribution to approximate a binomial distribution because the normal distribution contains real observations, while the binomial distribution contains integer observations.
First i will explain the binomial expansion
Binomial distribution is the basis for the binomial test of statistical significance. It is frequently used to model the number of successes in a sequence of yes or no experiments.
Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution. Binomial is the most preliminary distribution to encounter probability and statistical problems. On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.
Two independent outcomes with constant probabilities.