A binomial distribution can be considered as the probability of either success or failure outcome in an experiment that is repeated multiple times. In the binomial distribution, two possible outcomes impact the result of the whole experiment. For example, a coin is tossed 10 times which has only two possible outcomes: heads or tails. A class with 20 students is divided based on short and tall height. By using a binomial calculator you can easily sort your data into reliable results and implement further equations.
However, there are a few basic details that you must know while working with the binomial distribution method. There are 4 significant conditions that your data must meet before labeling as binomial.
- The trial number should be fixed.
- Every trial must have only two outcomes i.e. pass or fail.
- The outcomes of trials must be independent of each other i.e. outcome of one trial must not influence the outcome of other trials.
- The probability of success must be the same for each trial.
If an experiment follows all these conditions, you can say that the random variable is binomial.
Now, here comes the question of what are the conditions that explain when a random variable is not binomial:
When the number of variables is changing:
Suppose that you are going to conduct a test a fair test until you get the results as a pass for 5 times. And you keep the record of each pass and fail until you achieve the desired goal. Here the no. of test conducted is = x.
In this case, the experiment might seem to satisfy the condition of binomial calculator like 0.5 probability of pass and fail on each trial, each test trial has only two outcomes that are either pass or fail and the test are conducted fair and none of the tests influences the other. However, if you look carefully, the trial is not counting the number the pass it’s counting the no. of test till you get 4 tests passed. The experiment is not meeting the 1st condition as the no. of tests is uncertain. Here the number of passes is fixed rather than the number of tests.
If there are more than two outcomes:
Say if you are conducting a test of 40 students and concluding the result based on grades where grade A include the students with distinction and percentage of 85% to 90%, grade b include the students between the percentage 75% t0 85% and the grade c include the percentage between 65% to 75%.
In this situation, the experiment meets the condition of probability, independence, and limit of no. of trial. Yet, it fails to meet the condition that asks for only two outcomes that are either pass or fail. Here the outcomes are A, B, and C grade.
On the other hand, if you modify the above situation and looking for no. of students out of 40 falls in grade A. you binomial calculator will except this situation as here you are only considering whether the students fall for A grade or not.
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