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Binomial vs Normal Distribution

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1) The main difference between the binomial and normal distributions is that the binomial distribution is a discrete distribution whereas the normal distribution is a continuous distribution.

This means that a binomial random variable can only take integer values such as 1, 2, 3, etc. whereas the normal variable can take any real number value such as 1.2 or 2.314, etc.

2) The second difference between them is that a binomial random variable has a finite range whereas the normal distribution has an infinite range.

A binomial random variable can only take finitely many values 1, 2,…., n. On the other hand, a normal random variable can take any value between minus infinity to plus infinity, and therefore its range is unbounded.

3) The binomial distribution is limited in its applications. It is only used in situations where a trial can have only two possible outcomes – success or failure. For example, when tossing a coin many times we use the binomial distribution to calculate probabilities (since tossing a coin has only two outcomes – heads or tails).

On the other hand, the normal distribution finds many applications in real-life situations such as modelling the height or weight distribution of a population. The normal distribution can in fact be used to calculate probabilities for binomial distribution using the method of the normal approximation to binomial.

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