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Normal Approximation to the Binomial Distribution

Binomial distribution is a experiment that has fixed number of trials and has two types of outcomes: either success or failure. It is a discrete probability distribution.
On the other hand, normal distribution is a continuous distribution. It is represented by a bell-shaped curve.

Binomial distribution is often approximated to normal distribution. If a binomial distribution has a large number of trials and if success is scored as 1 and failure is scored as 0, then binomial distribution represents a very smooth curve that is quite same as normal distribution curve. This concept is called normal approximation to the binomial function.

The normal approximation of binomial distribution is shown in the following figure below:

Normal Binomial Distribution
Where, blue-colored strips show binomial probability function, while smooth curve represents normal distribution. Here, normal distribution curve is imposed on binomial function. We can say that binomial distribution here is normally approximated.

Conditions for Normal Approximation to Binomial Distribution

There are following conditions for binomial distribution to be normally approximated:

  • Total number of trials, i.e. the value of "n" is large enough.
  • The probability of success (p) is near to 0 or 1. For example - 0.08, 0.04 etc.
  • Total probability in each trial must be 1.
  • All the conditions of binomial distribution must be satisfied.
  • The product of number of trials and probability of success should be greater than or equal to 1, i.e. np $\geq$ 1.
  • The product of number of trials and probability of failure should be greater than or equal to 1, i.e. nq $\geq$ 1

Related Calculators
Cumulative Normal Distribution Calculator Binomial Distribution Calculator

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