Page 286 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 13: Binomial Probability Distribution

If a random variable satisfies the conditions of a theoretical probability distribution, then Notes
this distribution can be fitted to the observed data.
The knowledge of the theoretical probability distribution is of great use in the
understanding and analysis of a large number of business and economic situations.
Binomial distribution is a theoretical probability distribution which was given by James
Bernoulli.
An experiment consists of a finite number of repeated trials.
Each trial has only two possible, mutually exclusive, outcomes which are termed as a
‘success’ or a ‘failure’.
The probability of a success, denoted by p, is known and remains constant from trial to
trial. The probability of a failure, denoted by q, is equal to 1 – p.

Different trials are independent, i.e., outcome of any trial or sequence of trials has no effect
on the outcome of the subsequent trials.
The sequence of trials under the various above stated assumptions is also termed as
Bernoulli Trials.
The purpose of fitting a distribution is to examine whether the observed frequency
distribution can be regarded as a sample from a population with a known probability
distribution.
To fit a binomial distribution to the given data, we find its mean.

For a given value of p, which is neither too small nor too large, the distribution becomes
more and more symmetrical as n becomes larger and larger.
Binomial distribution is often used in various decision making situations in business.

Acceptance sampling plan, a technique of quality control, is based on this distribution.

13.5 Keywords

Binomial distribution: Binomial distribution is a theoretical probability distribution which
was given by James Bernoulli.
Experiment: An experiment consists of a finite number of repeated trials
Fitting of a binomial distribution: The fitting of a distribution to given data implies the
determination of expected (or theoretical) frequencies for different values of the random variable
on the basis of this data.
Posteriori inferences: These are the basis of results.

Priori considerations: These are the basis of given conditions.
Theoretical probability distribution: A theoretical probability distribution gives us a law
according to which different values of the random variable are distributed with specified
probabilities.

13.6 Review Questions

1. What do you understand by a theoretical probability distribution? How it is useful in
business decision-making?

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