How to Work a Binomial Distribution Formula

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Statisticians use the binomial distribution formula to compute the probability of success of a particular incident. Every incident can either be a success or a failure. This formula calculates the odds of success of the incident.


Statisticians use the binomial distribution formula in a small sample size. The entire population is represented by "N" and the sample is represented by "n." The binomial distribution formula is used as a good estimation. There are few steps involved in the computation.

  • Understand the problem carefully. For example, the problem may ask you to compute the probability of customers buying a particular color of a product. The company may the produce the product in two colors and 70% of the customers may prefer one color over the other. The problem may ask you calculate the probability of sale of a particular color product from a sample size.

  • Determine what you are required to calculate. The variable is denoted by "X". In the same example, you may be required to calculate the number of people preferring a particular color from a sample size. Figure out your "N" (entire population), "n" (sample size), "X" (the variable for calculation) and "r" (number of trials.)

  • Convert the binomial variable into percentage form. Express the same problem in percentages. 70 percent of the population would prefer color 1 and 30 percent would prefer the second color.

  • Input figures into this formula : P(X = r) = nCr p r (1-p)n-r. With this, you would know the odds of a particular number of individuals preferring color 1 over color 2. If you wish to determine the odds for color 2, subtract the success rate of color 1 from 1.

Tips & Warnings

  • Please note that the summation of success rates for both the colors should always equal one. If the odds for success of color one are 0.639; the success rate for color 2 would be 0.361. That is 1- 0.639 = 0.361.

References

  • Photo Credit Creatas/Creatas/Getty Images
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