Binomial Distribution

What are the requirements for a binomial distribution?

  1. The procedure must have a set number of trials.
  2. The trials cannot be dependent on each other.
  3. Each trial can only have two possible results.
  4. The probability for each trial must remain the same.

Notations for Binomial Distribution

  • n: the number of total trials
  • p: the probability of success in only one trial
  • q: the probability of failure in only one trial (1 - p = q)
  • x: certain number of success in only one trial

Example of Binomial Distribution

47% of dog owners in America sleep with their dog. You randomly select 10 dog owners in America. What is the probability that 5 dog owners sleep with their dogs?

In the example...

  • p = .47
  • q = .53
  • n = 10
  • x = 5
  • P(5)= 10C5 * .47^5 * .53^5 = .242
  • Mean= n * p = 4.7
  • Varience= n * p * q = 2.49
  • Standard Deviation= (n * p * q)^1/2