Binomial Distribution
What are the requirements for a binomial distribution?
- The procedure must have a set number of trials.
- The trials cannot be dependent on each other.
- Each trial can only have two possible results.
- 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