Binomial Distribution

Criteria

All of these criteria must be met to use a Binomial Distribution

where x = Number of Successes; p = probability of success; n = number of trials; N = population size:

1. n independent trials

   1. If n is less than 10% of population size then independence can be assumed.

   2. If n < 0.10(N), Independent

2. Only two possible outcomes for each trial

3. p is the same for each trial

4. n is fixed

Equations

P(X = x) = nCx * p^x * (1-p)^(n-x)

P(X ≤ x) = Σ nCx * p^x * (1-p)^(n-x) for x = 0 to x

Normal Approximation of the Binomial

1. X= number of successes

2. The binomial criteria (shown above) are all satisfied

3. Large Counts Conditions -

   1. np ≥ 10 AND

   2. nq ≥ 10 = n(1-p) ≥ 10