Binomial Probabilities

 » Exact binomial probabilities » Approximation via the normal distribution » Approximation via the Poisson Distribution
The logic and computational details of binomial probabilities
are described in Chapters 5 and 6 of Concepts and Applications.

This unit will calculate and/or estimate binomial probabilities for situations of the general "k out of n" type, where k is the number of times a binomial outcome is observed or stipulated to occur, p is the probability that the outcome will occur on any particular occasion, q is the complementary probability (1-p) that the outcome will not occur on any particular occasion, and n is the number of occasions.

For example: In 100 tosses of a coin, with 60 "heads" outcomes observed or stipulated to occur among the 100 tosses,
 n = 100 [the number of opportunities for a head to occur] k = 60 [the stipulated number of heads] p = .5 [the probability that a head will occur on any particular toss] q = .5 [the probability that a head will not occur on any particular toss]

Show Description of Methods

To proceed, enter the values for n, k, and p into the designated cells below, and then click the «Calculate» button. (The value of q will be calculated and entered automatically). The value entered for p can be either a decimal fraction such as .25 or a common fraction such as 1/4. Whenever possible, it is better to enter the common fraction rather than a rounded decimal fraction: 1/3 rather than .3333; 1/6 rather than .1667; and so forth.

 n k p q

Parameters of binomial sampling distribution:

 mean = variance = standard deviation = binomial z-ratio = (if applicable)

 Method 1. exact binomial calculation Method 2. approximation via normal Method 3. approximation via Poisson Method 1. exact binomial calculation Method 2. approximation via normal Method 3. approximation via Poisson Method 1. exact binomial calculation Method 2. approximation via normal Method 3. approximation via Poisson

 For hypothesis testing One-Tail Two-Tail Method 1. exact binomial calculation Method 2. approximation via normal Method 3. approximation via Poisson

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