here's a reference on binomial distribuion
http://stattrek.com/tables/binomial.aspx#distribution
the binomial distribution approximates the normal distribution when the number of trials is large the the probability of success or failure is not extreme.
the normal distribution is a bell shaped curve where the mean is in the middle and 50% of the values are below the mean and 50% of the values are above the mean.
the binomial distribution is based on the binomial.
this reference has a calculator.
you enter the probability of success and the number of trials and the number of successes and then hit the return.
it will look like it went and did your calculations for you but it didn't.
you have to click on the calculate button before it does its thing.
perhaps you don't even need to hit the return.
try it, you'll see what i mean.
i believe that the binomial distribution stems from the binomial expansion formula.
here's a link that explains that.
http://www.regentsprep.org/Regents/math/algtrig/ATP4/bintheorem.htm
the formula for determining the probability of x out of n successes is:
p(x) =
s is the probability of success.
f is the probability of failure.
x is the number of successes.
n is the total number in the sample.
nCx is the combination formula for the number of ways to get x things out of n things.
example:
n = 10
x = 3
s = .2
f = 1-s = .8
p(3) =
p(3) =
here's a table of data i created for this problem.
n = 10
x = 0 to 10
p(s) = .2
p(f) = .8
x p(x) 0 0.107374182 1 0.268435456 2 0.301989888 3 0.201326592 4 0.088080384 5 0.026424115 6 0.005505024 7 0.000786432 8 7.3728E-05 9 0.000004096 10 1.024E-07
here's a picture of the bar graph that was created from this data.
you can see that this bar graph approximates a normal distribution which is very similar to a binomial distribution.
any questions, write to dtheophilis@yahoo.com
hopefully this helps you understand better what the binomial distribution is and what it looks like.