SOLUTION: Recently missed a week of my statistics class,. Looking for help on the proper way to figure out a problem similar to this one:binomial distribution: consider the following data

Question 886154: Recently missed a week of my statistics class,. Looking for help on the proper way to figure out a problem similar to this one:binomial distribution: consider the following data to be normally distributed. 80% of the people surveyed indicated they like the color blue. Find the probability that
8 out of 11 randomly surveyed people will like the color blue.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for binomial probability is:
p(x) = nCx * p^x * q^(n-x)
in your problem:
x = 8
n = 11
nCx = 11C8
p^x = .8^8
q^(n-x) = .2^3
your formula becomes:
p(8) = 11C8 * .8^8 * .2^3
that probability becomes:
p(8) = 165 * .8^8 * .2^3 which is equal to .2214592512

nCx is the combination of n things taken x at a time.
the formula for nCx is:
nCx = n! / ((n-x)! * x!)

when n = 11, there are 12 distinct sets of probabilities.
they range from p(0) to p(11).

the sum of all probabilities must be equal to 1 or you did something wrong.

here's a list of all the probabilities for this problem.
as you can see, the total sum of all probabilities is equal to 1.

$$$

here's a link that explains binomial probabilities.

http://www.regentsprep.org/Regents/math/algtrig/ATS7/BLesson.htm
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