How Do You Calculate a Binomial Distribution Problem?

Biosyn
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Homework Statement



Find the value of Ʃn(18 n)(0.46)^2(0.54)^(18-n)
The sum is from n = 0 to n=18

Sorry, I do not know how to format it.



Homework Equations



I am using the Binomial Expansion Theorem:
4445cf49d9008c2cd8defb0dc7b83302.png


The Attempt at a Solution



Not sure where to start.

P = 0.46
Q = 0.54
n = 18
k = ?
 
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Biosyn said:

Homework Statement



Find the value of Ʃn(18 n)(0.46)^2(0.54)^(18-n)
The sum is from n = 0 to n=18

Sorry, I do not know how to format it.



Homework Equations



I am using the Binomial Expansion Theorem:
4445cf49d9008c2cd8defb0dc7b83302.png


The Attempt at a Solution



Not sure where to start.

P = 0.46
Q = 0.54
n = 18
k = ?

More generally,
(a+b)^N = \sum_{n=0}^N {N \choose n} a^n b^{N-n}.

RGV
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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