Question 357981
n=30
p=0.8
q=0.2
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A) {{{P(25)=142506 *(0.8)^(25)*(0.2)^(5)=0.172279}}}
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B) {{{P(28)=435 *(0.8)^(28)*(0.2)^(2)=0.033656}}}
{{{P(29)=30*(0.8)^(29)*(0.2)^(1)=0.009285}}}
{{{P(30)=1*(0.8)^(30)*(0.2)^(0)=0.001238}}}
{{{P=P(28)+P(29)+P(30)=0.044179}}}
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C) Using EXCEL's BINOMDIST to generate all of the probability values from 0 to 30, then summing {{{x*P(x)}}},
{{{mu=sum(x*P(x),x=0,30))=24}}}
or 
{{{mu=n*p=30(0.8)=24}}}
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D) Again using EXCEL's BINOMDIST, the result from C), and then summing.
{{{VAR=sum((x-mu)^2*P(x))}}}
{{{sigma=sqrt(VAR)}}}
{{{sigma=2.19}}}
or
{{{sigma=sqrt(n*p*q)=sqrt(4.8)=2.19}}}