It is estimated that 20% of students take an active part in a sports club in college. If 20 students are randomly sampled and asked if they are active participants in a college sports club what is the probability that more than 4 are active in a sports club?
So I am setting this up as a binomial and finding '1 - (p(0)+p(1)+p(2)+p(3)+p(4))'
However the N value is 20. Is there a simpler way of determining this?
I'm not sure why N=20 is bothering you.
Hopefully you got these:
$P(0)=\begin{pmatrix}20\\0\end{pmatrix}0.2^00.8^{20}$
$P(1)=\begin{pmatrix}20\\1\end{pmatrix}0.2^10.8^{19}$
$P(2)=\begin{pmatrix}20\\2\end{pmatrix}0.2^20.8^{18}$
......
You'll have to use calculator anyway.