Question

If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.

Answer 1

$$\begin{gathered} \text{S}\mathrm{tandard}\mathrm{deviation}\text{of the binomial distribution}=4 \\ \mathrm{Variance}={\left(\mathrm{Standard}\mathrm{deviation}\right)}^2 \\ \mathrm{Variance},\text{i.e.}npq=16 \\ \mathrm{Mean}=np=20 \\ \Rightarrow q=\frac{16}{20}=\frac{4}{5} \\ \text{and}p=1-q=\frac{1}{5} \end{gathered}$$