Question

In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
(a) 6
(b) 8
(c) 12
(d) 10

Answer 1

(c) 12

$$\begin{gathered} p\mathit{}=\frac{1}{4} \\ \therefore q=1-\frac{1}{4}=\frac{3}{4} \\ \mathrm{Standard}\mathrm{deviation}=3 \\ \Rightarrow \mathrm{Variance}=3^2=9 \\ \text{Or}\mathit{}npq=9 \\ \Rightarrow \mathit{}np=\frac{\mathit{9}}{q} \\ =\frac{36}{3} \\ =12 \\ \mathrm{Therefore},\mathrm{the}\mathrm{mean}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{binomial}\mathrm{distribution}\mathrm{is}12. \end{gathered}$$