In a binomial distribution, the probability of getting success is $\frac{1}{4}$ and standard deviation is 3. Then it's mean is :

12

The correct answer is Option (3) → 12

$μ=np$

Variance: $σ^2=np(1-p)$

$σ=\sqrt{np(1-p)}=3$

$p=\frac{1}{4},q=\frac{3}{4}$

$\sqrt{npq}=\sqrt{n.\frac{3}{16}}=3$

$\frac{3n}{16}=9$   (squaring both side)

$3n=144$

$n=48$

$μ=48×\frac{1}{4}=12$