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

24

The correct answer is Option (2) → 24

In a Binomial Distribution,

$σ=\sqrt{np(1-p)}$

$μ=np$

Probability of success = $P=\frac{1}{3}$

Standard Deviation = $σ=4$

$4=\sqrt{n×\frac{1}{3}×(1-\frac{1}{3})}$

$⇒\sqrt{\frac{2n}{9}}=4$

$⇒n=\frac{16×9}{2}=72$

∴ Mean, $μ=72×\frac{1}{3}=24$