In a binomial distribution, the probability of getting a success is $\frac{1}{3}$ and the standard deviation is 4. Then its mean is :
Answer & explanation
Correct answer: option 2
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, $μ=72×\frac{1}{3}=24$