If the mean of a binomial distribution is 24 and its standard deviation is 4, then the probability of getting success is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{3}$
In binomial distribution, the mean (μ) and standard deviation (σ) is,
$μ=n×p$ [n = Number of trials]
$σ=\sqrt{n×p×(1-p)}$ [p = probability of success]
and,
$np=24$
$σ=4$
$∴σ^2=np(1-p)$
$⇒16=24(1-p)$
$⇒p=1-\frac{2}{3}=\frac{1}{3}$