In a binomial distribution, the probability of getting a success is \(\displaystyle\frac{1}{3}\) and the standard deviation is 4. Then its mean is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24
For a binomial distribution, mean \(= np\) and variance \(= npq\). Here \(p = \frac{1}{3}\), \(q = \frac{2}{3}\) and the variance is \(4^{2} = 16\):
\( \displaystyle n \times \frac{1}{3} \times \frac{2}{3} = 16 \)
\(n = 72\)
\( \displaystyle \text{mean} = np = 72 \times \frac{1}{3} = 24 \)