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, variance = npq and mean = np. Here
\( \displaystyle p=\frac{1}{3},\quad q=\frac{2}{3} \)
Standard deviation 4 means variance 16:
\( \displaystyle n\times\frac{1}{3}\times\frac{2}{3}=16 \)
\(2n=144,\quad n=72\)
Mean:
\( \displaystyle np=72\times\frac{1}{3}=24 \)
Tip: The standard deviation is \(\sqrt{npq}\); square it before equating to npq.