If the mean of a binomial distribution is 12 and its standard deviati…

The correct answer is Option (1) → 18

For a binomial distribution B(n, p), the mean is np and the variance is npq, where q = 1 − p.

    \(np = 12\)
    \(npq = 2^2 = 4\)

Dividing the second equation by the first:

    \( \displaystyle q = \frac{4}{12} = \frac{1}{3} \)

    \( \displaystyle p = 1 - \frac{1}{3} = \frac{2}{3} \)

So

    \( \displaystyle n = \frac{12}{p} = 12 \times \frac{3}{2} = 18 \)

Tip: The standard deviation is given, not the variance: square it first (npq = 4, not 2).