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(D) Given that the probability of success is $p = \frac{1}{4}$.Then, the probability of failure is $q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4}$.The sta

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$12$

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(D) Given that the probability of success is $p = \frac{1}{4}$.Then, the probability of failure is $q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4}$.The standard deviation $(SD)$ of a binomial distribution is given by $\sqrt{npq} = 3$.Squaring both sides, we get $npq = 9$.Substituting the values of $p$ and $q$:$n 	imes \frac{1}{4} 	imes \frac{3}{4} = 9$$n 	imes \frac{3}{16} = 9$$n = 9 	imes \frac{16}{3} = 3 	imes 16 = 48$.The mean of a binomial distribution is given by $np$.Mean $= 48 	imes \frac{1}{4} = 12$.

In a binomial distribution, the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Then, its mean is

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