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In a binomial distribution the probability of getting success is $\frac{1}{4}$ and the standard deviation is 3 . Then, its mean is
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2246 Upvotes
Verified Answer
The correct answer is:
$12$
Given that
$$
\begin{aligned}
p=\frac{1}{4} \text { and } q=1-\frac{1}{4} & =\frac{3}{4} \\
\mathrm{SD}=3 \Rightarrow \sqrt{n p q} & =3 \\
\Rightarrow \quad n p q & =9 \\
\Rightarrow \quad n \cdot \frac{1}{4} \cdot \frac{3}{4} & =9 \\
n & =48 \\
\text { Mean }=n p=48 \times \frac{1}{4} & =12
\end{aligned}
$$
$$
\begin{aligned}
p=\frac{1}{4} \text { and } q=1-\frac{1}{4} & =\frac{3}{4} \\
\mathrm{SD}=3 \Rightarrow \sqrt{n p q} & =3 \\
\Rightarrow \quad n p q & =9 \\
\Rightarrow \quad n \cdot \frac{1}{4} \cdot \frac{3}{4} & =9 \\
n & =48 \\
\text { Mean }=n p=48 \times \frac{1}{4} & =12
\end{aligned}
$$
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