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Q)

The mean of a binomial distribution is $5$ and its standard deviation is $2.$ Then the value of $n$ and $p$ are

\[\begin{array}{1 1}(1)\left(\frac{4}{5},25\right)&(2)\left(25,\frac{4}{5}\right)\\(3)\left(\frac{1}{5},25\right)&(4)\left(25,\frac{1}{5}\right)\end{array}\]

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A)
Given mean $np= 5$
Standard deviation $\sqrt {npq} =2$
$npq= 4$
$\large\frac{npq}{np}= \frac{4}{5} $
$q= \large\frac{4}{5}$
$p=1-q=1-\large\frac{4}{5}=\large\frac{1}{5}$
$np=5=n \times \large\frac{1}{5} $$=5$
$n=25$
$(n,p)$ is $(25,\large\frac{1}{5})$
Hence 4 is the correct answer.
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