# Let a random variable X have a binomial distribution with mean $8$ and variance $4$. If $P\left ( X\leq 2 \right )=\frac{k}{2^{16}}$, then k is equal to :  Option 1) $137$ Option 2) $17$ Option 3) $121$ Option 4) $1$

$np=8$

$npq=4$

$q=\frac{1}{2}\: \: \: \: \: ,\: \: \: n=16$

$\Rightarrow p=\frac{1}{2}$

$P\left ( x=r \right )=^{16}C{_{r}}\left ( \frac{1}{2} \right )^{16}$

$P\left ( x\leq 2 \right )=\frac{16C_{0}+16C_{1}+16C_{2}}{2^{16}}$

$=\frac{137}{2^{16}}$

So, the value of $k=137$

Option 1)

$137$

Option 2)

$17$

Option 3)

$121$

Option 4)

$1$

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