Let a random variable X have a binomial distribution with mean 8 … - Vidyadip

MCQ

Let a random variable $X$ have a binomial distribution with mean $8$ and variance $4$. If $P\left( {X \le 2} \right) = \frac{k}{{{2^{16}}}}$, then $k$ is equal to

A
$17$
✓
$137$
C
$1$
D
$121$

✓

Answer

Correct option: B.

$137$

b
$\mathrm{np}=8$

$\mathrm{npq}=4$

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

$n=16$

$p(x=r)=^{16} C_{r}\left(\frac{1}{2}\right)^{16}$

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

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

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