Question

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

• A. 17
• B. 1
• C. 121
• D. 137

Answer 1

Answer: (D)

$np = 8 $
$ npq = 4 $
$ q = \frac{1}{2} \Rightarrow \; p = \frac{1}{2} $
$ n = 16 $
$ p\left(x=r\right) = ^{16}C_{r} \left(\frac{1}{2}\right)^{16} $
$ p\left(x\le2\right) = \frac{^{16}C_{0} + ^{16}C_{1} +^{16}C_{2}}{2^{16}} $
$ = \frac{137}{2^{16}} $