Question

If X is a binomial random variable associated with a binomial experiment with

Answer 1

For a binomial distribution over $n$ trials and with success probability $p$, the mean $\mu$ and standard deviation $\sigma$ ar such that

$\begin{cases}\mu=np\\\sigma=\sqrt{np(1-p)}\end{cases}$

$6=\sqrt{np(1-p)}\implies np-np^2=36$
$54=np\implies54-54p=36\implies p=\dfrac13$
$54=\dfrac n3\implies n=162$