Mean and standard deviation of binomial

$P(x)={_n}C_x \;P^x(1-p)^{n-x}$

$n$: number of trials

$x$: number of success in n trials

$p$: probability of success in each trial

$P(x)$: probability of getting $x$ successes (out of $n$ trials)

$\cdot$ binomialpdf $(n,p,x)$

$\cdot$ $\mu=np$

$\cdot$ $\sigma^2=np(1-p)$

$\cdot$ $\sigma= \sqrt{np(1-p)}$

Range Rule of Thumb (Usual VS. Unusual):
$\cdot$ maximum usual value $= \mu+2\sigma$
$\cdot$ minimum usual value $= \mu-2\sigma$