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$X$ ~ $B(n,p)$
$X$ = the number of successes in $n$ independent trials
$n$ = the number of independent trials
$X$ takes on the values $x=$ 0,1, 2, 3, ..., $n$
$p$ = the probability of a success for any trial
$q$ = the probability of a failure for any trial
$p+q=1\phantom{\rule{15pt}{0ex}}q=1-p$
The mean is $\mu =\mathrm{np}$ . The standard deviation is $\sigma =\sqrt{\mathrm{npq}}$ .
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