If $D\sim\operatorname{Bin}(n,p_0)$, the observed <binomial proportion> $\widehat p=D/n$ has <variance> $p_0(1-p_0)/n$. Consequently its <standard error> is proportional to $n^{-1/2}$. A common target therefore produces broad uncertainty at low volume and narrower uncertainty at high volume, forming the funnel-shaped envelope around the horizontal target. \b[The narrowing represents sampling precision, not a predicted change of <mortality> with volume.]

Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 38 / 5 / b / Solution

 Solution (source code)