= Solution
Under the target model $p_0=0.20$, the <normal approximation> gives
$$
\widehat p\approx N\left(0.20,\frac{0.20(0.80)}n\right).
$$
The pointwise 95% <binomial funnel control limits> are therefore
$$
\boxed{L(n)=\max\left(0,0.20-1.96\frac{0.40}{\sqrt n}\right),\qquad U(n)=\min\left(1,0.20+1.96\frac{0.40}{\sqrt n}\right).}
$$
Draw these curves around the horizontal 20% target, as in the figure. At $n=100$, the approximate limits are $0.1216$ and $0.2784$, so B and H are outside the nominal bands; that is a signal for investigation, not proof of inferior or superior care. The bands use the target <variance> rather than each hospital's observed rate. They are <control limits> for possible observations under the target model, not <confidence intervals> centered on the observed points.
Normal coverage is approximate, especially for the small hospitals; clipping does not repair that approximation. Exact binomial tail limits can be used if exact calibration is needed.
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