Past exam of the mathematics course of the University of Cambridge 2004 iii Paper 38 5 c Solution Created 2026-10-03 Updated 2026-10-14
Under the target model , the normal approximation givesThe pointwise 95% binomial funnel control limits are thereforeDraw these curves around the horizontal 20% target, as in the figure. At , the approximate limits are and , 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.