1. There is a growing interest in the use of Bayesian methods for profiling institutional performance. Hospitals are evaluated based on the mortality rates for their cohort of acute myocarditis patients. These values depend significantly on the talent of the hospital's doctors and staff and their procedures. Across all hospitals and patients the average mortality is 9.9 per hundred thousand patients (i.e., a randomly sampled individual patient has a probability p = 0.0099% chance of dying from the disease). An acute myocarditis patient either lives or dies, so viewing these as 0 or 1 results, the standard deviation of an individual patient outcome is 0.99494% (which comes from the formula px (1 - p)). Some hospitals generate consistently lower patient mortality than others. The standard deviation of average mortality per patient across hospitals is 0.6 per hundred thousand. That is, a 2-sigma' top hospital has an average patient mortality of 8.7 per hundred thousand patients, while a 2-sigma' bottom hospital has a patient mortality of 11.1 per hundred thousand patients. The WellCare Hospital recently opened and had 2 of their first 1,000 acute myocarditis patients die. One newspaper ran a headline, "Wellcare's acute myocarditis die at a rate 20 the national average." Using Bayes formula, what is your estimate of true acute myocarditis mortality rate of the WellCare hospital, expressed as an average mortality per hundred thousand patients? Give your answer to three decimal places.