Question: In the context of problem, a second random sample of 15 diners is asked to rate the foie gras, giving a mean rating of 95 and standard deviation of 1. Incorporate the new information to give a posterior distribution that accounts for both samplings and the prior distribution. Give a 95% HPD credible set for mean rating.
Problem: Claude Vrinat, owner of Taillevent-one of Europe's most highly acclaimed restaurants-is reported to regularly sample the tastes of his patrons. From experience, Vrinat believes that the average rating (on a scale of 0 to 100) that his clients give his foie gras de canard may be viewed as normally distributed with mean 94 and standard deviation 2. A random sample of 10 diners gives an average rating of 96 and standard deviation of 1. What should be Vrinat's posterior distribution of average rating of foie gras de canard, assuming ratings are normally distributed?