Question: Suppose that a second random sample of 20 days reveals an average of 5,020 barrels and standard deviation of 650. Create a new 95% HPD credible set.
Problem: An article in Forbes discusses the problem of oil and gas reserves around the world.6 Forecasting the amount of oil available is difficult. If the average number of barrels that can be pumped daily from an oil field is a normal random variable with mean 7,200 barrels and standard deviation 505 barrels, and a random sample of 20 days reveals a sample average of 6,100 barrels and standard deviation of 800, give a 95% highest-posterior-density credible set for the average number of barrels that can be pumped daily.