Figure from the original question paper Figure from the original question paper Figure from the original question paper Figure from the original question paper Figure from the original question paper A supermarket manager claims that the average billing time for customers is 12 minutes with a known standard deviation of 3.5 minutes. To verify this claim, a random sample of 49 customers was studied, showing an average billing time of 12.9 minutes. Let the null and alternative hypothesis be: ; . Find the P-value. Enter the answer correct to two decimal places. Consider the samples {1, 3, 4, 6, 2} taken from a Poisson Distribution with an unknown parameter . Using a Gamma(5, 8) prior, find the posterior distribution of .