Determine the probability using Posterior distributions and their mean, standard deviation, accounting for uncertainty.

~ . . . . . . selected The percentage p oldetective items in a large lot is to be estimated. Items are randomly from the lot and are teste . . . - ' is d. The outcome from the test is an indication of whether the item imperfect such that there is 0.06 probability that a truly defective item will pass the ICSI and there is 0.04 probabi 1in that a truly non-defective item will fail the test. . - - 55 this 3) Determine the probability that a randomly selected item Wlll fail the test. EXPre probability as a Function ofp. ' ' no rior b) Suppose three items are tested of'which two pass and one fails. Assuming p - - - ' i 5 mean and information is available, determine the posterior distribution ofp and I standard deviation. ' ' ' t 'tem to be c) Using the posterior distribution ofp, deterrnine the probability that the nex 1 tested will fail. Fully account for the uncertainty in p