The output of a certain integrated- circuit production line is checked daily by inspecting a sample of 100 units. Over a long period of time, the process has maintained a yield of 80 percent, that is, a proportion defective of 20 percent, and the variation of the proportion defective from day to day is measured by a standard deviation of 0.04. If on a certain day the sample contains 38 defectives, find the mean of the posterior distribution of as an estimate of that day’s proportion defective. Assume that the prior distribution of T is a beta distribution.