An investigator wishes to estimate the average number of defects per board on boards of elec-tronic components manufactured for installation in computers. The boards contain varying numbers of components, and the investigator think that the number of defects should be positively correlated with the number of components on a board.Thus, pps sampling is used with the probability of selecting anyone board for the sample being pro- portional to the number of components on that board. A sample of n = 4 boards is to be selected from the N = 10 boards of one day's production. The number of components on each of the ten boards are 10, 12, 22, 8, 16, 24, 9, 10, 8, 31 show how to select n= 4 boards with probabilities proportional to size. After the sampling was completed, the number of defects found on boards 2, 3, 5, and 7 was respectively, 1, 3, 2 and 1. Estimate the average number of defects per board, and place a bound on the error of estimation.