We are studying cluster sampling and I don't understand problem 8.24:

8 23 A large firm has its equipment inventories listed separately by department. From the 15 departments in the firm, 5 are to be randomly sampled by an auditor, who will then check to make sure that all equipment is properly identified and located. The proportion of in- ventory items not properly identified is of interest to the auditor. The data are given in the accompanying table. Estimate the proportion of inventory items in the firm not properly identified and place a bound on the error of estimation. Number of Number of items not equipment properly Department items identified 15 27 9 N - - WN 31 168.24 Suppose that for the firm discussed in Exercise 8.23 the 15 departments have the number of inventory items given in the accompanying table. Select a sample of three departments with probabilities proportional to number of inventory items. Number of Number of Department items Department items 12 31 9 10 26 27 11 22 40 12 19 DO JaUIAWN- 35 13 16 15 14 33 18 15 6 10