3. An industry is considering the revision of its retirement policy and wants to estimate the proportion of employees that favor the new policy. The industry consists of 87 separate plants located throughout the United States. Because the results must be obtained quickly and with little cost, the industry decides to use cluster sampling with each plant as a cluster. A simple random sample of 15 plants is selected, and the opinions of the employees in these plants are obtained by questionnaire. The results are as shown in the accompanying table. Number favoring Number of employees, mi new policy, ai Plant 1 51 42 2 62 53 3 49 40 73 45 5 101 63 6 48 31 7 65 38 8 49 30 9 73 54 10 61 45 11 58 51 12 52 29 13 65 46 14 49 37 15 55 42 a. Estimate the proportion of employees in the industry who favor the new retirement policy, and place a bound on the error of estimation. b. The industry modified its retirement policy after obtaining the results of the survey. It now wants to estimate the proportion of employees in favor of the modified policy. How many plants should be sampled to have a bound of 0.08 on the error of estimation? Use the data above to approximate the results of the new survey.