2. [44 points] We seek to estimate the proportion (and also the total number) of defective ball pens in a shipment of pens. The shipment contains 60 packs of pens. Some packs contain 3 pens, some 4 pens, some 6 pens, some 12 pens. We draw a simple random sample of 6 packs from the 60, and find the following data: Pack ABCDEF Number of pens 3 12 4 4 6 3 Number of defective pens 1 2 0 1 2 0 (1) [8 points] Estimate the total number of defective ball pens in the shipment. (2) [8 points] Place a bound on the error of estimation in Question (1).(3) [8 points] Estimate the proportion of defective ball pens in the shipment. (4) [8 points] Place a bound on the error of estimation in Question (3).(5) [6 points] Use the sample data above to find the appropriate sample size needed to estimate the proportion of defective ball pens with a bound of 5% on the error of estimation. (6) [6 points] If you knew that there were 300 pens in the shipment, use this additional information to give a different estimate than in Question (3), of the proportion of defective ball pens in the shipment, and place a bound on the error of estimation