17) An agriculturalist on a farm conducted a study to investigate whether ladybugs are effective in reducing damage caused by moths to the fruit of avocado trees. The agriculturalist randomly sampled 66 avocado trees from the farm and paired them based on size. One tree from each pair was randomly assigned to a greenhouse with ladybugs, and the other tree in the pair was assigned to a greenhouse without ladybugs. After one month, the number of damaged avocado fruit on each tree was recorded. All other variables were held constant over the one month period. The difference in the number of damaged avocado fruit per tree (without ladybugs minus with ladybugs) was calculated for each of the 33 pairs and is shown in the stemplot. DIFFERENCE IN NUMBER OF DAMAGED AVOCADO FRUIT PER AVOCADO TREE PAIR (without minus with) -3 0589 -2 3 7 7 8 9 0 0 0589 10279 6 6 2 244 2 3 4 5 0 2 Key: 5 | 2 = 52 Damaged Avocado Fruit a) Explain what a positive difference indicates in the context of the study. b) What type of experimental design did the agriculturalist use? c) Consider a scenario in which 5 tree pairs are randomly selected one at a time, with replacement, from the sample of 33 tree pairs. Let the random variable A represent the number of tree pairs out of the 5 selected with a positive difference in the number of damaged avocado fruit. i) What is the expected count of A? ii) What is the probability that at least 4 out of 5 trees have a positive difference