Monitoring the emerald ash borer. The emerald ash borer is a beetle that poses a serious threat to ash trees. Purple traps are often used to detect or monitor populations of this pest. In the counties of your state where the beetle is present, thousands of traps are used to monitor the population. These traps are checked periodically. The distribution of beetle counts per trap is discrete and strongly skewed. A majority of traps have no beetles, and only a few will have more than two beetles. For this exercise, assume that the mean number of beetles trapped is 0.4 with a standard deviation of 0.9. (a) Suppose that your state does not have the resources to check all the traps, so it plans to check only an SRS of n = 100 traps. What are the mean and standard deviation of the average number of beetles x in 100 traps?
(b) Use the central limit theorem to find the probability that the average number of beetles in 100 traps is greater than 0.5
(c) Do you think it is appropriate in this situation to use the central limit theorem? Explain your answer