The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is finite and strongly skewed, with standard deviation 0.7.
(a)What are the mean and standard deviation of the average number of moths in 50 traps?
(b)Use the central limit theorem to find the probability that the average number of moths in 50 traps is greater than 0.6.
