[2] (30 points) During early evening mountain goats come down to water in a Montana location at a rate of 5 per hour. Consider each goat's arrival independent of the next with arrivals consistent with the rate of 5 per hour. Assume a Poisson model applies. [a] If there is a 3-hour block of time considered "early evening\" what is the probability that more than 10 goats will come down to water in those 3 hours? [b] Your instructor hasjust seen one goat but only has 15 an hour more before he must go. What is the probability that he fails to see another goat before leaving? [c] A new camera system purports to estimate an animal's height and weight from the image processed through its system. The concern is that excessive drought is limiting the supply of grasses and lichens at higher altitudes and that weights may be reduced from that expected for a given height. Height estimates are considered very good, so expected weight (from previous literature, based on height) will also be considered good. Camera-processed weight reliability is at question. Assume that weight difference from expected is distributed normally. Fifteen goats measured found that camera determined weight less expected weight had a mean and sample standard deviation of J? = 8.2 lb,s = 3.1 lb. Test the null hypothesis Hoill = 0 vs Ham