2. The world's smallest mammal is the Kitti's hog-nosed bat, with a mean weight of 1.5 grams and a standard deviation of 0.25 grams. Assume that the weights are normally distributed, answer the following questions. For full credit you must show a sketch of the standard normal distribution for each part, labeled, and the correct area shaded. (12 points)

a) Find the probability of randomly selecting a single bat that weighs between 1.45 grams and 1.70 grams. (4 points)

b) If we randomly select 49 bats, find the probability that the mean of the 49 bats will weigh between 1.45 grams and 1.70 grams, that is (4 points)

c) What does a Kitti's hog-nosed bat need to weigh to be in top 15% of all Kitti's hog-nosed bat? (4 points)