9. Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does)from Mesa Verde park. Then x has a distribution that is approximately normal with u = 63.0 kg and standard deviation g= 7.1 kg. A doe is considered to be malnourished if it weighs less than 54 kg. a) If the doe population is healthy, what is the probability that a single doe captured, (weighed and released) at random weighs less than 54 kg? b) What is the probability that the mean weight of a random sample of 50 does is less that 54 kg if the does are healthy? c) It is thought that the deer in Yellowstone are larger than those in Mesa Verde. If a random sample of 36 does from Yellowstone has a mean weight of 64 kg, find a 95% confidence interval for the mean weight of Yellowstone does. Assume o= 7.1 kg. Show all calculations. d) Construct a hypothesis test to determine whether the Yellowstone does are, in fact, larger. Show all calculations. Use a 1% level of significance.