1. Suppose a certain species bird has an average weight of * = 3.10 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with o = 0.21 grams. For a small group of 13 birds, find the margin of error for a 75% confidence interval (Za/2 = 1.15) for the average weights of these birds. 2. Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. 1,247 1,254 1,224 1,207 1,151 1,280 1,271 1,283 1,233 Find a 95% confidence interval for the mean of all tree ring dates from this archaeological site. 3. Suppose a certain species bird has an average weight of *= 3.85 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with o = 0.31 grams. Find the sample size necessary for a 98% confidence level with a maximal error of estimate E = 0.09 for the mean weights of the hummingbirds