Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 11 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.32 gram. When finding an 80% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) zc = _______ (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) lower limit______ upper limit_____ margin of error____ (b) What conditions are necessary for your calculations? (Select all that apply.) uniform distribution of weights is known normal distribution of weights is unknown n is large (c) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.10 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) __________ hummingbirds.