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Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 10 Allen's hummingbirds has been under study in Arizona. The average weight for these birds in x= 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with a 0.20 gram (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 3.00 3.24 0.09 X X (b) What conditions are necessary for your calculations? (Select all that apply) normal distribution of weights a is known On is large a is unknown O uniform distribution of weights (c) Interpret your results in the context of this problem. We are 80% confident that the true average weight of Allen's hummingbirds falls within this Interval. We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.