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3. [10.3 Points] DETAILS BBUNDERSTAT12 7.1.015.FB. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Allen's hummingbird (Seiasphorus sasin) has been studied by zoologist_Bill Altherfr Suppose a small group of 17 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' = 0.40 gram. (3) Find an 80% condence 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 I upper limit I margin of error I (b) What conditions are necessary for your calculations? (Select all that apply.) [:I uniform distribution of weights D normal distribution of weights D J is unknown [:1 cr is known '3 n is large {c} Interpret your results in the context of this problem. 0 We are 20% condent that the true average weight of Allen's hummingbirds falls within this interval. 0 The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. 0 We are 80% condent that the true average weight of Allen's hummingbirds falls within this interval. (d) Find the sample size necessary for an 80% condence level with a maximal margin of error E = 0.07 forthe mean weights of the hummingbirds. (Round up to the nearest whole number.) I:I hummingbirds