Allen's hummingbird (Selasphorus sasin) has been studied byzoologist Bill Alther.† Suppose a small group of 17 Allen'shummingbirds has been under study in Arizona. The average weightfor these birds is x = 3.15 grams. Based on previous studies, wecan assume that the weights of Allen's hummingbirds have a normaldistribution, with σ = 0.38 gram. (a) Find an 80% confidenceinterval for the average weights of Allen's hummingbirds in thestudy region. What is the margin of error? (Round your answers totwo decimal places.) lower limit upper limit margin of error (b)What conditions are necessary for your calculations? (Select allthat apply.) n is large normal distribution of weights σ is unknownσ is known uniform distribution of weights (c) Interpret yourresults in the context of this problem. The probability that thisinterval contains the true average weight of Allen's hummingbirdsis 0.80. The probability that this interval contains the trueaverage weight of Allen's hummingbirds is 0.20. The probability tothe true average weight of Allen's hummingbirds is equal to thesample mean. There is an 80% chance that the interval is one of theintervals containing the true average weight of Allen'shummingbirds in this region. There is a 20% chance that theinterval is one of the intervals containing the true average weightof Allen's hummingbirds in this region. (d) Find the sample sizenecessary for an 80% confidence level with a maximal margin oferror E = 0.12 for the mean weights of the hummingbirds. (Round upto the nearest whole number.) hummingbirds