Allen's hummingbird (Selasphorus sasin) has been studied byzoologist Bill Alther.† Suppose a small group of 14 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 ? = 0.20 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.) normal distribution of weights uniform distribution ofweights n is large ? is known ? is unknown (c) Interpret yourresults in the context of this problem. The probability to the trueaverage weight of Allen's hummingbirds is equal to the sample mean.The probability that this interval contains the true average weightof Allen's hummingbirds is 0.20. There is an 80% chance that theinterval is one of the intervals containing the true average weightof Allen's hummingbirds in this region. There is a 20% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in this region. The probability thatthis interval contains the true average weight of Allen'shummingbirds is 0.80. (d) Find the sample size necessary for an 80%confidence level with a maximal margin of error E = 0.15 for themean weights of the hummingbirds. (Round up to the nearest wholenumber.) ___hummingbirds