Allen's hummingbird (Selasphorus sasin) has been studied byzoologist Bill Alther.† Suppose a small group of 20 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 = 0.22 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.) (b) What conditions are necessary for yourcalculations? (Select all that apply.) -n is large -σ is known -σis unknown -normal distribution of weights -uniform distribution ofweights (c) Interpret your results in the context of this problem.-The probability to the true average weight of Allen's hummingbirdsis equal to the sample mean. -There is a 20% chance that theinterval is one of the intervals containing the true average weightof Allen's hummingbirds in this region. -There is an 80% chancethat the interval is one of the intervals containing the trueaverage weight of Allen's hummingbirds in this region. -Theprobability that this interval contains the true average weight ofAllen's hummingbirds is 0.20. -The probability that this intervalcontains the true average weight of Allen's hummingbirds is 0.80.(d) Find the sample size necessary for an 80% confidence level witha maximal margin of error E = 0.15 for the mean weights of thehummingbirds. (Round up to the nearest whole number.) ______hummingbirds