Allen's hummingbird (Selasphorus sasin) has been studied byzoologist Bill Alther.† Suppose a small group of 13 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 ? = 0.36 gram. When finding an 80% confidenceinterval, what is the critical value for confidence level? (Giveyour answer to two decimal places.) zc = (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.) ? is known ? is unknown uniform distribution ofweights normal distribution of weights n is large (c) Interpretyour results in the context of this problem. The probability thatthis interval contains the true average weight of Allen'shummingbirds is 0.80. The probability that this interval containsthe true average weight of Allen's hummingbirds is 0.20. Theprobability to the true average weight of Allen's hummingbirds isequal to the sample mean. There is a 20% chance that the intervalis one of the intervals containing the true average weight ofAllen's hummingbirds in this region. There is an 80% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in this region. (d) Which equationis used to find the sample size n for estimating ? when ? is known?n = z??E ? n = z??? E 2 n = z??E ? 2 n = z??? E Find the samplesize necessary for an 80% confidence level with a maximal margin oferror E = 0.10 for the mean weights of the hummingbirds. (Round upto the nearest whole number.) hummingbirds