Allen's hummingbird (selasphorus sasin) has been studied by zoologist bill alther.%u2020 suppose a small group of 20 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 %u03c3 = 0.24 gram.(a) find an 80% confidence interval for the average weights of allen's hummingbirds in the study region. (round your answers to two decimal places.)lower limit 1upper limit 2margin of error 3 (b) what conditions are necessary for your calculations? (select all that apply.)uniform distribution of weights%u03c3 is knownn is largenormal distribution of weights%u03c3 is unknown(c) give a brief interpretation of your results in the context of this problem. there is a 20% chance that the interval is one of the intervals containing the true average weight of allen's hummingbirds in this region. the probability that this interval contains the true average weight of allen's hummingbirds is 0.20. there is an 80% chance that the interval is one of the intervals containing the true average weight of allen's hummingbirds in this region. the probability that this interval contains the true average weight of allen's hummingbirds is 0.80.the probability to the true average weight of allen's hummingbirds is equal to the sample mean.(d) find the sample size necessary for an 80% confidence level with a maximal error of estimate e = 0.13 for the mean weights of the hummingbirds. (round up to the nearest whole number.)6 hummingbirds