Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† 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 = 0.34 gram. (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)
lower limit=
upper limit =
margin of error =

(b) What conditions are necessary for your calculations? (Select all that apply.)
a. uniform distribution of weights
b. normal distribution of weights
c. n is large
d. is unknown
e. is known

(c) Interpret your results in the context of this problem.
a. We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.
b. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
c. We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.
d. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.12 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds