Allen's hummingbird (Selasphorus sasin) has beenstudied by zoologist Bill Alther.† Suppose a small group of 13Allen's hummingbirds has been under study in Arizona. The averageweight for these birds is x = 3.15 grams. Based onprevious studies, we can assume that the weights of Allen'shummingbirds have a normal distribution, with ? = 0.36gram.

(a) Find an 80% confidence interval for the averageweights of Allen's hummingbirds in the study region. What is themargin of error? (Round your answers to two decimalplaces.)

lower limit:

upper limit:

margin of error:

(b) What conditions are necessary for your calculations?(Select all that apply.)

-? is known

-normal distribution of weights

-n is large? is unknown

-uniform distribution of weights

(c) Interpret your results in the context of thisproblem.

-The probability that this interval contains the true averageweight of Allen's hummingbirds is 0.20.

-The probability that this interval contains the true averageweight of Allen's hummingbirds is 0.80.

-The probability to the true average weight of Allen'shummingbirds is equal to the sample mean.

-There is a 20% chance that the interval is one of the intervalscontaining the true average weight of Allen's hummingbirds in thisregion.

-There is an 80% chance that the interval is one of theintervals containing the true average weight of Allen'shummingbirds in this region.

(d) Find the sample size necessary for an 80% confidencelevel with a maximal margin of error E = 0.12 for the meanweights of the hummingbirds. (Round up to the nearest wholenumber.)

________ hummingbirds