Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 14 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 4.00 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.30 gram.

When finding an 86% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)

z_c =

(a)Find an 86% 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.)

is known

normal distribution of weights

is unknown

n is large

uniform distribution of weights (c)Interpret your results in the context of this problem.

We are 86% confident that the true average weight of Allen's hummingbirds falls within this interval.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.86.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.14.

We are 14% confident that the true average weight of Allen's hummingbirds falls within this interval.

(d)Which equation is used to find the sample size n for estimating when is known?

Find the minimal sample size necessary for an 86% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round your answer to a whole number.)