Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 67.0 kg and standard deviation σ = 7.4 kg. Suppose a doe that weighs less than 58 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2750 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 64 kg. If the average weight is less than 64 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x

for a random sample of 40 does is less than 64 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that x < 68.4 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)

8)Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 12 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 σ = 0.24 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.σ is unknown

c.normal distribution of weights

d.n is large

e.σ is known

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

a.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.

b.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

c.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

d.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.

e.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

(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