Let x be a random variable that represents the weights inkilograms (kg) of healthy adult female deer (does) in December in anational park. Then x has a distribution that is approximatelynormal with mean μ = 50.0 kg and standard deviation σ = 8.6 kg.Suppose a doe that weighs less than 41 kg is consideredundernourished.

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

(b) If the park has about 2700 does, what number do you expectto be undernourished in December? (Round your answer to the nearestwhole number.) does

(c) To estimate the health of the December doe population, parkrangers use the rule that the average weight of n = 65 does shouldbe more than 47 kg. If the average weight is less than 47 kg, it isthought that the entire population of does might be undernourished.What is the probability that the average weight x for a randomsample of 65 does is less than 47 kg (assuming a healthypopulation)? (Round your answer to four decimal places.)

(d) Compute the probability that x < 51.6 kg for 65 does(assume a healthy population). (Round your answer to four decimalplaces.)

Suppose park rangers captured, weighed, and released 65 does inDecember, and the average weight was x = 51.6 kg. Do you think thedoe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikelythat the doe population is undernourished.

Since the sample average is above the mean, it is quite likelythat the doe population is undernourished.

Since the sample average is below the mean, it is quite unlikelythat the doe population is undernourished.

Since the sample average is below the mean, it is quite likelythat the doe population is undernourished.