Let x be a random variable that represents the weightsin kilograms (kg) of healthy adult female deer (does) in Decemberin a national park. Then x has a distribution that isapproximately normal with mean μ = 60.0 kg and standarddeviation σ = 8.6 kg. Suppose a doe that weighs less than51 kg is considered undernourished.

(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 2900 does, what number do you expect tobe 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 = 65does should be more than 57 kg. If the average weight is less than57 kg, it is thought that the entire population of does might beundernourished. What is the probability that the average weightx for a random sample of 65 does is less than 57 kg(assuming a healthy population)? (Round your answer to four decimalplaces.)


(d) Compute the probability that x< 61 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= 61 kg. Do youthink the doe population is undernourished or not? Explain.

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

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

Since the sample average is below 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.