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 = 52.0 kg and standarddeviation σ = 9.0 kg. Suppose a doe that weighs less than43 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 2100 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 = 70does should be more than 49 kg. If the average weight is less than49 kg, it is thought that the entire population of does might beundernourished. What is the probability that the average weight

x

for a random sample of 70 does is less than 49 kg (assuming ahealthy population)? (Round your answer to four decimalplaces.)


(d) Compute the probability that

x

< 53.6 kg for 70 does (assume a healthy population). (Roundyour answer to four decimal places.)


Suppose park rangers captured, weighed, and released 70 does inDecember, and the average weight was

x

= 53.6 kg. Do you think the doe population is undernourished ornot? Explain.

Since the sample average is above the mean, it is quite unlikelythat the doe population is undernourished.Since the sample averageis above the mean, it is quite likely that the doe population isundernourished.    Since the sample average isbelow the mean, it is quite unlikely that the doe population isundernourished.Since the sample average is below the mean, it isquite likely that the doe population is undernourished.