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* = 63.0 kg and standard
deviation *σ* = 8.5 kg. Suppose a doe that weighs less than
54 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 2700 does, what number do you expect to
be undernourished in December? (Round your answer to the nearest
whole number.)

(c) To estimate the health of the December doe population, park
rangers use the rule that the average weight of *n* = 70
does should be more than 60 kg. If the average weight is less than
60 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 70 does is less than 60 kg
(assuming a healthy population)? (Round your answer to four decimal
places.)

(d) Compute the probability that *x* < 64.2 kg for 70
does (assume a healthy population). (Round your answer to four
decimal places.)

Suppose park rangers captured, weighed, and released 70 does in
December, and the average weight was *x* = 64.2 kg. Do you
think the doe population is undernourished or not? Explain.

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

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

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

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

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