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 = 8.6 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 2300 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 = 45 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 45 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 45 does (assume a healthy population). (Round your
answer to four decimal places.)
Suppose park rangers captured, weighed, and
released 45 does in December, and the average weight
was x = 68.4 kg. Do you think the
doe population is undernourished or not? (Circle answer below)
Since the sample average is above the mean, it is quite likely
that the doe population is undernourished.
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 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.