Letxbe a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Thenxhas a distribution that is approximately normal with mean=69.0kgand standard deviation=7.0kg.Suppose a doe that weighs less than60kgis 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 about2350does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)

does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight ofn=50does should be more than66kg. If the average weight is less than66kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weightx

for a random sample of50does is less than66kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability thatx

<70.5kg for50does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released50does in December, and the average weight wasx

=70.5kg.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 unlikely 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 likely that the doe population is undernourished.