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=60.0kgand standard deviation=7.1kg.Suppose a doe that weighs less than51kgis 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=45does should be more than57kg. If the average weight is less than57kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weightx

for a random sample of45does is less than57kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability thatx

<61.9kg for45does (assume a healthy population). (Round your answer to four decimal places.)