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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 = 55.0 kg and standard deviation σ = 6.2 kg. Suppose a doe that weighs less than 46 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 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does

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LammettHash

The probability of a randomly selected deer being undernourished is

[tex]P(X<46)=P\left(\dfrac{X-55}{6.2}<\dfrac{46-55}{6.2}\right)\approx P(X<-1.45)\approx0.0733[/tex]

Out of 2100 does, you should expect about [tex]0.0733\cdot2100\approx154[/tex] does to be undernourished.

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