Let x be a random variable that represents the weights in kilograms (kg) of heal

Question

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 mu = 68.0 kg and standard deviation sigma = 7.8 kg. Suppose a doe that weighs less than 59 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 2800 does, 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 of n = 60 does should be more than 65 kg. If the average weight is less than 65 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight bar x for a random sample of 60 does is less than 65 kg (assuming a healthy population)? (Round your answer to four decimal places.) (d) Complete the probability that bar x

Explanation / Answer

a) P(X<59)=P(Z<(59-68)/7.8)=P(Z<-1.1538)=0.1243

b) expected number =np=2800*0.1243=348

c)std error =std deviation/(n)1/2 =1.007

hence P(X<65)= P(Z<((65-68)/1.007)=P(Z<-2.9792)=0.0014

d)P(X<69)=P(Z<0.9931)=0.8397

e)since above mean not undernourished

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.