Before 1918, approximately 55% of the wolves the New Mexico and Arm region were
ID: 3176645 • Letter: B
Question
Before 1918, approximately 55% of the wolves the New Mexico and Arm region were male, and 45% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present. approximately 65% of weaves in the regimen are mate, and 35% are female. Biologists suspect that mate wolves are more likely than females to return to an area where the population has been greatly reduced. (a) Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 0 or more were male? What is the probability that 9 or more were female? What is the probability that fever than 6 were female? For the period from 1918 to the present, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or move male? What is the probability that 9 or move were female? What is the probability that fewer than 6 were female?Explanation / Answer
a. The underlying distribution in question is binomial in nature, with n=12 independent, random trials, probability of success, p=0.55, which is constant throughout the trials. The specific number of success in n trials is denoted by r. Use, P(X,r)=nCr(p)^r(1-p)^n-r.
P(X>=9)=1-P(X<9)=1-P(X<=8)=1-[P(X=0)+P(X=1)+...+P(X=8)]=1-[12C0(0.55)^0(1-0.55)^12+12C1(0.55)^1(1-0.55)^11+...+12C8(0.55)^8(1-0.55)^4]
=1-0.8655=0.1345 (ans)
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For n=12, p=0.45, compute P(X>=9)
P(X>=9)=1-P(X<9)=1-P(X<=8)=1-0.9644 [use formula in Excel =BINOMDIST(8,12,0.45,TRUE) to compute P(X<=8)]
=0.0356 (ans)
b. For, n=12, p=0.65, compute P(X>=9)
P(X>=9)=1-P(X<9)=1-P(X<=8) [Type formula in Excel =1-BINOMDIST(8,12,0.65,TRUE)]
=0.3467 (ans)
For n=12, p=0.35
P(X>=9)=1-P(X<=8)=0.0056 [Type formula in Excel =1-BINOMDIST(8,12,0.35,TRUE)] (ans)
P(X<6)=P(X<=5)=0.7873 [Type formula in Excel =BINOMDIST(5,12,0.35,TRUE)](ans)
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