How to get answer with table and formula p(r)=(nCr)(p)^r(q)^n-r 17.| Ecology: Wo

Question

How to get answer with table and formula p(r)=(nCr)(p)^r(q)^n-r 17.| Ecology: Wolves The following is based on information taken from The W in the Southwest: The Making of an Endangered Species, edited by David Brown (University of Arizona Press). Before 1918, approximately 55% of the wolves in the New Mexico and Arizona region were male, and 45% were female. However, cattle ranchers in this area have made a determined effort exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male 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 was the probability that 6 or more were male? What was the probability that 6 or more were female? What was the probability that fewer than were female? (b) Answer part (a) for the period from 1918 to the present.

Explanation / Answer

Here' the answer to the question:

a.

p(r)=(nCr)(p)^r(q)^n-r
n = 12
r = 6

P(6 or more males) = (12C6)(.55)^6(.45)^12-6 + ..+(12C12)(.55)^12(.45)^0 = 0.7393

P(6 or more females) = (12C6)(.45)^6(.55)^12-6 + ..+(12C12)(.45)^12(.55)^0 = 0.4731
P(4 or less females) = (12C0)(.45)^0(.55)^12-12 + ..+(12C4)(.45)^4(.55)^8 = 0.3044

b.
P(6 or more males) = (12C6)(.7)^6(.3)^12-6 + ..+(12C12)(.7)^12(.3)^0 = 0.9614
P(6 or more females) = (12C6)(.3)^6(.7)^12-6 + ..+(12C12)(.3)^12(.7)^0 = 0.1179

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