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    Find probabilities using binomial distribution

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    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 to 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.

    1. Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male?

    What is the probability that 9 or more were female?

    What is the probability that fewer than 6 were female?

    2. 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 more were male?

    What is the probability that 9 or more were female?

    What is the probability that fewer than 6 were female?

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    Solution Preview

    1. Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male?
    Answer: We use binomial distribution. Now n=12, p=0.55, so P(9 or more were male)=P(X>=9)=P(X=9)+P(X=10)+P(X=11)+P(X=12)=C(12,9)*0.55^9*0.45^3+C(12,10)*0.55^10*0.45^2+C(12,11)*0.55^11*0.45^1+C(12,12)*0.55^12*0.45^0=0.1345

    What is the probability that 9 or more were female?
    Answer: We use binomial distribution. Now n=12, p=0.45, so P(9 or more were ...

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