Before 1918, approximately 55% of the wolves in the New Mexico and Arizona regio

Question

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 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.)

(a) Before 1918, in a random sample of 9 wolves spotted in the region, what is the probability that 6 or more were male?
1

What is the probability that 6 or more were female?
2

What is the probability that fewer than 3 were female?
3

(b) For the period from 1918 to the present, in a random sample of 9 wolves spotted in the region, what is the probability that 6 or more were male?
4

What is the probability that 6 or more were female?
5

What is the probability that fewer than 3 were female?
6

A research team conducted a study showing that approximately 15% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight
1

(b) more than two ties are too tight
2

(c) no tie is too tight
3

(d) at least 18 ties are not too tight
4

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that seven married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)

(a) all of them dislike their mother-in-law
1

(b) none of them dislike their mother-in-law
2

(c) at least five of them dislike their mother-in-law
3

(d) no more than four of them dislike their mother-in-law
4

Explanation / Answer

4.a.The probability that all seven married women dislike their mother-in-law is:

0.85^7=0.32

b.The probability that none of them dislike their mother-in-law is:

(1-0.32)=0.68

c.The probability that at least five of them dislike their mother-in-law is:

0.85^5*(1-0.85)^2+0.85^6*(1-0.85)+0.85^7

=0.387

d.The probability that no more than four of them dislike their mother-in-law is:

0.85*(1-0.85)^6+0.85^2*(1-0.85)^5+0.85^3*(1-0.85)^4+0.85^4*(1-0.85)^3

=0.002

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