Mathematics, 02.11.2019 05:31 tiaemrich146

Ask your teacher before 1918, approximately 60% of the wolves in the new mexico and arizona region were male, and 40% 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? what is the probability that 6 or more were female? what is the probability that fewer than 3 were female?
(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? what is the probability that 6 or more were female?

Answers: 2

Show answers

Answers

Answer from: jraghubir50

a) 0.482 , 0.099 and 0.231 respectively

b) 0.609 and 0.053 respectively

Step-by-step explanation:

We can modeled the number of wolves in New Mexico and Arizona as a binomial random variable.

The binomial random variable has the following probability distribution :

$P(X=k)=(nCk)p^{k}(1-p)^{n-k}$

Where P(X=k) is the probability of the variable X to assume the value k

p is the success probability

n is the sample

a) Before 1918.

We define the random variables :

X : ''number of male wolves''

Y : ''number of female wolves''

X ~ Bi (9,0.6)

Y ~ Bi (9,0.4)

$P(X\geq 6)=P(X=6)+P(X=7)+P(X=8)+P(X=9)$

$P(X\geq 6)=(9C6)0.6^{6}0.4^{3}+(9C7)0.6^{7}0.4^{2}+(9C8)0.6^{8}0.4^{1}+(9C9)0.6^{9}0.4^{0}$

$P(X\geq 6)=0.251+0.161+0.060+0.010=0.482$

$P(Y\geq 6)=P(Y=6)+P(Y=7)+P(Y=8)+P(Y=9)$

$P(Y\geq 6)=(9C6)0.4^{6}0.6^{3}+(9C7)0.4^{7}0.6^{2}+(9C8)0.4^{8}0.6^{1}+(9C9)0.4^{9}0.6^{0}$

$P(Y\geq 6)=0.074+0.021+(3.54)10^{-3}+(2.62)10^{-4}=0.099$

P(Y

b) For the period from 1918 to the present.

X and Y are the same random variables but with a different distribution :

X ~ Bi(9,0.65)

Y ~ Bi(9,0.35)

$P(X\geq 6)=P(X=6)+P(X=7)+P(X=8)+P(X=9)$

$P(X\geq 6)=(9C6)0.65^{6}0.35^{3}+(9C7)0.65^{7}0.35^{2}+(9C8)0.65^{8}0.35^{1}+(9C9)0.65^{9}0.35^{0}$

$P(X\geq 6)=0.272+0.216+0.100+0.021=0.609$

$P(Y\geq 6)=P(Y=6)+P(Y=7)+P(Y=8)+P(Y=9)$

$P(Y\geq 6)=(9C6)0.35^{6}0.65^{3}+(9C7)0.35^{7}0.65^{2}+(9C8)0.35^{8}0.65^{1}+(9C9)0.35^{9}0.65^{0}$

$P(Y\geq 6)=0.042+(9.79)10^{-3}+(1.32)10^{-3}+(7.89)10^{-5}=0.053$

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

Another question on Mathematics

Mathematics, 20.06.2019 18:04

Kinu wants to buy topsoil for a section of her garden that has the dimensions shown in the figure. each bag covers 2 square yards. how many bags of topsoil should kinu buy? explain how you found the answer.

Answers: 1

Answer

Mathematics, 21.06.2019 14:00

Brook states that the distance on the line is 4 units. caleb states that the whole line does not have a distance because it continues on forever. vivian states that the line is 6 units long. which distance did brook measure? which distance did vivian measure?

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

The difference of three and the reciprocal of a number is equal to the quotient of 20 and the number. find the number.

Answers: 2

Answer

Mathematics, 21.06.2019 23:20

6cm10 cma conical paper cup has dimensions as shown in the diagram. how much water can the cup hold when full?

Answers: 1

Answer

You know the right answer?

Ask your teacher before 1918, approximately 60% of the wolves in the new mexico and arizona region w...