Mathematics, 21.01.2020 03:31 steven2669

Amarketing company wants to estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign. further, the company wants the estimate to have a margin of error of no more than 5 percent with 90 percent confidence. of the following, which is closest to the minimum number of consumers needed to obtain the estimate with the desired precision?

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Answer from: jaylynC

271

Step-by-step explanation:

When the prior estimate of population proportion is not given , then the formula to find the sample size is given by :-

$n=0.25(\dfrac{z^*}{E})^2$

, where E = Margin of error.

z* = Critical z-value.

As per given , we have

E = 5%=0.05

Confidence level = 90%

The critical value of z at 90% is 1.645 (By z-table)

Put all values in the formula , we get

$n=0.25(\dfrac{1.645}{0.05})^2$

$n=0.25\cdot32.9^{2}$

$n=270.6025\approx271$

Thus, the minimum sample size needed = 271

Hence , the correct answer is 271 .

Answer from: jbearden

To estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign, we can use formula of sample size.

The minimum size needed is 271.

Given:

The margin of error is $E=\dfrac{5\%}{100}=0.05$ .

Confidence level = 90%

Refer the z-table critical value of z at 90% confidence level is 1.645 .

Calculate the sample size by using following formula.

$n=0.25\left (\dfrac{z^*}{E}\right )^2$

Substitute the value in above equation.

$n=0.25\left(\dfrac{1.645}{0.05}\right)^2\\n=0.25\times 39.9^2\\n=270.6025\\n\approx271$

Thus, the minimum size needed is 271.

Learn more about what sample size is here:

link

Answer from: Quest

there are lots of ways. pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula. the area is half the sum of the cross products of the sides.

a(-2,6) -2(2)-6(-5) = 26

b(-5,2) -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3) 4(3) - (-3)(5) = 27

e(5,3) 5(3) - 3(1) = 12

f(1,3) 1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 + 18 + 27 + 12 + 12) = 57

that checks!

Find the area of the following shape. you must show all work to receive credit. need asap timed tes

Answer from: Quest

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

$a=9\times 12=108\text {ft^2}$

so the area of the floor is 108 square feet, converting that into square yards we get,

$108 \times 0.1111= 12 \text{yd^2}$

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

$\$15 \times 12=\$180$

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

$a = 12 \times 15=180\text {ft}^2$

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

$180 \times 0.111=20 \text {yd}^2$

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

$\$15 \times 20= \$300$

so, it will cost $300.

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