20. Jorge conducted a survey by asking 120 students whether they use a pencil to take notes. Of the students surveyed, 90 responded favorably. Which margin of error matches each confidence level for this situation? 1. 90% =
2. 99% =
3. 95%=
options- 0.102, 0.338, 0.216, 0.077, 0.256, 0.065

Margin of error for 90% C.I: 0.065

Margin of error for 99% C.I: 0.091

Margin of error for 95% C.I: 0.077

Step-by-step explanation:

In this question, for each student, there are only two possible outcomes. Either they use a pencil to take notes, or they do not. Students are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial confidence interval:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

For this problem, we have that:

120 students, so

90 responded favorably, so

Margin of error for 90% CI:

Here , z is the value of Z that has a pvalue of , so .

The margin of error is:

Margin of error for 99% CI:

Here , z is the value of Z that has a pvalue of , so .

The margin of error is:

Margin of error for 95% CI:

Here , z is the value of Z that has a pvalue of , so .

The margin of error is:

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.