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Answer:
The sample proportion is 0.88.
The margin of error is of 0.04.
The interval likely to contain the true population proportion is (0.84,0.92).
Step-by-step explanation:
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 z-score that has a p-value of .
Margin of error:
The margin of error is of:
Sample of 230 teenagers, 202 would like to have smaller class sizes at their school.
This means that , and that the sample proportion is:
The sample proportion is 0.88.
Standard 95% confidence level
So , z is the value of Z that has a p-value of
, so
.
Margin of error:
The margin of error is of 0.04.
Confidence interval:
Sample proportion plus/minus margin of error. So
0.88 - 0.04 = 0.84
0.88 + 0.04 = 0.92
The interval likely to contain the true population proportion is (0.84,0.92).
There are three parts to this figure: a rectangle and two triangles that are congruent.
We'll add together the area for each to get the total area.
We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.
We know that . Substitute and solve for
:
Now, double this to get the total length of the rectangle, which is inches.
The area of the rectangle is equal to its length times its height:
Now, we'll find the area of one of the triangles and double it since they're congruent.
The area of a triangle is one-half of its base times its height, which we then double.
The and the
cancel each other out.
Substitute and solve:
Finally, add the rectangle's area to the two triangles' area.