In the survey, there is a margin error of +/– 2%. What is the range of number of people who think tuition is too high at the university if 2004 of the 3421 students said it was and there are over 25,000 students at the university?

A. 14,252 to 14,938 students
B. 14,352 to 14,438 students
C. 14,652 to 14,938 students
D. 14,352 to 14,938 students

Question

In the survey, there is a margin error of +/– 2%. What is the range of number of people who think tuition is too high at the university if 2004 of the 3421 students said it was and there are over 25,000 students at the university?

	A.	14,252 to 14,938 students
	B.	14,352 to 14,438 students
	C.	14,652 to 14,938 students
	D.	14,352 to 14,938 students

anonymous · Answer

@KyanTheDoodle

anonymous · Answer

@mathmate

anonymous · Answer

@Here_to_Help15

mathmate · Answer

@serenacox 
What is the proportion of students surveyed said tuition was too high?

anonymous · Answer

umm idk

mathmate · Answer

Please read the question again, and extract any information that you think might help to find the answer!

anonymous · Answer

ok  there is a margin error of +/– 2%.  2004 of the 3421 students said it was and there are over 25,000 students at the university

mathmate · Answer

Good, you've collected all the useful numeric values.
Which of these numeric values will help you find the proportion of students surveyed said tuition was high?

anonymous · Answer

$$\frac{ 2004 }{ 3421 }*\frac{ x }{ 25,000 } cross multiply $$

anonymous · Answer

but were does the margin of error come in??@mathmate

mathmate · Answer

Good work!
After you've found x, which is the estimated number of students (out of 25000) who said yes to tuition too high, the two percent applies to the value of x.
That is to say, the lower limit is (1-0.02)x and the upper limit is (1+0.02)x, both numbers (of students) must be rounded to the nearest integers to avoid fractional number of students.

anonymous · Answer

u multiply 2004 and 25000 right

anonymous · Answer

to find that

anonymous · Answer

so 50100000

mathmate · Answer

Once you find x, the $\pm 2%$ apply to x.

mathmate · Answer

x is the estimated of students who answered yes. 
The 2% applies to that.
If x = 10000 students, then the lower limit is 10000(1-0.02)=9800, and upper limit is 10000(1+0.02)=10200, so the range within the 2% margin of error is 9800 to 10200 students.
But you need to find x first (using the proportion equation that you proposed).

anonymous · Answer

oh ok

anonymous · Answer

@M4thM1nd help

anonymous · Answer

@mathmate can u explain it to me as if u were explaining this to a 10 year old

anonymous · Answer

im dumb

mathmate · Answer

Can you first find x from the equation you gave earlier?
Then I can draw a diagram to help you visualize the numbers.

mathmate · Answer

Sorry, I was afb for a nap.