General Statistics

Question

Answer the following questions:
1. If 20% of the 20,000 UM-Flint students major in a humanity, how many humanities majors are there?


2. Last year on UM-Flint’s campus there were 45 burglaries reported among the 20, 000 students, what is the burglary rate for each 1,000 students; what is the rate for every 10,000 students?



3. Last year in Detroit the birth rate was 41.39 per 1,000 women. If there were 294,277 women in Detroit, how many births were there?

Answer 1

1.

 

Generally, in a word problem, "of" means you should multiply and "is" means equals. So, let's turn that phrase into an equation:

 

"20% of 20,000 students is what?"

0.2 × 20000 = n

4000 = n

 

That means there are 4,000 humanities majors.

 

 

 

2.

 

Now, it's a good idea to use proportions. If there are 45 burglaries out of 20,000 students, there are how many burglaries per 1,000 students? Usually "out of" and "per" mean you should divide.

 

"45 out of 20,000 students is how many out of 1,000 students?"

45/20000 = n/1000

 

Cross-multiply to solve for n:

 

45(1000) = 20000n

45000 = 20000n

2.25 = n

 

The burglary rate for each 1,000 students is 2.25.

 

 

You can expect the rate for 10,000 students, which is 10 times 1,000, to be 10 times 2.25, or 22.5. We'll go ahead and do the math just to make sure:

 

45/20000 = n/10000

450000 = 20000n

22.5 = n

 

The burglary rate for each 10,000 students is 22.5, or half the rate for 20,000 students.

 

 

 

3.

 

Again, we'll set up a proportion equation to solve:

 

41.39/1000 = n/294277

12180125 = 1000n

12180.125 = n

 

There were approximately (to the nearest whole-number) 12,180 births.