Question

Lucy collects data from a random sample of seventh-graders. Out of 40 respondents, 7 attend afterschool programs. Of the 200 seventh-graders attending Lucy’s school, how many would be expected to attend afterschool programs?

Answer 1

To find the number of seventh-graders expected to attend afterschool programs, set up a proportion: 7/40 = x/200. Solve for 'x' by cross-multiplying. It can be expected that 35 out of the 200 seventh-graders would attend afterschool programs.

Step-by-step explanation:

To find the number of seventh-graders expected to attend afterschool programs, we can use the concept of proportions. We know that out of 40 respondents, 7 attend afterschool programs. So, the proportion of seventh-graders attending afterschool programs is 7/40.

To find the number of seventh-graders attending Lucy's school who would be expected to attend afterschool programs, we can set up a proportion. Let 'x' represent the number of seventh-graders who would be expected to attend afterschool programs. The proportion is: 7/40 = x/200.

To solve for 'x', cross-multiply: 7 * 200 = 40 * x. Simplifying gives us 1400 = 40x. Now divide both sides by 40, and we get x = 35.

Therefore, it can be expected that 35 out of the 200 seventh-graders attending Lucy's school would attend afterschool programs.

Answer 2

Out of 40 respondents, 7 attend afterschool programs.
`(7)/(40)=0.175`, so 17.5% of students attend afterschool programs.

`0.175*200=35`.
So, out of 200 seventh-graders, 35 would be expected to attend afterschool programs.