Question

D Randy chooses to survey every 5th student in the

cafeteria. He surveys a total of 140 students and finds

that 84 students support buying new PE equipment. If

this is a representative sample, how many total students

could he predict would support the purchase of new PE

equipment out of the entire student body?

~ 280 students

® 84 students

© 588 students

0 420 students

Answer 1

Answer:

Total number of students surveyed in cafeteria is $700$

Total number of students who support New PE equipment will be $420$.

Step-by-step explanation:

Given that,

Randy surveyed every 5th student in the cafeteria. he surveyed total of 140 students. He got 84 students supports buying new PE equipment.

So,

Basically Randy surveyed 5th student in the cafeteria.

then he will next survey 10th student in the cafeteria.

Means,

        Position of students surveyed             Total No. of students surveyed

               $5th student$                                                        $1$

              $10th student$                                                        $2$

               $15th student$                                                       $3$                      

                         .

                         .              

                         .  

              $700th student$                                                     $140$

Here,

we get that total number of students surveyed in cafeteria is $700$.

For the number of PE equipment supported by  $84$ out of $140$ students.

Let the Number of students who support PE equipment out of $700$ be $x$.

∴                                       $\frac{x}{700}=\frac{84}{140}$

Applying cross-multiplication We get,

                                         $x=\frac{84\times700}{140}$

                                         $x=420$

Hence,

Total number of students who support New PE equipment will be $420$.