Question

students are surveyed
8th grade soccer: 16 8th grade tennis:20 8th grade football:14
7th grade soccer:29 7th grade tennis:4 7th grade football:17
if there are a total of 1000 7th graders and 8th graders, how many are expected to prefer tennis

Answer 1

To find out how many students are expected to prefer tennis, we first need to determine the total number of students surveyed for each sport in each grade.

From the given data:

**8th Grade:**
- Soccer: 16
- Tennis: 20
- Football: 14

Total for 8th grade = 16 + 20 + 14 = 50

**7th Grade:**
- Soccer: 29
- Tennis: 4
- Football: 17

Total for 7th grade = 29 + 4 + 17 = 50

**Total surveyed** = 50 (8th grade) + 50 (7th grade) = 100 students.

Next, we calculate the proportion of students who prefer tennis based on the survey results:

Total number preferring tennis = 20 (from 8th grade) + 4 (from 7th grade) = 24 students.

Now we find the proportion of students who prefer tennis:

\[
\text{Proportion preferring tennis} = \frac{24}{100} = 0.24
\]

Now, to find the expected number of students who prefer tennis out of 1000 total students (7th and 8th graders combined):

\[
\text{Expected number preferring tennis} = 0.24 \times 1000 = 240
\]

Thus, we expect 240 students to prefer tennis.