### Home > INT1 > Chapter Ch11 > Lesson 11.1.1 > Problem11-6

11-6.

Delenn is re-examining the difference in backpacks among different grade levels at her school. Now she has collected a new random sample of $100$ students to see if there are categorical relationships between carrying backpacks and graduating classes.

 Freshmen Sophomore Junior Senior Totals Backpack $8$ $16$ $18$ $19$ $\textbf{61}$ No Backpack $3$ $6$ $14$ $16$ $\mathbf{39}$ Totals $\mathbf{11}$ $\mathbf{22}$ $\mathbf{32}$ $\mathbf{35}$ $\mathbf{100}$
1. Based on her sample, what percentage of students do not carry a backpack at school?

What is the total number of students at Delenn's school?
What is the total number of students who do not carry a backpack?
Use those numbers to find the percentage.

2. If a junior is chosen, what is the probability they are carrying a backpack?

Use the same method as part (a), but limit the numbers to juniors only.

3. If a student is not carrying a backpack, what is the probability they are a junior or senior?

$\frac{30}{39}$

4. Is there a relationship between graduating class and carrying a backpack at school? Show your evidence.