a We want to know what percentage of students do not carry a backpack at school. To do so, we divide the number of students who do not carry a backpack by the total number of students. Let's take a look at the given data.
Freshmen
Sophomore
Junior
Senior
Backpack
8
16
18
19
No Backpack
3
6
14
16
Total
11
22
32
35
Let's first find the number of students that do not carry backpacks.
No Backpack: 3+6+14+16=39
Now we find the total number of students.
Total: 11+22+32+35=100
With this information, we can calculate the percentage of students who do not carry a backpack.
39/100=39 %
bProbability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
In this case, whatever student we choose, they must be a junior. This means we will only consider students who are juniors. We know 18 of them have a backpack, and there are 32 juniors in total. With this information we can calculate the probability that a randomly chosen junior is carrying a backpack.
P=Number of favorable outcomes/Number of possible outcomes
c In this case we choose from the students who do not carry a backpack, and we want to know what the probability is of choosing either a junior or a senior. First, we find the number of juniors or seniors, and the total number of students who do not carry a backpack.
junior or senior:& 14+16= 30
no backpack:& 3+6+14+16= 39
With this information, we can calculate the probability that a student who does not carry a backpack is a junior or a senior.
P=Number of favorable outcomes/Number of possible outcomes
d If there is a relationship between graduating class and carrying a backpack, we should be able to see it by examining the relative frequencies for each class. To do so, we divide the number of students who do not carry backpacks by the total number of students in that class.
Freshmen:& 3/11=27 % [0.8em]
Sophomore:& 6/22=27 % [0.8em]
Junior:& 14/32≈ 43.7 % [0.8em]
Seniors:& 16/35≈ 45.7 %
As we can see, the number of student that do not carry backpacks is greater for higher classes.
