To solve this problem, you need to calculate the relative frequency, which is a measure of how often a particular event occurs in comparison to the total number of events. Specifically, we want to find out how often people who use public transportation eat fast food 0-2 times per week and 3 or more times per week.
Here are the steps to calculate the relative frequency for each category:
### Step-by-Step Solution:
1. Identify the relevant variables from the problem:
- Total population of people using public transportation: [tex]\( \text{total\_population} = 100 \)[/tex]
- Number of people eating fast food 0-2 times per week: [tex]\( \text{relative\_0\_2} = 40 \)[/tex]
- Number of people eating fast food 3 or more times per week: [tex]\( \text{relative\_3\_or\_more} = 60 \)[/tex]
2. Calculate the relative frequency for 0-2 times per week:
The formula for relative frequency is given by:
[tex]\[
\text{Relative Frequency} = \frac{\text{Number of occurrences}}{\text{Total number of events}}
\][/tex]
For 0-2 times per week, plug in the values:
[tex]\[
\text{Relative Frequency for 0-2 times per week} = \frac{\text{relative\_0\_2}}{\text{total\_population}}
\][/tex]
[tex]\[
\text{Relative Frequency for 0-2 times per week} = \frac{40}{100} = 0.4
\][/tex]
3. Calculate the relative frequency for 3 or more times per week:
Similarly, for 3 or more times per week, use the relative frequency formula:
[tex]\[
\text{Relative Frequency for 3 or more times per week} = \frac{\text{relative\_3\_or\_more}}{\text{total\_population}}
\][/tex]
[tex]\[
\text{Relative Frequency for 3 or more times per week} = \frac{60}{100} = 0.6
\][/tex]
### Final Results:
a. Relative frequency of people who eat fast food 0-2 times per week:
[tex]\[
\text{Relative Frequency for 0-2 times per week} = 0.4
\][/tex]
b. Relative frequency of people who eat fast food 3 or more times per week:
[tex]\[
\text{Relative Frequency for 3 or more times per week} = 0.6
\][/tex]
These results show that 40% of the people who use public transportation eat fast food 0-2 times per week, and 60% of them eat fast food 3 or more times per week.
