Let's break down the problem step-by-step:
### Step 1: Calculate Relative Frequency of People Who Prefer Mocha Cold
First, we need to find out the total number of people who prefer mocha (both hot and cold):
- Hot Mocha: 25
- Cold Mocha: 12
Total people who prefer mocha = 25 (hot) + 12 (cold) = 37
Next, we focus on the number of people who prefer Cold Mocha:
- Cold Mocha: 12
The relative frequency of people who prefer Cold Mocha is given by:
[tex]\[ \text{Relative Frequency of Cold Mocha} = \frac{\text{Number of People who prefer Cold Mocha}}{\text{Total Number of People who prefer Mocha}} \][/tex]
[tex]\[ \text{Relative Frequency of Cold Mocha} = \frac{12}{37} \approx 0.32 \][/tex]
### Step 2: Calculate Relative Frequency of People Who Prefer Hot Latte
Now, we need to find out the total number of people who prefer hot coffee:
- Hot Regular: 11
- Hot Mocha: 25
- Hot Latte: 19
- Hot Cappuccino: 30
Total people who prefer hot coffee = 11 + 25 + 19 + 30 = 85
Next, focus on the number of people who prefer Hot Latte:
- Hot Latte: 19
The relative frequency of people who prefer Hot Latte is given by:
[tex]\[ \text{Relative Frequency of Hot Latte} = \frac{\text{Number of People who prefer Hot Latte}}{\text{Total Number of People who prefer Hot Coffee}} \][/tex]
[tex]\[ \text{Relative Frequency of Hot Latte} = \frac{19}{85} \approx 0.22 \][/tex]
### Step 3: Determine the Type of Coffee with the Highest Percentage of People Preferring It Cold
We should calculate the percentage of people who prefer each type of coffee cold:
1. Regular:
- Hot Regular: 11
- Cold Regular: 17
- Total who prefer Regular: 11 + 17 = 28
- Percentage who prefer Cold Regular: [tex]\( \frac{17}{28} \approx 0.61 \)[/tex]
2. Mocha:
- Hot Mocha: 25
- Cold Mocha: 12
- Total who prefer Mocha: 25 + 12 = 37
- Percentage who prefer Cold Mocha: [tex]\( \frac{12}{37} \approx 0.32 \)[/tex]
3. Latte:
- Hot Latte: 19
- Cold Latte: 20
- Total who prefer Latte: 19 + 20 = 39
- Percentage who prefer Cold Latte: [tex]\( \frac{20}{39} \approx 0.51 \)[/tex]
4. Cappuccino:
- Hot Cappuccino: 30
- Cold Cappuccino: 27
- Total who prefer Cappuccino: 30 + 27 = 57
- Percentage who prefer Cold Cappuccino: [tex]\( \frac{27}{57} \approx 0.47 \)[/tex]
The type of coffee that has the highest percentage of people who prefer it cold is Regular with approximately 0.61 or 61%.
### Final Answers
- The relative frequency of people who prefer mocha cold is [tex]\(0.32\)[/tex].
- Of the people who prefer hot coffee, the relative frequency of them preferring a latte is [tex]\(0.22\)[/tex].
- The type of coffee that has the highest percentage of people who prefer it cold is Regular.
