Answer :
Let's solve each part of the question step-by-step, based on the provided table.
1. Relative frequency of people who prefer mocha cold:
To find the relative frequency of people who prefer mocha cold, we need to consider the number of people who prefer mocha cold in relation to the total number of people who prefer mocha.
- Number of people who prefer mocha cold: [tex]\(12\)[/tex]
- Total number of people who prefer mocha (hot + cold): [tex]\(25 (hot) + 12 (cold) = 37\)[/tex]
So, the relative frequency of people who prefer mocha cold is:
[tex]\[ \text{Relative frequency} = \frac{\text{Number who prefer mocha cold}}{\text{Total number who prefer mocha}} = \frac{12}{37} \approx 0.32 \][/tex]
2. Relative frequency of people who prefer hot coffee and selecting latte:
To find the relative frequency of people who prefer hot coffee and select latte, we need to consider the number of people who prefer hot lattes in relation to the total number of people who prefer hot coffee.
- Number of people who prefer hot lattes: [tex]\(19\)[/tex]
- Total number of people who prefer hot coffee: [tex]\(11 (Regular) + 25 (Mocha) + 19 (Latte) + 30 (Cappuccino) = 85\)[/tex]
So, the relative frequency of people who prefer hot coffee and select latte is:
[tex]\[ \text{Relative frequency} = \frac{\text{Number who prefer hot lattes}}{\text{Total number who prefer hot coffee}} = \frac{19}{85} \approx 0.22 \][/tex]
3. Type of coffee with the highest percentage of people who prefer it cold:
To find the type of coffee with the highest percentage of people who prefer it cold, we need to calculate the percentage for each type.
- For Regular:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer regular cold}}{\text{Total number who prefer regular}} = \frac{17}{11+17} = \frac{17}{28} \approx 0.61 \][/tex]
- For Mocha:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer mocha cold}}{\text{Total number who prefer mocha}} = \frac{12}{37} \approx 0.32 \][/tex]
- For Latte:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer latte cold}}{\text{Total number who prefer latte}} = \frac{20}{19+20} = \frac{20}{39} \approx 0.51 \][/tex]
- For Cappuccino:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer cappuccino cold}}{\text{Total number who prefer cappuccino}} = \frac{27}{30+27} = \frac{27}{57} \approx 0.47 \][/tex]
Comparing these percentages, we find that the highest percentage is for Regular coffee at approximately [tex]\(0.61\)[/tex].
Therefore, the type of coffee with the highest percentage of people who prefer it cold is Regular.
### Summary:
1. Relative frequency of people who prefer mocha cold: 0.32
2. Relative frequency of people who prefer hot coffee and select latte: 0.22
3. Type of coffee with the highest percentage of people who prefer it cold: Regular
1. Relative frequency of people who prefer mocha cold:
To find the relative frequency of people who prefer mocha cold, we need to consider the number of people who prefer mocha cold in relation to the total number of people who prefer mocha.
- Number of people who prefer mocha cold: [tex]\(12\)[/tex]
- Total number of people who prefer mocha (hot + cold): [tex]\(25 (hot) + 12 (cold) = 37\)[/tex]
So, the relative frequency of people who prefer mocha cold is:
[tex]\[ \text{Relative frequency} = \frac{\text{Number who prefer mocha cold}}{\text{Total number who prefer mocha}} = \frac{12}{37} \approx 0.32 \][/tex]
2. Relative frequency of people who prefer hot coffee and selecting latte:
To find the relative frequency of people who prefer hot coffee and select latte, we need to consider the number of people who prefer hot lattes in relation to the total number of people who prefer hot coffee.
- Number of people who prefer hot lattes: [tex]\(19\)[/tex]
- Total number of people who prefer hot coffee: [tex]\(11 (Regular) + 25 (Mocha) + 19 (Latte) + 30 (Cappuccino) = 85\)[/tex]
So, the relative frequency of people who prefer hot coffee and select latte is:
[tex]\[ \text{Relative frequency} = \frac{\text{Number who prefer hot lattes}}{\text{Total number who prefer hot coffee}} = \frac{19}{85} \approx 0.22 \][/tex]
3. Type of coffee with the highest percentage of people who prefer it cold:
To find the type of coffee with the highest percentage of people who prefer it cold, we need to calculate the percentage for each type.
- For Regular:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer regular cold}}{\text{Total number who prefer regular}} = \frac{17}{11+17} = \frac{17}{28} \approx 0.61 \][/tex]
- For Mocha:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer mocha cold}}{\text{Total number who prefer mocha}} = \frac{12}{37} \approx 0.32 \][/tex]
- For Latte:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer latte cold}}{\text{Total number who prefer latte}} = \frac{20}{19+20} = \frac{20}{39} \approx 0.51 \][/tex]
- For Cappuccino:
[tex]\[ \text{Percentage} = \frac{\text{Number who prefer cappuccino cold}}{\text{Total number who prefer cappuccino}} = \frac{27}{30+27} = \frac{27}{57} \approx 0.47 \][/tex]
Comparing these percentages, we find that the highest percentage is for Regular coffee at approximately [tex]\(0.61\)[/tex].
Therefore, the type of coffee with the highest percentage of people who prefer it cold is Regular.
### Summary:
1. Relative frequency of people who prefer mocha cold: 0.32
2. Relative frequency of people who prefer hot coffee and select latte: 0.22
3. Type of coffee with the highest percentage of people who prefer it cold: Regular
